 So I simply want to give you a little bit of a viewpoint of a material scientist, how to find some materials, and I think recently it's totally easy to find all these materials since you have to go only to a web page and you click click about materials and then you know whether it's topological or not, okay. So and in this sense I have two parts of the talk and in between I will have a break. The first time is how to find, we find some materials and then what we do with our simple measurements, okay? So to give you a little bit what you can measure. And the motivation I think for me is especially, so I have some background in density functional theory and all the theoreticians normally cry if they see me, you know, people who do density functional theory are not very popular in the theoretical community. But now with topology we are quite happy for the moment with a single practical picture so it's very trivial. And what I think is really amazing is many of the properties since these are global properties, so they come from the bike of a material, you have some really new interesting properties which can be quantized transport, but I'm originally also from the community of spintronics so because spin momentum is locked you might even have new spintronic devices. And there are quite new properties like the viscous flow of electrons so some of the electrons and I give you an example also at the end I hope that the electrons behave different than Drutegas so it's not really a single particle picture and I think we are now ready and you guys are hopefully and girls are ready to go beyond the single particle picture. And what we aim for is like as material scientists we are more practical, you know, we are not happy in the milli-kevin range that we like to have room temperature effect. So I want to give you a little bit of impression of how we find the materials and I think after a short introduction and then how we measure. So as I said topology is the global properties and this is a school where everybody knows what topology means that we simply look for the topology and the electronic structure and the genius is different for football and German roles compared to donuts and coffee pot. And for even in other fields topology plays an important role and I tell you this because I'm also interested to making a bridge between topological materials and soil-state physics and having impact maybe to chemistry so because there is also a lot of topology in molecules and chemistry and there are very very similarities many similarities which can maybe also be an area or direction beyond what we are doing now so we know especially carbon and this graphene carbon atoms play a major role also in the field of topology has four ligands and I can have the same ligands but making two molecules which are topologically distinguished because they cannot bring into they are they have different also based on this chirality they have different properties and this is the origin of the life or origin of life so most of the people connect topology with the origin of the universe with meta-antimeta and chiral anomaly but you see there's also strong connection and because of DNA they have also different chirality based on the carbon atoms. So another very nice example in chemistry makes even a nice bridge between donuts and maybe a stripe and it's again strongly related to graphene is that in chemistry you count the electrons of a p-electron system so this is Benzene. Benzene is the unit to build the primary unit to build graphene and so we have a few p-electrons in graphene which are six so you see here double bond there double bond and there and the picture is everybody knows wrong because the electrons are not localized this would look like we have a double bond between two carbons here and the single bond and the double bond and the single bond so there should be different bonding distance between the carbons but this is not the case the bond the electrons are delocalized and you can even simply by predicting by counting the carbon atoms and counting the or the atoms and counting the p-electrons you can predict whether a system is aromatic which means the electrons are delocalized or whether they are not. So here for example if we take the example Benzene we have six carbon atoms and six p-electrons and they are aromatic because it fulfills this 4n plus 2 pi electron rules if we say n is equal to 1 it's six electrons and this is exactly what we have. So now we can put two rings together or an infinitive number of rings together and then we end up with graphene and this is also why graphene is very special because these electrons are delocalized here over the whole sheet of graphene and if you strain it if you want to make it asymmetric it's very difficult because then you must localize the electrons which graphene doesn't like. So in this sense graphene is a flat surface because of all these p-electrons are delocalized and it's symbolized in the sense like a bio-donut. So but what you can do you can also make this kind of molecules which have a twist in real space and then this rules whether something is aromatic which means the electrons are delocalized or not delocalized is different. So if I have a flat atom a flat molecule so the rule is as I explained to you the number of p-electrons should be 4n plus 2 to be aromatic and to localize the electrons it's if we have 4n electrons okay but if we make a twist in the molecules the rules inverts so if I have a mobius kind of molecules they are aromatic with 4n electrons and they are anti-aromatic with 4n plus 2 electrons and this you can simply see if you do a Hucke calculation or a very simple kind of tight binding calculation in the Sikola equation I don't want to explain it but I think it's maybe a direction in the future to think about in the context of topology what we are doing now at distance how it's saved. So you see really the resonant integral is different and can we really make this molecule it's indeed so in chemistry this is a big field to try to make this mobius kind of anolines which have different properties so you make a big molecule and you should think it doesn't matter whether the molecule is really twisted looks more like a mobius stripe or whether it's a planar kind of aromatic molecule like graphene but it is so they show two different properties even on the first view the atoms are all the same the connection of the atoms are the same the only thing is that at one place there is a twist. Okay so but we want to go back to the solid state and I want to give you a little bit impression how we identify the materials and the nice thing is because so like in physics oops what is this in physics you like to think about I have to be careful what I'm doing here. Red pokerspace and in chemistry so we want to translate it into real space on material science because we want to make the crystals and we want to measure something but the nice thing is as I said for the single particle picture is more or less now there is a direct connection so if somebody draw makes a picture of a band structure or you have a Hamiltonian you draw a picture of an electronic structure it's very easy to translate this in to the real space and therefore the whole field of topology is so successful because there's a prediction in quite after a short time so if there are not too many correlated electron involved it can make the material and measure even and I'm quite surprised because more or less like what the theoretician predicts we measure you know it's it's amazing so it's like you're the generation you know only topology but I know high-techies and everybody who worked in high-techies recognized after ten hopeless prediction of theoretician you gave up and you looked for something else okay so because there's a direct connection between the electronic structure the crystal structure and even if I will talk shortly about the new fermions the band connectivity is very strongly related to the position of the atoms if I want to have an eight-foot degeneration here so I need atoms on high with the high biker biker position here they must be on positions which are highly symmetric highly symmetric okay so and this is a little bit also still an introduction here so I want to at the end so that you see really clearly the connection between reciprocate space and real space and maybe get this I will not explain in detail or something because this is the viewpoint of Andre Bernoulli how he identify the materials and I was a part of this in a certain point so by starting with atomic orbiters using the key dot p theory look for this elementary band representation and then via graph theory he can identify with the help of vanier functions whether he gets a topological semi-mental trivial semi-mental or this disconnected EBR so people who want to read this is a few hundred pages but nowadays there are two nice papers and this are even better for us in material scientists material scientists there one paper from one of the former postdocs of under Bernoulli which is a catalogue of topological materials they are both pre-princes they are both icing thousand pages but the nice thing is now more or less from all the existing materials which are already known in the database they are categorized by trivial and topology so in this sense every simple material non-magnetic it's only valid for non-magnetic and simple materials whether one the one particle approximations and if he works is but this is nice because you can go now to two servers one is to build bow it's a little bit more complicated it's like unbrace things and find out if you have a material but that's topological here it's even predictive so if I make a new material I can go there because as I explained to you more or less from the from my crystal structure and the position of my atoms I can now conclude with a number of valence electrons without even doing a bench structure calculation whether this is a high probability that my material is topological but there's a very nice web page also and if you want you can immediately this you should write down because here it's really very very convenient this is from the chen paper so you click you go to this web page you have a periodic table and then you click for example I want to know whether there's a calcium tin oxide which is topological so I click on calcium I click on tin I click on oxide oxygen and then I get this as an answer so and you see this as a compounds this as a space groups and then this as a topological classes so I see