 So, Professor Falco, when you are ready, you can go ahead. I'm trying to get rid of multiple bars that appeared. Do you see the additional bars on my screen? Do they obstruct the view or not? I think we're good. We're good. No, we're good. Okay. We're fine. We're fine. Can you move your cursors? Do you see my pointer? Yes. Yes, I can see your pointer. Yes. Right. Please go ahead. Okay. Thank you very much for giving me an opportunity to give online talk. I would like to do in this presentation is to tell about the system that we studied over the recent years. Basically to describe the possibility to tune system parameters and to achieve various regimes for artificial lettuces that one can get in position, not all the healthy and I buy layers by changing the twist angle or choosing the pair of materials that form the interface. Just some reason it's what I don't. Sorry, I got into troubles because bar appeared, which it doesn't allow me to move. Oh, no, I can. Oh, do I get rid of it? All right. So the systems that I'll be talking about today are slightly twisted by layers of transition metal to recognize from the group which is shown on the slide. These are mid band gap semiconductors. And they are interest for applications was driven by the strong light matter interaction in the systems. And that is why at the end I'll describe the option that we got for heterostructures of same hulk engine. To have to host quantum dots that may provide single photon emission functionality in the telecommunications range. And that comes from very strong confinement that one can achieve in those systems and to understand where this confinement of electrons and holes in the quantum dots comes from. So we need to discuss several effects which occur, mostly starting from the structural properties which we also studied in detail both theoretically and tested experimentally. And there will be several experimental results that we used to compare our calculations. The results have been obtained by the group of Roman Herbert shelf who developed the method of transferring to dimension layers of fundamentals materials in ultra high vacuum achieving extremely high quality of the interfaces. And upon annealing reaching the regimes that we call lettuce reconstruction and marginally twisted by layers and by marginally twisted. We understand small angles and how small we'll discuss in the next couple of slides. So what is the starting point for this discussion it is that the physics of twisted structures with either the same lettuce in both layers or slightly incommensurate lettuce with slightly different lettuce constants is physics of more super lattice and in more super lattice you have periodic variation of a mutual position of atoms in the two layers, which has a period dependent on the waste angle. And for transition metal the healthy guides it is also important to take into account the orientation of the unit cells of the two crystals, one we call parallel and this you can imagine when if you take the same layer cut it into two halves and then move by parallel transposition to put one half on the top of the other so then the unit cells of the material will be parallel to each other. And the other way you can assemble a structure is by rotating by 60 degree due to 120 degree symmetry of the crystal it's the same as rotating by 180 and due to the lack of inversion center in the individual layers, these two structures have different properties both in terms of how electronic properties are set but the first thing that we'll discuss today will be how this affects the structural properties of the layers. The way to talk about the about the more super lattice. It starts by saying we put two layers on the top of each other we look at the effect of the rotation of the crystals as rigid objects. But what we'll discuss first today is that it is not necessarily like that. It happens that the, even despite week, when there was coupling between the layers, because those layers are so sin, there is reconstruction of the layers happening. And the first thing to do is to establish when the conditions when this reconstruction takes place. And what we find is that reconstruction occurs into networks of the main and the main walls, and then there is a bit of classical physics of those structures related just to lattice reconstruction and physical effect that we need to take into account having in mind that the individual layers have no inversion symmetry. And for parallel orientation of the unit cells of the crystals we find a week for looking charge transfer which was quite entertaining exercise, which was also observed experimentally. And after I describe those effects that determine later the band structure of the electrons close to the bandages in the conduction band and valence band now affected by the periodic strain by periodic piece of electric charges or variation of the interlayer charge transfer for electric type. Then we can talk about the more superlattice minibands for electrons and look at the regimes how these minibands get narrower upon elongating the period of the superlattice which can be achieved for homobiliars by choosing smaller angle of misalignment. And then after I describe what we learned about the homobiliars with a strong lattice reconstruction, I'll then focus on the case that we found quite interesting recently, which is about same halcogen bilayers of TMDs with different metals like molybdenum, disulfate and tungsten disulfate. And for those I'll show that there is additional effect of strain which is not present in homobiliars which comes through the hydrostatic strain which has opposite sign in the two layers because they initially have slightly different lattice constants which locally upon adjusting produces hydrostatic strain of opposite sign in the two layers. And that effect has a very pronounced effect