 I'd like to thank the organizer first. Invite me to this very nice place. In fact, I should confess that this is my first time to visit London, except kind of passing through the hydro several times. So it was really great. And I actually liked the conference that many speakers actually has generous in one hour, or even just kind of go beyond in one hour. Volodya actually already set the record. And another nice thing is my talk is toward almost the end. And a lot of introductions has been done. A lot of things has been mentioned. So I don't have to go through the many introductions and directly go through the point. I think that's another good chance. On the other hand, it turns out that I have to kind of scoop really deep and pull out some of the most recent result. So as you will see, some of the result is just published, or some of them are not published. Some of them are not even analyzed. But I want to share some ideas and excitement and some of the comments, especially critical comments. And also, I think I know that this is getting the afternoons and after lunch, especially. So unless I should be a little bit more energetic, everybody can easily fall asleep. So what I propose is just a storm at any time if you want to ask the questions. If you don't like it, then if you disagree, just storm me any more months. And we can kind of have the discussions on site. I think that's something I want to do. All right, so the original title of the talk is Graphene and Hexabron Nitride Heterostructures. But then it becomes clear that only with this topic probably I cannot cover one hour. So I will start with this. But on the way that we are going to visit a few different topics that I just chose. OK, so the motivation of going for the hexabron nitride graphene heterostructure is basically the quest for the higher mobility in graphene. And why higher mobility? Well, the past historian, the two-dimensional electron gas, already told us that whenever you have the better samples, better mobility sample, you start to see the different physics. That's one of the main motivations. And many people try to improve the quality of the sample and realizing that most of the limitation of the sample quality, especially comes from the substrate. Either it was roughness, or it is the charged electron hole puddles, the charged traps. Whatever it is, most of them actually comes from the substrate in an extrinsic effect. So the obvious thing is you want to kind of get rid of the substrate and suspend the graphene. And then as Andre showed, the beautiful result already in this conference, once you get rid of substrate and properly unear the sample, the mobility of the graphene can reach several millions of the levels. So that's actually good directions. But on the other hand, suspend sample has its own limitation because it's fragile. As you imagine, that's one atomic big sample. So if you want to design a bit more complicated devices or if you want to do something more robust type of the experiment, say thermal cycles many times and so on, this may not be the best sample you want to deal with. Especially if you want to make the multi-probe samples with less strain on the sample, it becomes quickly, technically challenging. So the natural direction we want to look is are there any other substrates that kind of mimic the vacuum, the best substrate we can think about? Well, it turns out the nature provides those kinds of substrates. We already heard the boron nitride, especially hexaboron nitride, which is very close to the graphene like the forms, but it's an insulator simply because you can think about two carbon atom in the inner series replaced by boron and nitrogen, completely broken symmetry state in terms of graphene languages, therefore open up the large gap. And all of these things, and especially if you have the high-quality boron nitride sample, which such as the crystal we obtained from our Japanese colleague in the names, that can be a good substrate that more or less mimic the vacuum. Well, this is some of the recent results. Again, the microlaborated Columbia, the POPs-Pathis group's S-TEM result. So here we put the boron nitride, the graphene on the boron nitride, and do the STM studies. Michael Klamy actually showed that similar image yesterday. So what you see here is up to, say, a few tens of microns, completely flat in terms of the flatness. It's under a few sub-enstroms of the roughness only. Do it just presently coming from still the same resolutions? Yet, there's a beautiful, this hexagonal network of the graphene is there, not much disturbed by the surface, and extended over the quite a large area. So you can imagine that this is one of the really kind of great substrates provided to the graphene to the best quality of the electronic properties here. Now, one way we can characterize such electronic properties that I'm going to use, I'm going to show you, is quantum artifact in setting in this sample, and showing that that's actually quite different. Much better than what we usually see the sample on the silicon oxide, for example. I'm showing here some of the old results that we had at the same time with the Manchester Groups. The quantum artifact, seeing that this sort of graphene sample is sitting on the silicon oxide, this is one of the hallmark results showing that indeed graphene is quite different from any two-dimensional system. Most... the notable thing is this quantizer steps, going on the four times of half-integer steps, can be explained by, again, between these pseudo-spins and better phase and all of these things. But nevertheless in retrospect, here the sample is disordered, you know, so that each lambda level that correspond to the forming of the quantum whole step, we should consider that as a spin degenerate as well as a pseudo-spin degenerate or valley-spin degenerate, whatever your preference calls. Now, the pseudo-spin or valley-spin should be degenerated in single particle picture. Okay, but now assuming the spin degenerate means that each lambda level is broad enough so that you don't see that kind of... the Z-manifact is not big enough to split your lambda level. So, in a sense, it is a pretty much disordered system. In retrospect, if we had much better sample than this, maybe seeing that this valley phase and the pseudo-spin out of the structure might not be straightforward. So, the nature already gave us initially the disordered enough sample so we can quickly figure out this half-integer shifted quantum whole. But as you go to the better sample, such as that sample that I showed you, the graphene sitting on the boron nitride, things immediately start to change. For example, when you look at this at the zero-field characteristic resistance versus gate voltage, the first thing we notice is that this is an extreme shock and if you just take this half width of the full maximum as an upper bound of the disorder, the charge in homogeneity we have here is much less than 10 to the 11, electron per square centimeter. On such a good sample, when you apply the magnetic field, what we are seeing is, well, those kind of these half-integer quantum effect are now turning to the just-integer