most of them are trivial insulators there's only this inverse perovskite is a topological crystal insulator so I think everything which is on a simple basis in first approximation sometimes I think there's still I would say because it's DFT based not hundred percent correct but there's a way to do it okay so but how can you understand how we think and find intuitively topological insulators this is like you know so so because the world has changed now because before we had simply normal insulators so we have a conduct conduction band and the valence band and the Fermi energy which separates conducting electron and valence electron and depending from the size of the gap we distinguish insulators semi-metals semi-conductors and metals so an insulator normally material science you expect is like a four EV bandgap so I think we will never find a topological insulator okay because we will never find the material and maybe later you understand it's not possible to find the four EV bandgap I think with a band inversion maybe in a crystalline insulator but I think because the point is you have to have this overlapping band and I explain later so if the bandgap is smaller so like so we even in solar energy we talk about semi-conductors and this is our 1.6 EV bandgaps also which is still quite large and this are yellow powders you know so if and I still think we cannot find really here the topological insulators this must be smaller like my estimation from intuition would be like one EV or so but I don't know because they are always surprising topology the compounds which yesterday were not topological are topological today so we know from Bismuth Bismuth was not topological but now it's a higher order topological insulator so for us it's good okay we grow the crystals whatever at the end we put them in the and we store them and later they become topological okay so so semi-metals I can be have a tiny overlap between the conduction band and the valence when I will also talk about semi-metals and if we have semi-conductors which have a direct band gap where the conduction band and the valence band has a maximum and a minimum maximum at the same point so we have this kind of band structure for a semi-metal but they can be also a different point in the reciprocal space and we have this kind of band structure for semi-metal so what is the best topological insulator and this was one thing there's no insulating elements only with very wide band gaps so gases even they have super wide band gap so in the periodic table so this was a motivation after the prediction with graphene so therefore it was made sense to take look for two elements this is how we do so okay so what is the topological insulator we need a band inversion and this is the picture which normally is drawn so like we have a normal semi-conductor like silicon or Garnier-Marzenik as I said we have the valence band and the conduction band and the band gap and what can also happen as I said we can have semi-metals where we have an overlap between the conduction and the valence band and then we get this crossing points here and the band structure and depending from the symmetry of the bands we can have here forbidden crossing which means the crossing is not allowed and we open up a band gap and so we don't so if we have this crossing point and if we have sorry sometimes makes what it wants so if you have this crossing point and we have heavy elements so spin orbit coupling can help to open up this crossing here because the spin is not a good quantum number and we get the band structure which we see as the band structure for topological insulator where we have a part of the valence band and here a part of the conduction band in the same band and this is symbolized by the Möbius tribe while this is symbolized by Donut so but there are different reasons to open up a band gap here it has not always be spin orbit coupling but if you have crossing points spin orbit coupling helps you to open up band gaps okay so after the prediction from Cain and Mailer that graphene should be topological insulator and you know graphene is here in the top of the periodic table this is my periodic table which guides you also through my talk so and the numbers here is the numbers are the electronegativity here beyond the atoms and they help you to understand whether materials are very ionic because if you so this is nitrogen the numbers tells you how how much the atoms like to have the electron so we know fluorine likes mostly the electrons while the atoms on this side they don't like the electrons and so therefore we have a unique compound if we combine for example sodium with chlorine we have sodium chloride it's a white powder white white white band gap so this doesn't help for topological insulators so therefore this is a little bit of help with these numbers and here we know that the spin orbit coupling increases if we go to heavier element compound so it was clear when the prediction was done for graphene even graphene is a very special compound with a very nice band structure and this crossing points is direct points so the spin orbit coupling is very small because it's just on top of the pair in the top area of the periodic table so but if you go to the bottom where you have more spin orbit coupling so we know all the rare earths and actinides are metal so they're not insulators or semiconductors and so so people thought there's no topological insulators in the element at this time and everybody was there for looking for two elements which was good for me as material scientists because then people are interested in getting some advice anyway nowadays we know if we can make one layer of tin or one layer of bismuth and bismuth itself is also higher order topological insulators over time we have even more higher more complex topological properties and so it's not hopeless if you have yet like if you have made the crystals okay so then this was what then Shoshan did and under Bernoulli they looked for two elements and two elements semiconductors are used in electronics and in solar cells and as I said in solar cells you have a band gap around two so the materials you're looking for is cadmium selenide and cadmium telluride but this was too big the heavy element compounds have very often very small band gaps and even negative band gaps and this was why Shoshan predicted McCree telluride because this you see is a small band gap even a negative band gap and the people in solar cells and electronics they like to draw this like the energy gap versus the lattice constant because they like to make devices so if you have compounds with the same lattice constant you can make a nice devices because you can grow them on top of each other without having strength so this was the prediction and then soon after this there was a realization and Shoshan even told me the story so when they looked into McCree telluride compared to cadmium telluride here you see cadmium telluride this is your way to draw the band structure this is my way to draw the band structure you know you have a conduction band which has S character and we know above the fermi energy all the bands are anti-bonding by below they are bonding or non-bonding you know so NTSR fermi energy and this is a sigma type B bonding so it looks like this so this has so this changed the face here and this changed the face anyway so in McCree telluride indeed this S electron band comes below the fermi energy at the beginning some paper thought it's related to spin orbit coupling but this is not the case it's a relativistic effect if you go to heavy element compounds every heavy element has the so-called 6s electrons or even 5s electrons contracted due to the relativistic effect so 1s electrons are so close to the core so they are contracted and therefore there is a tendency that the S electrons always come below the P and other conduction electrons so this is already in the atomic limit so and I think the the the the bonding or the heaviness of McCree telluride makes really that that there's an overlap between the conduction and the valence band anyway so the problem is that here we have an S electron which is only not degenerated and the P electrons even in the relativistic case are degenerated so which means if we change the position we end up with the semi-metal and it's not a topological insulated far away from being topological insulating so Schoen told me so he was quite frustrated when he saw this band structure but then he got the German thesis of a PhD student and he since he was in Germany as an undergraduate he could read it and then he recognized if he makes a quantum wave structure between cut me tell her right and make me tell her right he can get more or less best of both words by making a certain sickness of the McCree tell her right he can have a bent inversion and still a band gap but the band gap is then very small because he started from a zero band gap and in a quantum well you cannot get a 0.3 EV band gap which means you have to measure properties at very low temperature like here at 0.3 0 3 Kelvin and Lawrence Molenkamp at this time when Schoen visited him he already had the samples in stock so this was why the prediction was only one year before the experimental realization where they found this quantum spin hall effect in this quantum bed another way is if you already know Bismuth is not too bad but it's the same in metal it's also not an insulator you can think about what can you do with Bismuth a lie Bismuth for example sorry is this is German I took it from German sorry so then you can think about allowing are making a 2 another Bismuth compound with the second element to make Bismuth a topological insulator and this is the case for Bismuth selenite and Bismuth tell right and anti-mone tell right and so on the series of this compounds they can make this very nice quintuple layered compound it's even a 2d quasi 2d material but this is a super big single crystal made by Bob cover so which you see so it's also not the way here we really have the I don't have the picture here but I'm sure you have seen this so here you have really theoretically an insulator with the 300 milli V bandgap which should be a topological insulator at room temperature so then later people predicted many compounds so we try to make it in a certain order is this is 2014 nowadays it's as you have heard so you go simply to the web page click click click and you will find like thousands of topological insulators so you still not the optimal compound is not found yet but you know they