on the band structure creating the arrays of self-organized quantum dots both for electrons and poles at the same place so that we get self-organized quantum dot arrays for excitons as well. So this is my plan and I start with the discussion of what happens with the structure. What is shown here is the calculation using density function theory of the interlayer distance dependence of the crystal energy for various ways to put one monolayer on the top of another. With this analysis for all TMDs and also we looked at the heterostructures forcefully making the lattice constants equal and we check that it doesn't matter whether we fit lattice constant for example tungsten disilinide to monobdenium disilinide. The results for what we need for the analysis of the structures as a measure scale they coincide. So what you see in these panels on the left-hand side is analysis of bilayers with anti-perlostacking of the unit cells and not to surprise that the lowest energy configuration comes as to H stacking which is what grows in the bulk material. The next one on the energy scale is the stacking where you put metal on the top of metal in the two layers but now the halcogens are not on the top of each other the halcogens because of the anti-perlamentation of the unit cells are actually the largest distance from each other and actually the distance between halcogens when it is the largest determines the energetics of the interlayer interaction because the halcogens are in the outer sublayers of the crystal and also they have p-orbitals which are sticking out which provide the interlayer interaction repelling from each other and therefore the largest distance between halcogens is what the crystal wants to have to minimize its energy. Then the highest energy corresponds to the case when the two halcogens are on the top of each other we call it XX prime stacking so that halcogen in the top layer appears to be on the top of halcogen in the bottom layer. There is a similar behavior in terms of XX stacking for the for this biolayers with parallel orientation of the unit cells but for the lowest energy we actually have two degenerate configurations two configurations with the same with the same energy they are mirror images of each other they're basically the twins of each other and they correspond to that in the bottom layer halcogen appears to be under the metal in the top layer whereas the other subletuses in each layer they appear in the middle of the hexagon in the layer above or below and there are two configurations that you can get one from the other by mirror reflection they have the same energy and what we also did in this analysis we calculated energies for actually multiple ways to offset one layer with the respect to the other to obtain the analytical expression by interpolation which allows us to describe the dependence on the interlayer distance for any arbitrary offset of the atoms in the top layer crystal with respect to the bottom layer crystal why do we want to do that because for small angles of misalignment the local stacking of the two layers varies slowly at the scale of the lattice constant so that the local calculation we did in the DFT allows us to describe the dependence of adhesion energy on the local stacking and this local stacking is the reason for the layers or this energy of adhesion is the reason for the layers to adjust the lattice constant or the atomic positions to each other from the initial one to the energetically more preferential locally it happens by a bit of swelling for each of the offsets and then adjusting by displacement inside of the top and in the bottom layers by deformations that of course cost the strain energy and then all together if we minimize this we get the overall structure of the deformations and overall structure of the atomic positions in both crystals so what the starting point here before this relaxation is done numerically we implement the moiré periodicity by this which is determined by small misalignment angle which is accounted as rotation of one crystal with respect to another and also by a small mismatch of the two lettuces of the two materials and for the combination of this transition metal dehalcogonize that we look at this parameter delta is less than few percent for the same halcogen by layers delta is even less than one percent so that we're talking about really long period structures with the description that we get from this analytical formula for the interpolation formula for the adhesion energy combined with the macro scale, mesoscale mesoscale elasticity theory it gives us a sufficient accuracy to describe the deformations and to obtain the atomic positions of the two layers with respect to each other so then after we have this instrument we can look at different situations we can look at larger angles of misalignment and smaller angles of misalignment and what we find is that for this TMD systematically if for anti-peril orientation of the unit cells they are more than one degree and for parallel if they are more than two and a half degree then there is very little reconstruction of the lattice taking place and this is understandable based on the argument of comparing the area of domains that may form by reconstructing into energetically preferential stacking configurations and the energy cost of the main walls of the superlattice so that if angle is not small enough or there is a lattice mismatch which is large enough then the period of the superlattice is too short for the domains of preferential stacking to develop to take over the energy cost of the deformations which are required for the formation of the domains and if the angles are smaller than those then a distinct structure of domains appears and the structure of domains is different for anti-parallel and for parallel orientation of unit cells so in the right hand side in