all have in common from the viewpoint if you are material scientists they have in common the so-called what I called in a pair effect that the 6s electron are contracted and they are made by atoms like Bismuth like this is compound which has if you count the electrons 3 plus why Bismuth is in row 5 where you expect 5 plus but this already gives you a hint that the 6s electrons are not really giving away because of the relativistic effect they are now closer to the core so they are stabilized close to the core and you can still have a gap with the 6s to configuration without giving the s electrons away so therefore all this heavy element like Bismuth tin and lead and thallium in this area they all have by too reduced valence state if they are topological insulators so this is what you can call in chemistry in a perfect but it's like a relativistic effect emphasis so then if you look for example so one condition as I said is now that we have the band inversion and the second condition you can only look for centrosymmetric compounds if I didn't choose the mercury teller right here is that you look whether you have superiority change in the eigenvalues otherwise you do what is easier for you but not for me because there's that two classification to identify topological insulators so for me as I said the s electrons come down here I compare kappa selenite with silver teller right so again light elements versus heavy elements and the same band structure as the mercury teller right but here because it's centrosymmetric I'm allowed to draw the picture so I have an anti-bonding s electron here and bonding p electron here but they are sigma type they are bonding directly so I can determine the parity this is negative and this is minus and then if I change the symmetry so if this s electron pair this s orbiters come below the fermion energy and the kappa and the selenium so they change the sign as you see they become bonding and they change the parity and this is what we need as a second condition for the topological insulator so it's very easy so what is important as I said now I want to explain a little bit more in a very very fast way what do we need as ingredients one is the crystal structure if you want to understand topology we need to understand the crystal structure of this material and the crystal structure is made by the lattice and the atoms and our atoms are now fishes and the crystal structure is the symmetry the the lattice points can the atoms can sit on lattice points but they don't have to so they can also sit on different points but this lattice points and the degeneration and the symmetry of the look at symmetry of the lattice points are very important if you later look for new fermions because then they have to be very high symmetric and if you look for chiral fermions it's also very so therefore it's very important oops okay so then we can if you have a lattice so then we can build up a unit cell I don't I think this you all know so the unit cell has to be described in ABC and three angles this gives us the smallest repeated unit so we have to make a lattice which you see here from a unit cell which can be if you repeat it so build up in this the whole crystal structure so you see this is the unit cell and you can distinguish what is the smallest unit cell easily okay so and then you need despite of the ABC and the angles of your lattice you need here the example graphene because this is also an important compound for topology so we can have two kinds of unit cell here this is simply the difference here between these two unit cells is simply the origin so if I set the origin here in an atom this is my unit cell if I set the origin in the middle of my hexagon this is the unit cell and both are equivalent it's the but then if you are set the unit cell different the atomic positions are different so which describe and as I said this also important if you want to describe the topological properties so it but as I said the atoms can be it doesn't matter if you shift the origin so the result is exactly the same then you can do this for all the possibilities you end up with seven crystal classes and 14 bravet let us how we call this and then if we even put atoms here we end up with 230 space groups which for all the compounds you find this in this database the ICSD database and this was also the database which under Burnivix team and the other team and also Ashwin uses if they want to identify all topological materials and they also contain magnetic materials and highly correlated materials so it's maybe also useful for the future so more or less if you know this you already know a lot and this is a slide from Maya and Andre you see what they need to do their their general principle in based on some things which already suck did in 1982 so this paper in nature was based on some work of tack so as they have all the ingredients if you know the 230 space groups and if you know the atomic positions and everything of this is in this database in this ICSD and database okay so this is the way however so we have a little bit also a different approach so we try really to make this connection directly by thinking if you want to have a certain electronic structure how intuitively should be the crystal structure look like where should be the position of the atoms and the inner pair effect we already know we have to go simply to heavy element compounds so as I told you so we have a crystal how why what is if I have two atoms from my periodic table for example how can I even predict how the crystal structure looks like I even don't need the database so one easy assumption and which is more or less valid and 70 percent of the cases sorry is that as I said in the periodic table the fluorine and the oxygen has assigned numbers they like to take the electrons why the the Akali earth atoms and the alkaline atoms they have very low numbers they don't like the atom so they give electrons so they give their electrons normally to the atoms sitting here on the left side of the periodic table so which means if I take as an atom if I take the electrons I become bigger because of columbar repulsion if I give my electrons away I become smaller so the crystal structure very is determined by the negative charged atoms the anion and they all like to be treated like oranges they built the close packed letters so if you see a staple of origin on the market looks like this and you can imagine in the crystal structure I like to have a staple of oranges of the anion for example in oxide this is the oxygen to minus or in fluoride this is a fluorine one minus okay and there's any metals it's simply that the metals are not charged so metals in the periodic table like also most of the metals are stapled in this way so they are close packed but there are two ways so staple oranges so you can staple them like here on the picture it's a b c because the third staple looks different from the first staple but this is not always necessary because this staple the third layer of orange and doesn't know what has happened in the first layer because they are totally deconected okay so there are two possibilities to staple the third layer so and this are the two close packed units which we have in all compounds and all metals and they are energetically the same so it's not always clear for us to to say what is the difference why some of them doing the a b a stapling and a hexagonal play a close pack or why they are doing the a b c stacking and the cubic close pack and the packing goes in cubic along the one one one direction why it's in hexagonal along the one zero zero direction so then if you close you think you have packed your oranges closely but they're still voids because the cations the atoms which gives the electrons away like sodium plus or so they're much smaller than the anions and then I can put the cations into the voids or the holes here so and there are two ways to have holes and one is simply you know if if I see a layer of close packed atoms it looks like a beautiful flower so you have one atom the second the third then the next goes into so this is my this is the one layer so if we simply take three of them so the next atom for sure on the next layer falls on top and now you have a void here which is a tetrahedron okay so but there's a second possibility which is even building a bigger void is the so-called octahedral hole if you have an arrangement of my atoms like this okay and then in the middle we have our octahedral hole so depending on the size of my cations they the smaller goes in the tetrahedral side and the bigger goes into the octahedral side and you can even do a simple geometric calculation to see this and this is what then you already understand many many crystal structures which you maybe know because if you have a close cubic close packed lattice along the one-on-one direction if you fill all the tetrahedral voids you end up with kites and fluoride structure if you fill half of the tetrahedral sites you have mercury telluride so which is also filled like a tetrahedral so and if I fill all the octahedral side we have the sodium chloride lattice and if we feel all fill all the tetrahedral and all the octahedral sites we have so-called lithium-3 bis mode okay so and you see always in most cases the the cations are in the voids okay but it even explains more complex structures because the sodium chloride filling the big octahedral voids like in sodium chloride you can put also dumbbells like sulfide dumbbells in there or oxygen dumbbells or you can even have a close packed filling from cesium 60 so cesium 60 is a quiet round so the cesium 60 builds a close packed oranges and in the voids you find the potassium okay so then you can already explain nearly most of the structures which you may be meet in your life is like by simply having a hexagonal close packing and the cubic close packing and filling here's the all octahedral side it's a so-called nickel arsenate structure also sodium chloride the rock salt structure here's mercury telluride the zinc blender there is also a hexagonal version of the zinc blender and but in hexagonal we cannot fill all the tetrahedral side because they come too close to each other so the filling is more difficult therefore we know also I have the feeling more cubic structures okay so this is like simply the zinc blender and the water is again only a difference taking of the tetrahedral okay so but simply here to show you all hexagonal all tetrahedral sites cannot be filled in the hexagonal lattice because different here are all