the bottom we have the examples of what we get if we take this angle very small for anti-parallel configuration of the unit cells of the two crystals the domains that form are two H stacking domains so that's where the hulk regions are about metals and metals are about hulk regions in both layers and the domain walls that separate them they have this network structure with corners which are different there are three corners where the hulk regions are on the top of each other and there are other three corners where the metals are on the top of each other and this is energetically not so bad for the bilayers structure and that is why these corners are kind of swelled they are actually small seeds of this m and prime stacking with the size of several nanometers for the parallel orientation of the unit cells the structure is different it's a triangular lattice it's triangular lattice with domains of mx and xm stacking these domains are the lattice structure of these domains is a mirror image of each other and these domains are separated by the main walls which are nothing but partial dislocations normally in a 3R structure of bulked MDs and in the corners of the domain wall network we have small areas kind of dot-like objects with xx prime stacking which is energetically least favorable just to mention that the domain walls in the case of anti-parallel orientation of the unit cells the domain walls that separate consecutive two h-stacking domains are nothing but full screw dislocations and the partial dislocations are as a feature of the crystal that allow for the points and as I mentioned before some halcogen hetero bilayers they have such small lattice mismatch that if we align them sufficiently then the reconstruction of the lattice into two h-domains or xm and x prime domains would take place just because the long period of the superlattice allows for the for the adhesion energy to take towards energetic cost of the strength we had a chance to check the calculations with quite a lot of details this has been done against the measurement using skinning transmission electron microscopy performed by the group of Hague Sara Hague did multiple structures analysis the transmission electron microscopy is sensitive to positioning of metal atoms with respect to each other because in the case of sulfate they carry more electrons and therefore they are more obstruction for transmission of the electrons from the microscope and we compared in details various situations and we got a lot of confidence in that the numerical analysis on the structure it does correspond to what happens in reality so that we had a chance to start looking at a bit more physics that can be related to the networks of these domains and the main walls in particular to start with the main walls and to implement this piece of electric polarization stuff that I promise but before that I would like to clear my mind and my conscience and to say a couple of words about the situation when the lattice reconstruction is actually weak where the main effect of the lettuces swelling in the vertical direction if it actually happens the physics in this case is more or less the physics of more mini bands where you can take into account the interlayer hoping between the layers which is also periodically modulated taken into account this change of the interlayer distance and the influence of the interlayer hoping of the local stacking on the interlayer hoping matrix elements and obviously the interlayer hoping is the strongest when you have bandages as close as possible to each other in the two layers such situation is realized in malibdanium, disilinite and tungsten, the sulfide heterostructures for the conduction bandage and then there is a bit of resonant interlayer hybridization for electrons at the key points of the hexagonal brillian zone of the crystal which represent in monolayers the bandages both in conduction band and also in the balance band and then what we did we just calculated the mini bands for the electrons we calculated those also for various orientations of the unit cells with small variation of the angles from the perfect alignment to identify when the when the mini bands are narrower when the bands are seeker and we also realize that when you have an electron in the hole present one can start doing the hybridization between the intra and interlayer accidents where the effect of the electron hole binding additionally promotes the alignment of the electron energy in the conduction bands in the boss layers enhancing the effect of hybridization and therefore producing strongly hybridized intra and interlayer accidents so this has been calculated and also measured in optical microscopy where it was possible to see not only that's exit on hybridized but also that there is formation of mini bands which through the processes allows for additional absorption branches which were detected in the resonance reflection experiments also if you start playing with same with homo bilayers like tungsten desilinate bilayers but now twisting the angle going from higher misalignment to lower misalignments one can also look at those mini bands they would appear boss for conduction band and balance band one would have to be very careful what to discuss in terms of absorption properties for example for absorption it would be necessary to look at what happens with the key points of the brilliant zone for discussing the electric transport properties or P or end up material one would have to understand where the actual band ages are and due to the interlayer hybridization gamma point is promoted very strongly in the team D so one has to understand what happens with the more mini bands on the around the gamma point bandage in those materials and also there is interesting physics that may happen in the Q point due to the interlayer hybridization as well so what