the tetrahedral sites filled in the ABC cubic lattice and you see they don't have trouble but here you see automatically if you would do this in the hexagonal it's not possible anyway so good so then we can think can be so as I said when it was clear we don't find a topological insulator in an element so one thought about two elements and end up with mercury telluride so but if you have two elements you can take also three elements and you have even more fun okay so by for example filling here not only is the tetrahedral side you can have tetrahedral side you can fill all the octahedral side plus half of the tetrahedral side and this is the so-called half voiceless structure which is also interesting in many regards for topological properties and you see we if you come now back why do we can why can we go from diamond or silicon which is the diamond lattice to zinc blender so we can simply can go and count electrons and it's the same conductor because it's a closed filled chain so here we have simply the density of states and if we fill all the electrons in a certain band we know and the Fermi energies in the band get we have a semi conductor so so silicon is a four four semi conductor because here even in silicon the silicon atom are not on the same positions they are like in zinc blender you can say silicon silicon so we have a four four semi conductor and in zinc blender and macrochloride we have a two six semi conductor which means we have in total eight electrons and this filling up the s and the p-bands because we have two electrons and an s-band and six electrons and three p-bands so we have a closed shared situation so we can now think also we can make this eight fill this eight electrons bands with three atoms by having a first row element a second row element and the fifth row element a one two five semi conductor so this is also looks exactly the same but it's even better for if you go to three elements you maybe can even take the D electrons into account and many people who wants to work on correlated materials or magnetic materials like D electrons okay so then despite of the one two five equal eight electrons we have now two ten additional D electrons five bands we can make an 18 valence electrons semi conductor so this looks like this so we have now the additional these states here they are still localized and they are not magnetic in some of the soyslaw but then we have 18 valence electrons here one the so-called sp3 states in silicon like in silicon plus the D electrons so we can make semi conductors which are much more complicated now like silicon nickel tin so which has eight 18 electrons now you can imagine to distribute 18 electrons on three atoms it's even gives you more possibility and then we know we have also the F electrons and they are really strongly localized and therefore are very correlated so normally we ignore the F electrons because they are so localized that they don't contribute to the valence band so if there are even additional rare earth compounds in this ternary semi conductors the F electrons contribute maybe to the magnetism on the side but they don't contribute to the valence electrons and rare earths normally have three valence electrons and the F electron so now you can imagine that we can even play much more with many more compounds than in macro channel right and now you can understand that we simply can go from two element semi conductors to three elements semi conductors by simply counting to eight or 18 valence electron and realizing the same band structure like macro channel right a trivial top of a trivial semi conductors versus in macro channel right a bit of a bent inversion we simply have to rename it like scandium nickel antimony it has a real band gap or lantern and platinum bismuth which has this negative band gap negative band gap is here because the S electron is below like macro channel right so why should we do this why is this interesting this is exactly because we have F electrons here which might give us condo topological insulators or magnetic topological insulators or even here also non-magnetic materials which have a bent inversion is this accidentally are superconductors and this are non-centrosymmetric superconductors with a very low charge carrier concentration so they are all superconductors but they are not superconductors so this is the question is this really interesting for topological superconductors some people are working on this because they think they're topological superconductors for me it's too low one Kelvin is too low so because we like room-temperature effect okay anyway you can make this nice thing in crystals in this compound and as I said also the equilibrium compound is the Fermi heavy fermion with the highest gamma value nobody looked for the the game between the topological insulator band inversion and maybe the reason why a terbium has the highest gamma value as a super heavy fermion is maybe related to topology serum has a very strange Fermi surface so we had no time to study this so far that's for sure something interesting and so on so some of them people read the papers on galenium platinum bismuth which is a in magnetic field induced by semi methods this is the best while semi matter we have I think we chose all the properties predicted by Siri also the gravitational anomalies this paper will be written up soon so so there is a nice way to play so as I said depending from the position in the periodic table the LA the anion like more the electrons so if they are heavy like nitrogen is more on this side they are more ionic here's therefore I draw have drawn or calculated by DFT simply the charge density because I think it's also nice picture so if you have silicon the highest charge density is exactly between the silicon atoms because the silicon two silicon atoms on these two different sides are exactly the same so if you make this quite a ternary compound with aluminium and silicon sorry it's not me so you see already so the electron density goes more here to the silicon compared to the aluminium and if you have nitrogen here you see it looks like an iron and the density of is much closer to the nitrogen so this is also very interesting but you see also if you make a D electron system I told you with 18 valence electrons which looks more like a like three metals together give a semi conductor it looks still like a more ionic compound even in this complex structure so because you simply and you still have a gap because in this in this tetrahedral structure you have very strong bonding sorry bonding okay so the future is in 2d material how can we do to do material you can say you are talking about boring 3d material who cares okay we want to have to be it's not so it's so difficult so because in 2d materials very often 2d materials have layered structure and we can come from the 3d material to do the material by removing one layer we remove one cut ion layer then we have a van der Waals gap between the anionic layer how can this happen so this happened not in oxides and fluorides because they are very tiny so they are very on the top here so if they like very much the electrons as you see the values are very high nitrogen oxygen fluoride and you saw already they like to be very ionic okay so we cannot polarize them they are very round but if you go lower in the periodic table so the various become smaller and if you go in this direction where you also become smaller but especially here so then in iodide and sulfide and selenide and telluride for example they are the the the atoms even the anions are much larger and you can easily polarize this which means I can remove one layer of cations to make this unisotropic bonding I show you the example so for example I said if you have a hexagonal closed packed lattice filled with all the octahedral sides nickel so you come to the nickel asinic structure so but if you remove one layer of nickel so this would be nickel 2 asinic 2 so if we move one layer of nickel we come to the cut mu diiodide structure which is related also to the MOS2 structure and all of this you see so we have we remove simply here we still have the cut ions here remove the cut ions and here we still have the cut ion so we end up with two layers anions and if they would be oxygen the repulsion would be very large because the concentration on charge on a small anion is much higher than if I have a big polarizable anion so if I have iodide like cut mu myodide or selenide I can remove a layer I can have this structure sorry so and therefore it's cut mu diiodide because the iodide has one likes to have one electron so cut mu likes to give two electrons away so the ratio has to be one to two so we cannot make nickel asinic structure with cut mu iodide we need cut mu diiodide so the bit they like to build out this layered structure instead of for example this three-dimensional kaizen fluoride structure as you see here we have this fundamental gap so this is a simple way so then you can get this MOS2 structure and MOT2 and tungsten T2 structure and depending from the crystal field we can have the second layer we can have this 2H structure which is here nicely an octahedral crystal field and a 1T structure and a 1T prime structure and this small changes even I don't know the small changes even makes a difference whether your compound is metallic metallic and the vile semimetal or even a normal trivial insulator but anyway I hope you've got an impression now that you can make many of this how to make 2D materials and this is like I always like to go back to my Heusler compounds you can do it with all kinds of structure so like so if you take this Heusler structure you remove here one layer so you end up with a so-called PBFCL structure which you don't know but in topology people know zirconium silicon sulfide which is also the same structure and you can have even the high TCs in this layered structure so this is the way how we think about structures okay so then you can have even a longer list the first list you already saw hexagonal closed packed qubit closed packed filled all the voids now you fill the voids only partially in layers and then you can come to all this very famous structural layers so which also include MOT2 etc okay so now after we understand the crystal structure and we count electron we can maybe go beyond and for me in chemistry we have one hero in Roy Tofman who got the Nobel Prize in the 80s for organic chemistry and I still think his what he did in organic chemistry strongly related to the topology of chemical reactions anyway he did also very nice work on a very simple picture which was solid so he simply and we already discussed about benzene so if we simply start this is like how you can coming from a more chemical viewpoint on a linear combination of atomic orbital how you can come to the solid from simply come starting from a simple molecule with two atoms you know you add as big as the circle becomes we add more and more orbitals until we end up more or less with an electronic band structure so and we always see very nicely if we see here the lower orbitals but this you know all I don't have to explain you have no nodes and then if you go higher the number of nodes increases and so you have here what we call in chemistry bonding orbitals and anti-bonding orbitals if we have the highest number of nodes so why is this interesting because you simply can use this like what you would do with the Bloch Bloch theory to you can already think about how the bands looks like if I simply assume a wave function made by atomic functions and we have an e over k i n Bloch function and then we can simply say if k is zero here in our band structure on our s orbital has the same sign and this if k is p over a we put it in the equation it changes the sign from atom to atom which means the lowest energy has is at k equals zero because all the wave function the the chain of our hydrogen atoms have all the same sign and if you go to p over a the hydrogen atom so we think here simply I was maybe a little bit too fast that we have this chain here of hydrogen atom which was here symbolized with this so which explains us already if we have an s wave function our bands always go uphill because the k equals zero is always the lowest energy because they all overlap here this has no nodes while if I have p over a and a is my lattice constant here more or less in my chain of hydrogen atom it goes up so if we would have the same situation only with p orbitals but which are born sigma type which are in the same direction lying on a chain so we would simply have no phase shift if we have k equals zero so which means I get this orbital scheme and if I go to p over a I get change the phase from atom to atom so here you see this is more bonding than this so this p sigma type bonding goes always uphill so now you can imagine if there is an overlap between s and p this always leads to some crossing points because they simply go in two different directions anyway something else which is also important for topology is straightforward here if I have now this hydrogen chain going here to there and we all know in one band we can have two electrons but in the hydrogen saying hydrogen has only one electron we only have this band half filled and if we go to half filled we immediately see at p over 2a that we have a degeneration of states here which easily can be lifted which we know as a pious instability and this is why our hydrogen is a molecule and not a chain of atoms even if people put a lot of pressures they still still didn't succeed or this to make a really nice hydrogen crystal which has equal distances so because of the half filled band we get this back folding of the band which you all know and we get the demeritization of the electrons but this also tells us if we are looking for the crossing points like graphene degenerated point like Dirac points it's more often in the band structure than we think and a nice a nice thing also where we have this change in the electronic structure a nice example which I discussed with Andrey it was the square net of many many crystal structures have a layout of square nets and very often it's very interesting so this if it's a half filled band in a square net so it's not stable it does a pirates distortion so because we can do a small structural distortion to lift the degeneration here and open up a band gap which is bad for topology because if you want to have Dirac and white semi metal the structural distortion is bad but what is very interesting and I don't understand this is a question to you the theoretician if the atoms are heavier this pirates distortion doesn't appear so it looks like that's been orbit coupling helps us even to have more white semi metals and I always speculate that white semi metals only maybe semi metals in general can only appear in heavy element compound but this is not proven it's simply an intuition maybe sometime when somebody proves it because here's this was was written in Andrey's paper that you have this Bismuth square net this distortion so it doesn't happen so which opens up big band gaps so you stay with a very nice topological band structure and so in all the space group 129 and 139 if you have heavy elements you have this very nice topological materials and one example is again the zirconium silicon sulfide which people are working on because of nodal lines and many of the bismuth compounds so many of the bismuth compounds in this space group or antimon compounds or tin or lead compound are still interesting to investigate okay so then coming back to graphene and then I make a break because then we are nearly through the first part is like so graphene is not heavy but it's still interesting because it's a very special compound in some sense for me also topological because the electrons cannot so you cannot have this double bond so you cannot destroy graphene or strain graphene or do something a pilot's distortion is not possible even if the atom is light because everybody knows if we lift this degeneration we get localized double bonds and the gain we have because of the aromatic structure of graphene is so much that that therefore graphene is very special and I think on this carbon compounds there might be also more and more interesting properties still to appear therefore this this graphene has so many interesting properties like high mobility high mean free pass even in very light element compounds even with very low charge carry concentration I don't want to tell you about the structure of graphene but very similar like with a simple LCOO approach of Fricke you can also easily explain that the graphene band structure exactly has to look like this with this degeneration point at the k point but here we look for the p electrons so the the p electrons are perpendicular to the bonding direction so the sigma bands gives the lattice and all these electrons are totally delocalized in graphene anyway you get the slides and with this I want to make a break for five minutes so we might be meet at ten past ten okay so it's enough for one cigarette and a little bit of fresh air thank you very much so I'm sorry it was late and no problem yeah no problem yeah I stayed in the car yeah yeah yeah yeah yeah I only had to find the entrance took me some time do you have a stick do you have a stick or should I put it in the dropbox I maybe start no because they come then maybe I have one next time what ah ring the bell why that's okay that's a fact I can just see I just read time yes thank you so now we can you can now think so one of the question which we ask ourselves as designing materials can we make graphene simply more heavy how can we increase the Norbit coupling for graphene and Siri very often does it they put something on top of graphene but our approach was something else so since the macro teller right have a diamond has a diamond structure so and graphene or graphite they they what I can make this three-dimensional structure with carbon and I can make this read a two-dimensional structure with carbon so in a similar way I can take combination of atoms which gives this 18 valence electron or eight valence electron you remember two six semiconductors and makes a layered kind of structure which looks like graphene and graphite you know so so more or less all so we can play around and this has even some advantage why we thought mercury teller right has a big disadvantage I told you this is cadmium teller right the S band on top in mercury teller right we have the band inversion the S band comes below but we have the degeneration at the Fermi energy which is a semi-metal so we don't have a topological insulator so but if we could break the symmetry of the crystal structure then we could even have a topological insulator right so a cubic structure we learn from the crystal structure here in cubic we have a equal b equal c so in a hexagonal structure we have more degrees of freedom because we have a equal b but c is different so we already naturally breaks a symmetry if we go to a hexagonal structure but the other way is also to go away from the cubic structure is like for example silver teller right you can have a distorted cubic structure where the a is not any longer equal b or you can go what the people do in solar said they start from cadmium teller right but nowadays everybody knows there's kappa indium cellanite solar cell and in kappa indium cellanite we double the unit cell of the zinc blender so here we have c is not equal ab so there are different ways to break the symmetry to lift the degeneration at the fermi energy to make a real topological insulator okay and this is exactly what we did in the next step we simply looked we can break the symmetry by going to cycle provides like in the solar cells or we can go break the symmetry like going from diamond to graphite to heavy graphite and if you count here the electrons this is one mercury antimony antimony is five instead of mercury cellanite at six so it's just the same number of elements electrons the structure is different it's a layered structure and then if you look at the band structures the red band is here the s so you see a band inversion in mercury teller right you see a band inversion in silver teller right in in the distorted silver teller right you open up a small band gap but in the cycle provides a doubling of the unit cell you open also a band gap you see the band inversion and you open a bigger again band gap these are now really calculated band structure and also in this potassium mercury antimony you really see a nice band gap at the fermi energy because it's hexagonal and you have the s band below the fermi energy very similar like in the cycle provide so first we look on the cycle provides so normally we do the dft band structure simply of the bike and this is the dft band structures of the bike and we look for the vent inversion this is there in the cycle provide as well as in the hexagonal in the graphite so if we do this cycle provide sorry this is terrarium termination you see nicely if you calculate now slab and this is a nice