is shown here on this plots is how the mini bands change when the angle decreases and what you see that and this is not a very difficult thing to expect because when you have bandages and when they're modulated for heavy carriers you get objects which start resembling more and more quantum dots and then the separation the linear scale separation in terms of distances between zones quantum dots which follows the decreasing just through the longer period of more superlatives it makes the bands network and just transforms the system into the arrays of quantum dots from what otherwise we would describe as quantum material with mini bands and this is where the reconstruction of the crystal starts playing even more important role because of the form and the nature of and position across the supercell of the quantum dots that we're talking about will be strongly affected by the developing deformations by electric potential by electric charge transfer and also by the band gap normalization that takes place in the system so this is an example of how this looks at the mesoscale at the distances of many nanometers when it's again looped in transmission of the microscopy what you see here are the main walls because that's where the variation of the local stacking takes place inside the domains transmission of microscopy here does not give information for example whether it is Mx or Xm stacking for pylorentation of the cells of the crystals and what you see in the two examples on the left-hand side is the sequence of hexagonal like domains with two two H stacking separated by dislocations and on the right-hand side for pylorentation of the cells of the two materials you see the triangular network of domains and the main wall met the main walls with the dots here representing the stacking which corresponds to halcogen sitting on the top of each other when you have deformations then in each of the two layers these deformations when they're in homogenous they produce piezoelectric charges this is because the materials we talk about don't have inversion symmetry and also because there is charge transfer between the atoms because it's not purely pylorent bonding in the crystal there is a bit of polar coupling in the materials and as a result we have charges that get accumulated around the main walls in each of the two layers now what happens in the anti pylorentation of the unit cells of the two crystals is that there is a constellation of two minuses that happen producing the same charge accumulated in both layers on the top of each other the reason is that the deformations you need to develop or crystals need to develop to bring their lettuces together they have the opposite signs and therefore produce opposite sign of strain tensors at the same places in the geographic pattern but at the same time the two unit cells of the two crystals are inverted and therefore material constants of piezoelectricity are also of the opposite signs those two minuses cancel and then we get a modulation of charge which produces modulation of electrostatic potential the same sign in both layers and this basically starts modulating the position of the bandages in the same way for the conduction and balance band and as a result of this is that the corners of the domain wall network which in fact is the largest they start becoming the minima and maxima of potential of piezo potential producing kind of quantum dots which separate geographically on the more pattern the minima of energy for electrons and poles so those we can identify and also we can use that correspond to this they have been measured by scanning Kelvin probe microscopy and they recently correspond to what we calculated knowing the piezoelectric parameters of the crystals so what we did with this we use that together with the modulation of the interlayer hybridization of bandages in different parts for different relevant parts for the local minima and maxima of conduction band and balance band respectively and we had to do that because as I mentioned before the hybridization between the bandages in the two layers is the strongest around the gamma point that's where electrons have less problem to tunnel from one layer to another and that's what we thought about when we look at different different parts of the of the band structure of the brilliant zone we have different answers about what happens with the bandages for example for the balance band for systematically for team D's well maybe except for tungsten disilinate balance band at the two stacking domains and at the same time when we look at the the electrons which may be in the K point or due to interlayer hybridization of orbitals at another local minimum in the brilliant zone which is called the Q valley which is the the minima of the energy in the corners of the main wall network so it starts looking like we get a variety of opportunities which can be also tuned as you can see from the comparison of small angles and large angles by changing the angle of the twist another piece of physics that we came across is the interlayer charge transfer which we call for electric effect and this comes from the lack of inversion symmetry in the structure with the orientation of the two layers because both of them don't have inversion symmetry just to mention that to each stacking is inversion symmetric because the top layer is inverted image of the bottom layer but for general way to put top layer on the top of bottom layer there is no also mirror symmetry which in principle permits out of plain polarization of the bio layer which we established by both calculating the charges and with density functional theory and also the potential of the double charge layer which here is a parameter delta so when we calculated it for various teams we got numbers between 60 to 70 electron volts and this quantity is actually measurable because