thing of the topological insulators you simply calculate the slab again with dft or and when you function you see nicely is crossing the surface state which you want to have in a topological insulator diracone surface state so if you now look for the here for the mercury potassium mercury antimony band structure so then you see here's cut me tell right the band structure is very similar like the light version in this crystal structure like potassium thing phosphide so there there is but here it's a layered structure so therefore we have at the gamma point the same band structure as at the a point because of the now c direction so and in mercury tell right we have the band inversion which leads also to this dip in the band structure and then potassium mercury antimony you'll see also this nice dip here in the band structure and the s electron coming below however when we try to calculate the surface state we have no surface state in the trivial potassium thing phosphide unfortunately we have no surface state even in the inverted band structure at this time we were very disappointed because the reason is here we have two times the band inversion very similar like in bismuth so at this time it means okay if you have two times a band inversion we end up with a trivial band structure okay so but then we saw it we are smart we might have can generate situation where we have a band inversion at one point at the gamma point and no band inversion at the a point but if you can imagine then the band gap is very small so there are few compounds which are here seen in gray which show exactly this band structure with a very tiny band structure but then at the same time the weak topological insulator came up thanks to Siri thanks to you or you maybe I don't know who did weak topological insulator and we recognize that this compound doesn't have a nice surface state here on top of the main surface but it has a surface state perpendicular to a layer and this has a weak topological insulator so then if you calculate the band structure you see here's the surface state and the crossing point so you can find here trivial strong topological insulators with tiny gap because of the double inversion at the gamma and the z or a point and and you can have weak topological insulators anyway at the same time as sometimes later Andre recognize that this compound is even more interesting because if you really look in detail what we saw here at the edge state at this edge it's a it's a sorry in this direction it's a hourglass fermion which was then published even in nature after we had this very nice prediction and it's indeed also proven in Aper's Ingle Risotto photo mission here you see along the gamma z direction it's really interesting because this is like this crossing point it looks like an hourglass and this might be interesting for other properties so this maybe has also inspired here and you again said this was a compound I showed before so inspired work about the new fermions because these compounds have very special and this was in this article where Andre and co-workers were looking for degeneration beyond Dirac and white fermions so they were looking for band structures which have more than like you saw in macrochelorite this simple double degeneration many more degeneration and the interesting thing is if you want to have this many degeneration for interesting surface state you need atom sitting on highly degenerated points also wick of position so if an atom is sitting on a 16 fold position you have a chance to find a 16 fold degenerated point but what are in common beside of the nice physics which you are interested this was a commentary of Benakar about the paper which was very nice for us so if you could put on the universal letters then you might have to find even very interesting fermions which could morph this is a citation from Heisenberg a protons and tool whatever but I don't believe this anyway it was nice but all this crystal structures are non-symorphic here so they are all cubic so because if you want to have a high degeneration or most of them are cubic or hexagonal you have to go to space groups which have extremely high symmetries because otherwise you know from the space group if a is not equal b then you already lift the degeneration from the space group what you learned before structural distortion lift degeneration and here we want to force you want to have enforced degeneration on the highest level as possible you know so then you have to go really to look for cubic space groups and very high symmetry so with the high numbers 225 or something like this okay so and you have to look for non-symorphic crystal structures to get this and non-symorphic crystal structures is that you combine a lattice movement together with the point symmetry so for example here you have a rotation axis but then it mirrors the hand on the other side but you move along half of the lattice distance here along c direction this is so-called non-symorphic group and why do I think these new fermions are interesting so now it comes back that I look on the materials which were predicted in this paper from the viewpoint of chemistry and if you see this new fermions are new fermions because they have this high degeneration point but it's much more all the crystals more or less all the crystals most of the crystals have a chiral crystal structure and I think there will be a paper of a Fossan coming out soon about chiral topology and most of the crystals are superconductors if they're not magnetic okay so the question is here also again uh if they're not magnetic is there a relation between this highly degeneration of the of the band structure and maybe that they're superconductors and one famous class of superconductors are the A15 superconductors which are still the superconductors mostly in application and I think this is always luck if you have an 80 years old co-worker because he was working at the time of niobium antimony and he said at this time already the people thought maybe superconductivity in these compounds were related to the highly degenerated band structure which then I have to say at the superconducting transition slightly distorted there's a martensitic phase transition anyway to think whether the new fermions are related to the crystals chiral crystal structure and superconductivity is something which smart theoretician could think about the future as in a similar way that I say all the semi metals are heavy element compound there are no semi metals beyond graphene which have light elements anyway so and then the other group of materials are so now we are coming really to this crossing points so sometimes we looked the whole time now for lifting the degeneration and topological insulators but nowadays people think even from the physics is much more richer if I stay with the crossing point and so I go to buy semi metals and to direct semi metals so and how can I achieve this so simply if I look for the three-dimensional band structure I have the overlap between the conduction and the valence band if I have a forbidden crossing here around this line I end up with the topological insulator which is insulating hopefully in the band in the gap and has this very nice surface state which we already saw but what could happen that it not opens up everywhere so I end up I end up with crossing points or lines even but crossing points at certain points and this even leads to more interesting physics experimentally so we have this dirac points or y points here at the where I don't have the lifting up of the degeneration and dirac and y points are related by symmetry so dirac points occur at high symmetry points in the bryan zone if I draw my band structure it's easy to find the dirac point if I draw my band structure it's impossible to find y points but because dirac points are four fold degenerated and they split if they split up in y points if I have a crystal structure with a lower symmetry or if I have magnetic material this can be splitting up or if I apply magnetic field into y points they are much more difficult to find because they are somewhere hidden in the bryan zone so therefore this is I think there are many many more compounds which have y points than we know because they are hidden okay and if I have this y points in the bike they have chirality and now we are back to my DNA left hand right hand molecule so I promise I tell you I want to do catalysis with this y semi-metals so they have chirality so they lead Fermi though at the surface we don't have a dirac cone like surface state we have this Fermi arcs which are connected on both sides of my crystals so as I said so the dirac cone is four times degenerated like in graphene if I strain graphene which I cannot do easily so because I destroy the aromaticity so I would get y points or if I apply magnetic field I always turn a dirac point into y points and then I get this very interesting Fermi arcs which are chiral so here we come back so then sometimes life helps or it's more complicated another question to the theory which I simply say intuitively is like graphene is a very special case because here is a band structure of graphene which I showed you before and here we have the degeneration of the points we have a dirac cone and the if you see the band dispersion it's like 30 ev and minus 20 ev it's a 50 ev band inversion and this is the case because the carbon has a very strong covalent bond and so therefore we have this giant band dispersion which we don't find in so many compounds you can go again you don't find this nice kind of nice bands and there's nothing else and this P band around the Fermi energy so and this is a very nice type one vibe a dirac point where the it's really pointy at the Fermi energy if the Fermi energy is just there so this is a band structure but life is always more gray and not simply white and black and in many of the compounds the real solids we are investigating the the the cone is not nicely uh standing up and the point is not really a point so it's much more complex the cone is tilted so very often I get the points above the Fermi energy below the Fermi energy or electron and hole if the cone tilts I automatically get electron and hole pockets and my feeling is this is also even not so bad because it helps us to stabilize this nice linear dispersion and the linear dispersion brings really the interesting properties like this giant mobilities this giant magneto resistance effect etc you know so that which I think will have maybe very interesting properties in the future so this was the semi metal I come back to the semi metal at the end but there are also metals and uh so if you are in material science or chemistry you always learn gold has a very beautiful color and the origin of the nice color of the gold is because the six s electrons which I told you before comes much closer to the core so they are sorry they are they are if you compare it to silver therefore the transition from 4d to 5s in silver here to 5d to 6s because the construction of the s electrons is much smaller so this leads to this very nice uh color so it's a relativistic effect so then at the same time if you read old papers about chocolate uh and the surface state of chocolate and so because we were interested as I told you we are interested in using really making big money out of topology by using it for catalysis we said let's go back to uh to the surface state which we have in platinum in gold and especially because also platinum has the highest berry curvature for any non-magnetic material so it already shows that we have crossing points in platinum some interesting electronic structure in platinum so and then we went back to the papers of chocolate who said okay who invented surface states by uh looking for surface states in a periodic potential and now mostly reticent I know also are working on this and he wrote in his abstract if you have two bands with different parity you get a surface state which is more or less the definition of a topological insulator you know different parities we said s and p for example so if they cross we can have this topological surface state so and this is exactly the case also in gold so in gold and uh platinum we have the same situation as in a topological insulator here we have a crossing between the p at the s band because of here the contraction of the s band and the p band in the band structure and we would get exactly as expected if gold would be a semi conductor or an insulator we would get exactly a nice diracone like in bismuth selenite but life is a little bit more difficult the fermi energy of gold so you have to mercury is by the way that better you have to dope gold if you want to go exactly there and the other thing is the surface state of gold are slightly banded and therefore we normally have seen only this part of the electronic structure and thought about this part and nobody thought about topological and banded version in the context of gold and platinum but uh because in the past people thought about the surface state like a shock least state like this but the reality is like this you have a rush bus splitting okay then you can think it's a rush bus splitting but indeed you see this and this is what we then calculated here in gold so you nicely see the s band coming below the fermi energy and the p band above the fermi energy and you see gold is quite gapped in the band structure and indeed it has this banded version which leads then to the surface state of gold which really connects conduction band with valence band and we had a nasty referee and he wanted to see it experimentally thinking you cannot measure unoccupied states but this is a two-photon electron spectroscopy which really shows this and now I know Richard Martin writing a big 700 pages explanation that this is indeed the case that the chocolate states are always topological surface states okay so for a few minutes I simply show you how to measure the property so we make many of very nice single crystals from all this materials but also sometimes it's nice to have uh sin films uh but here it's very easy we have these crystals and uh they are useful because now even some people in high energy physics and in astrophysics they ask us maybe can we collaborate theoretician in astrophysics okay because this could be maybe tabletop experiment uh because quantum field theory is a common thread for uh high energy physics and astrophysics anyway this is our motivation really to push it and the way we do this so somebody predicts by theory something interesting we go to cunt mart or we just we know we work with under it very well so we have the predicted material we grow the single crystals so then we do our first to verify the properties or stm okay and then because very often you are more interested if you combine topology with superconductivity and at the end we want to make really if you want to say quantum anomalous all effect at room temperature or something like this okay so it would be good if you predict more magnetic uh white semi-metals with room temperature okay please this is one to do on your list so what we do we measure more or less most of the time not quantum effect we do a simple hall measurement we take a single crystal and measure transport in a magnetic field so they all have their quantum counterpart which the measurements are similar but you know in the field quantum measuring the quantum counterpart is for us the next step on the between most of the time don't do by ourselves so because we simply identify the interesting materials here so and we can despite of the hall effect we are now very very much interested in the anomalous hall effect we measure this is the case in the hall effect we apply magnetic field and we measure transport in the anomalous hall effect we have a magnetic material and measure an additional contribution to the hall effect which is the anomalous hall effect and this is really a good measure possibility for us to measure the barrier curvature I don't know who knows about the barrier curvature okay most of you know okay so therefore for us it's a lot of fun now if you measure high anomalous hall effect we know already we have crossing points at the Fermi energy we have increasing magnetic structures okay so and I think if we from our conclusion is if we if we measure so if you want to have quantum hall effect without a magnetic field the quantum spin hall effect we need topological materials this is quantum hall effect this shows this very nice edge current with different spin direction but in quantum hall effect which was invented from clitzing from clitzing so you need a magnetic field a high magnetic field so in quantum spin hall effect you don't need it and people know maybe if they know talks from clitzing he always says he now can have the NIST and the PTB in Germany to make the kilogram more correct and everything so so they they did this with his measurement but they are already doing this also with the quantum spin hall effect together with law and small income so if people still debating about the quantum spin hall effect it seems to go in even the first application so because here you do the same without a magnetic field and if you want to make devices which do more than only the quantum spin hall effect the magnetic field is always bad nobody likes magnetic fields in the lab okay so having no magnetic field is already nice and if you have a magnetic material which has the same properties as a quantum spin hall effect you can have the quantum animal assault effect which gives your poor spin current and this magnetic field is now the intrinsic magnetization so it's no external magnetic field okay so and our goal is to do this at room temperature this at room temperature is graphene so finding magnetic materials which have a large quantum animal assault effect at room temperature so and then you can also despite of a voltage you can always apply a terminal gradient which gives you then the Nernst or here's the the CPEC or the Nernst effect and I think because we find really giant anomalous soil effect we also find giant anomalous Nernst effect based on the buried curvature maybe we can have some impact even for energy conversion because this allows us to violate the Wiedemann Franz law and make maybe really much more efficient energy conversion system so we have a patent with Ohio State with Sariman on this so far at low temperature but we are working on higher temperature and you see it's very simple you know we take our single crystal here's our tiny single crystal then we make contact on a puck which we which simply fits into a ppmS and then we have a voltage it's a little bit more complicated if you apply a gradient in not the voltage if you apply a terminal gradient but it's the same and we put it in the ppmS we press a button and we measure so now you can imagine that Andrei Bernoulli as a cirurgician everybody knows Andrei so he wants to come up with a lab he wants to grow his own single crystals and he wants to do ppmS measurements and he has shown a scene in our lab that is not so difficult okay now the cirurgician come and compete with us huh what is left for us huh okay good so I'll show you the example of the Wides so measuring the Wides and this is really as I said this was the first prediction we're really also experimentally one succeeded the very simple binary compound niobium phosphide niobium arsenic tantalum phosphide tantalum arsenic the band structure looks like this so you have additional electron and hole pockets and the crystals are easy to make I have a movie but I maybe show it at the end if I find it you know you do take a polycrystalline sample you take some iodide and then you grow very nice single crystals here and as I said it's very difficult very often to find the Y points because they are hidden somewhere in the bright and so on so this is the Y point they are somewhere inside and most of the time we like to only show the nice high symmetry point so then very often we miss it okay so you need some intuition and here as I said you have additional electron and hole pockets anyway so this is your prediction I assume some of the people did some predictions and so so so for Y points there were already a lot of nice interesting physical prediction so because if for a very special situation if you apply a magnetic field in the direction of the current I told you so we measure always the current but in our measurement we apply magnetic field and we can apply the magnetic field in all kinds direction but for the special case if current and field is perpendicular so you can do this chiral anomaly in Y semi metals this is the first standard level so if you transport electron density from one from one level here from this direction and there so you make a chiral anomaly because then it's not the same number here on each side and this leads to many interesting properties like the anomalous all effect and intrinsic anomalous all effect in non-magnetic materials or the planar hall effect the chiral anomaly and the axial gravitational anomaly which