if you scan the surface of the bio layer placed on the top of a metallic plate with the metallic tip that measures local potential then until there are two steps of twice this delta when you cross the border between consecutive domains which are mirror image of which other and therefore they have the opposite direction of the out of plain electric polarization so this has been done and tested and what you see here is statistics obtained on multiple domains in different parts of the structure with different local values and the value of this diagram built from this obtained data is the value of twice this delta which reasonably well corresponds to what we calculated in density function series experiment gives something like 60 millivolts for delta and in the DFT for malibdanium sulfite which was studied in this experiment it also can be tested in a different way one can apply out of the out of plain electric field and start changing the shapes of the domains and when one changes the shapes of the domains one can start moving the main walls and we developed a bit of physics a bit of theory to describe the variation of the structure even merging of partial dislocations into full dislocations and this has been also tested by the observations of the variation of the shapes of the domains in various ways in particular this experiment is a recent measurement produced by a TAWA group where they see this change of the main wall and the different shapes produced by the locally applied electric field so I now jump into the last part of what I would like to describe and this is about the hetero bilayers which contain the same halcogen materials in both monolayers and the reason why they are interesting is because they have pretty close lattice constants so that those allow for a strong lattice reconstruction of slightly different type is compared to what happens in twisted homo bilayers and twisted homo bilayers the strain has to compensate the rotation of one layer with respect to another and therefore in that case strain was dominantly sheer and the difference is the lattice constants then slightly different things happen we need to compensate this difference by hydrostatic strain and then what happens is that over large areas of domains the hydrostatic strain in each layer is small, the lattice constant adjusts to each other but the remaining or the missing material has to be squeezed or taken into the main walls and in the main walls we get the largest effects of the hydrostatic strain in fact the largest appears to be in the main wall network corners around this in particular on this places where the local lattice structure is least energetically favorable these are the places where the halcogens appear on the top of each other then why this hydrostatic strain is so important first of all because it appears to be quite large in those corners reaching several percent of strain and the reason why we care about it is because when we look at the evolution of bandages in the material as a function of strain hydrostatic strain, sheer strain does not do much but hydrostatic strain changes the bandages quite a lot if the hydrostatic strain component in these two layers has an opposite sign then the bandages in the two layers move against each other in fact for the conduction bandage which appears to be in his interstructural and molybdenum layer it goes down in the main wall corners and for the tungsten layer the bandage as the K point goes up they basically come towards each other and this means that for electrons will get the quantum dots in those corners of the main walls where we have xx prime stacking and for the holes we also have quantum dots in the same place so we are getting quantum dots for the excitons at the same time as for electrons and holes in the same place which was not by the way in homo by layers where the bandages for electrons holes appear to be in different positions and when we combine together all the factors that we established before the effect of piezoelectric potential and also the interlayer transfer of electric type which also produce the interlayer energy shifts we check that for a small range of misalignment angles between zero and one degree the effect of hydrostatic strain is numerically quantitatively the strongest and this determines a different physics of those hetero by layers as compared to twisted, marginally twisted homo by layers so we basically modeled the strain for various misalignment angles inside structure starting from zero degree to several looked at the evolution of the bandages and from that we were able to construct the distribution of bandage energy around these corners of the main networks we calculated the bound states for electrons and bound states for holes for the range between zero and one degree this quantum wells for electrons and holes appear to be so deep that they host not only the lowest S state but also the P type state bound in the same quantum dots so one can start looking into physics of intra dots terahedron transitions in those systems but most importantly for us we now have the electrons and holes localized in the same place so we looked at the interband optical transitions we looked at how the energy of this transition is shifted with respect to the energy of the excitons interlayer excitons or interlayer excitons inside the domains and the shift we computed with respect to the interlayer exciton ranges between half and 0.9 legging vault for various angles of misalignment between zero and half degree and this large shift with respect to the non exciton energies places the resulting transition in the telekinesis range of photon activity which may be quite a nice thing to use in terms of applications because then we would get single photon emitters from those quantum dots exactly in the telecom range so this is what excited us we calculated because of this we calculated the optical polarization of these transitions and for all possible polarizations we computed the oscillator strengths in one configuration of the structures which provides the strongest coupling between the exciton and light and after we used the known parameters for the quantum efficiency of the exciton and the computed values for the optical oscillator strengths of the exciton we came to the conclusion that the quantum efficiency for this quantum dot emission which may be 1% of the exciton in the malibdanium disulite or malibdanium disulite and for those systems whether for those quantum dots whether for expect that there might be maximum repetition rate of light emission for heavily pumped dots going into the range of 100 mega which is quite good repetition rate for generating single photons so this is what is the last thing that we got and that's what I wanted to describe and just to repeat what we just summarized what I was talking about this is an interesting system where self-organization of the lettuce allows to get the arrays of quantum dots with strong localization of charge carriers for homo bilayers this would be separate places across more structure where electrons hold would be localized and we have all the information about where the bandages are across more superlatives as a function of the angle and quantitative description of the corresponding quantum dots potentials and for hetero bilayers with the same halcogen we get really strong self-organized quantum dots localizing both electrons hold the same place and therefore getting the best results to finish I would like to thank my collaborators so the modeling part of what they described has been done in my group at National Griffin Institute by Vladimir Genaldiv and Jayce Marcus Fabio Ferrer is graduating students this year and Sam Magorian, Victor Giorgio Omi, as well Yelgiel and David Trousty-Hirina, they have already left to start their jobs elsewhere and the experimental results I described in this talk they were obtained on the material developed by Roman Gorbachev and the experiments on transmission electron microscopy were done by the group of Sarah Haig we collaborated in optical characterization of the system with Tarkovsky group at Sheffield and with Philip Kim at Harvard also with David Smith and Saul Sampton and scanning microscopy of the structures has been done by Olga Kazakova at NPL and the group of Peter Beter and lots of them thank you very much for your attention thank you we have a couple of questions in the audience yes thank you could you please comment about why do you say that these quantum dots are self-organized please they are self-organized because when two layers are put on the top of each other and annealed then reconstruction happens just to provide with some a dynamic state it's not the in the case of homobiliars it's not the most energetically favorable which would be when two layers would actually rotate microscopically but because of the average misalignment angle this rotation does not happen due to the boundary conditions at long distances so it's self-organized because you just let it go and it forms you don't need to do etching like in old style semiconductors you don't need to do patterning just cutting pieces it just happens by itself any further questions or comments on the online audience is there a yes yes the question about twisted by layer of the Hulk magnets so other good one-dimensional chiral states on the boundaries between domains and can one describe them with S matrix yes and no just I probably need to see if I have may have an image but I struggle the answer is the quantum dots are the dominant objects there are quantum dots there are kind of large area quantum dots which are like boxes I'll find an image in a minute which may be best to look here for example so do you see my screen now yes yes so in the case of for example gamma valley holes the large areas of hexagonal domains are the boxes where the valence band has a maximum and therefore where the holes would be localized then you have boundaries which are basically the barrier so this is a case of which is more similar to domains in metals rather than quantum dots for electrons for example in the cave valley the story is different these are the two of them there is a minimum of energy and you would have quantum dots for electrons with strong triangulation of their shape and you can call those aphiruses going out from the dot as quantum wires but those wires have bandage higher than the bandage in the dot so they're not really interesting things happens in the case of of the parallel lined bilayers where the bandage modulation is actually funny for the Q valley bandages so the Q valley in terms of the brilliance on appears to be just six points related by rotational symmetry somewhere in the middle of the brilliance zone not in the center not in the corners and in those areas of the brilliance zone the anisotropy of the mass produces also the anisotropy of everything of the mass which as you can see from the top right hand side image are actually the places for bandages so in principle one can have the quantum wire structures which would be quantum wires with orientation rotating to the minimum of the bandages are when you go from for example the the valley Q1 to valley Q3 or to valley Q2 so that there is a bit of one-dimensional physics that may happen here but it's funny if I mention one-dimensional physics due to the three valleys in this system they are actually chiral they can be described as one-dimensional but one would need to take into account the additional quantum numbers and for each of them the set of kind of the network of wires would be rotated by by 60 degree when you go from one valley to another okay any further questions Professor Boko again so we have a copy break until 11