means for us we measure if we have the B field and the current in the same direction a negative magneto-resistant and otherwise the B square behavior so simple simple equation what what are the results of all these predictions why is this so interesting and I think I'm not sure whether all the theoretician know why it's so super interesting you know so but since I'm not a deeply thinking theoretical physicist you know I rely on Wikipedia so I went to Wikipedia and try to understand what is really the interesting thing about the chiral anomaly okay so and I'm really into amazed because it this is a way to explain the asymmetry between matter and antimatter so so you have an analogy between the wild or direct semi metals and the vacuum state of particles and antiparticles and both are related to the chiral anomaly which is a way maybe to break fundamental laws of physics via relativistic quantum field theory so I think this is really worse to think even much more deep about this you know so because I think my slunk has an institute in Heidelberg where people wait positrons versus electrons and they hope they find a difference in weight so when I started to discuss with them about my ideas about catalysis they want to now wait left-hand molecules versus right-hand molecules but I I don't believe that you find something in the way I think if we really can show that we really can measure the chiral anomaly in some sense directly I think it's also a little bit more evidence that this is the origin of the matter antimatter asymmetry so I think it's worth to think about more experiments in this direction so the first prediction was that this white semi-metals have fermi acts and then this is not so difficult because you do ingress or photo emission and you do again your surface state calculations have been hired it's a surface state calculation and niobium phosphide is lighter than tantalum phosphide and tantalum adenine and you see nicely how the the the distance between the white points depends on the spin orbit coupling and you see that if you measure the fermi acts it's really nicely in a very nice agreement with the experimental data so we know already there is interesting physics to find anyway so here is only the results because I'm running out otherwise of time so we did niobium phosphide and bike it doesn't show the chiral anomaly but if we make this very nice nano ribbons we just stop the fermi energy to the right point accidentally sometimes accidentally is good so and the good thing is so then we measure the magneto resistance which means the resistance in a magnetic field and as I said the prediction was there should be a positive magneto resistance if the b field is not perpendicular under negative if the b field is perpendicular and we should fulfill this b square behavior and this is indeed what you see if the magnetic field is perpendicular to the current you see positive magneto resistance effect and this wickets here are quantum oscillation so it's very nice we exactly can conclude with the fermi energies in our material because all the semi metal shows this nice quantum oscillation and if it moves the magnetic field perpendicular to the current we show a nice we see a nice negative magneto resistance effect even up to room temperature so but then we wanted to look on the mixed gravitational anomaly which was predicted by super such f and some astrophysicists and their prediction was you have to apply instead of a voltage you apply a thermal gradient and the prediction was here that then if you measure the thermal conductance so it should be going at low fields with square to the magnetic field and at high field it should diminish and this is an experiment so here it's a voltage and the b field it shows nicely this is b square behavior at least at the certain area and then you see here if you see the term you do the same experiment with the thermal gradient you see exactly what was predicted the b square behavior and then it turns around and tries to diminish so this shows how nicely you can even work on questions which were asked in the context of astrophysics if we get our astrophysics and find interesting physics anyway so we had a difficult referee because the soviet subject theory was based on a hydrogynamic theory and the referee said we have to remove the hydrogynamic because it's bullshit okay you can read the discussion in blocks of nature and the fights of certain people there okay yes anyway we still believe that this hydrogynamic flow maybe plays an important role in this compound which was topology because in 2016 there were three papers published at the same time two on graphene and one on palladium cobalt O2 from Drayston, Philip Mall and Andy McKenzie they claim that they have found materials where the electrons don't flow like a drudegas they flow much more correlated like a viscous liquid and there were different experiments how they did this because this is like electron gets scattered on the nucleus this is a symbol here for the nucleus our electron simply flows through the crystal so one was the terminal transport so which shows the with the violation of the Wiedemann Fanzler it shows that the phonons are decoupled in some sense from the electrons scattering the other was that there's a size dependent like if you do viscous experiments in the first semester of physics if you still have to do experimental physics you know so if you have different size of pipes and you try to put a viscous liquid in there it doesn't work if you have very thin pipes okay so this is an experiment which you can do with crystals and I think then this was the work done here and we took another Y semi-metal tungsten phosphide to do the experiment because it was protected Y because the Y points with the same charity was close to each other and this differential relative far from each other so the annihilation is not a problem and this compound had a very large our values so the resistance at room temperature and lower temperatures strongly different it's even like the resistance at low temperature is extremely small even better than clean copper so more or less accidentally even by terminal transport we made a very clean single crystal which has a mean free path which is larger than the crystal size okay so we use this material for the experiment so we have half a millimeter mean free path in this material to look whether we can see some evidence for hydrodynamic flow and we use this crystal to do all the experiments and at the end we had more open questions and solution as usual so the first experiment we did the pipe experiment the size dependent experiment of the viscous flow of the electron so we made crystals of different size and we really see that the resistance changed strongly so it goes up and it can become even very resistant and this is not only tungsten phosphide if you see the experiment in literature it's there for cadmium arsenic for the direct sodium metals and for other also even if the people don't investigated have investigated this unless it's time and there was a prediction that if it's a viscous flow it should go with the width to the square and if it's if it's through the gas it should have no widths dependent and here you see as a function of temperature the widths dependent and you see here there's no widths dependent and the end at low temperature the width dependence of the square which shows really evidence for hydrodynamic flow in this materials. The second proof was look for the violation of the Wiedemann Franz Law there you have to compare thermal transport with electrical transport and normally it always has the Lorentz numbers also the thermal transport over the normal conductivity always leads to the Lorentz number there's always a small this violation intrinsically at low temperature but here in this materials in the semi-metal you see that there's a fully break down of the Wiedemann Franz Law and Cameron Benjamin has measured it too and he sees also recovery of the Wiedemann Franz Law at very low temperature so you can even then calculate the viscosity for this electrons which is like liquid nitrogen and then the second the third question which was not investigated up to now was simply when I saw this behavior that depending from the size you know here's your conductivity resistivity as a function of temperature and with smaller size it the resistance become much larger this is like what you observe also in a magnetic field and if you see in 9 Tesla here's the upper curve you see this curve if you would not know that this is 9 Tesla looks like a topological insulator and this is a typical curve for every Dirac and by semi-metal okay so if you apply magnetic field it looks like a topological insulator so it has a plateau here at the end and so comparing the magnetic field dependence and the size dependent brought us to the idea to look for magneto hydrodynamic which people have very nice equation for plasma physics and indeed the datas which you get from Wiedemann metals totally fit to the equation which were developed for flat plasma physics so this is a row to multiplied by the width square and this is a theory is gray and this are the datas of the wires or of the single crystals then Johannes is interested in astrophysics so therefore and also in terminal transport so he really got all the relaxation times out of all this datas we had the momentum relaxation time and the thermal energy relaxation time which shows then really that at high temperatures the momentum relaxation time it's really but I'm done now so it's only nice so it's like so this is a line which is a plunge in bound of dissipation and amazingly the momentum relaxation time lies at high temperatures on the plunge in bound of relaxation and the energy relaxation thermal energy relaxation time at low temperature and I only can tell you Jan Zahnen he scrapped his head and he said this cannot be don't ask me why maybe some of the older theoretician can ask this question but it simply tells us there's a lot of interesting physics which can be still discovered in this field of topology and this is I want to finish and I hope I gave you a little bit an insight how to find new materials and that there's a lot to do and maybe as an outlook I can tell you we are now interested in magnetism on topology and since in magnetism we nearly have even more wire semi-metals than a non-magnetic material so I think we are not running out of business for the next five years okay with this I thank you for your attention and I'm happy to ask questions