quantum effect. Basically, here, as you sweep the field we see that not only 2 and 6 originally we saw, but we see also the signature of the 3 and 4, and basically we are seeing more or less all the integer quantum whole steps appears. Probably better pictures, better data is we fixed the magnetic field at 14 Tesla and sweep the gate voltage, then we are seeing not only 2, but we see 1, 0, and if you go to the high-magnetic field, we see the 3, 4, and so on. On the lambda level, we start with completely split in such a better quality sample. So that's an interesting part. In fact, this was seen in the sample on the silicon oxide, but you have to go to the really high-magnetic field, such as 40 Tesla and 45 Tesla at that level. And then, first of all, G-man splitting eventually went over, so we know that at least all these quantum whole effects split in two, but on the top of that, we are seeing also this ballast or pseudo-spin also got split off, that basically splits all the lambda levels. So this effect itself was seen before, but what is interesting is now those kind of effects can be seen, you don't have to go to the high-magnetic field lab, but you can just do it at home for the look at this experiment. Of course, human nature is greedy, so when we see such a good sample, we just bring this sample immediately to the magnet lab and here is the high-magnetic field data. You see that beyond the 15 Tesla, so 35 Tesla, I see that two and three steps here, but on the top of that, there are other steps up here and in the magnitude of whole resistance, we combined with zero of this rxx, showing that there is additional quantum effect and if you just see that what is the corresponding fielding factors, that's actually corresponding to 4, 3rd and 8, 3rd we are seeing this basically fractional quantum effect that corresponds to 4, 3rd and 8, 3rd in multi-terminal geometry, properly made whole bar geometries. So seeing diffractions is another new thing in a sense in the graphine was reported a few years ago by Ivan Drey groups and my group that for the signature of 1, 3rd but that sample is two-terminal suspense sample but real observational fractional quantum effect should come from both the multi-terminal measurement in the whole measurement and the longitudinal resistance measurement and this is in a sense the strong evidence we can present as the fractional quantum effect. Now again, we fixed the largest magnetic field in this case the 35 Tesla and if you sweep this gate voltage what you are seeing is that again 1, 2, 3, 4 on the top of that in between that you see that all these blips and corresponding this deep so we know that there are many of these diffraction appears if you start to assign 4, 3rd, 8, 3rd which actually appears here is very strong and some of them 10, 3rd, 11, 3rd, 13, 3rd are there and if you are bold enough you cannot assign the other things such as 8, 5th and 7, 3rd and so on. So at this point this again zoo of the diffractions and so on well we know that all these fractions actually do appear in the gallium arsenide and gallium arsenide support probably more than 10s of the fractional quantum effects and so on. So in a sense it is expected simple qualities becomes better than you see that some of the strongly correlated or not the strongly correlated correlated electron phenomena such as the fractional quantum effect the question you can ask here is whether these series of diffraction can be different from what you are seeing in the conventional tool manager system so to make this long story short my conclusion is that yes they are somewhat different and then I'm going to kind of argue that what's the difference so to make to argue the difference we have to kind of step back so the fractional quantum effect as I said is the correlated electron states and usually can be only explained when you think about the many-body type of the effect and one-third of the fraction was the first one that observed in gallium arsenide 2-deck and was explained by the Bob Rufflin and by setting up this the famous Rufflin's wave function here and basically that this many-body wave functions and that they explained now what you're seeing this Rufflin's wave function by the way it only contains orbitals and that it's kind of spin sector is not there and when Rufflin actually wrote this wave function he assumed that well all the spin is polarized and that makes sense because usually this quantum effect fractional quantum effect appears at relatively high magnetic field where probably Zeeman's energy will align all the spins in one direction and have to consider its spin sector of the symmetry so the only consideration is anti-symmetry of this wave function part and that's the basic motivation of writing this Rufflin's wave function but then soon it realized that actually by the help of it if you just compare the energy scale there's just something that one has to be very careful now I just plotted out here the energy scale of this typical the two-dimensional electron gas with finite mass basically the cyclotron energy scale the distance between the Landau level is the largest and then that's basically we start with the single particle pictures and then construct this many-body effect considering the Coulomb energy scale which is about a few tens of percent of this cyclotron energy now compare with these two energy scales and if you just plot it out the Zeeman energy it's actually only a percent of this cyclotron energy scale it's extremely small therefore in approximation probably the better picture we just start with is we start with this spin-degenerate Landau level and construct this wave function from there and that's what actually helps to show how we can do that in fact this picture can be even better explained if you just kind of throw in the so-called composite phenomenon pictures in that picture basically as the composite ferraments each electron grabs two flux quanta and they form the composite ferraments and the composite ferraments Landau level basically is responsible for the solid fractions there in that picture what happens for the one-third state is basically among this composite ferraments there's been polarized by the many-body interactions or residual interactions or ferromagnets among the composite ferraments in this system so the reason I'm telling you here is basically even for the one-third state in fractional quantum state basically the alignment of the spins and the spin polarizations has some of the interesting origins there now taking that message back to the graphene becomes much more complex the reason is on the top of the spin we have a spin of the electron in the graphene we are dealing with the pseudo-spin or valley spin here so your wave functions of each electron has a 4 degree of freedom coming from choosing the spins and the valley spins and of course energy scale the same story that I mentioned in the Gallulus arsenide more or less works with the special G-man energy scale therefore it becomes essential like the one-third state in Gallulus arsenide this four component of spinors let me call this SU4 structure becomes quite important to understand the fractional quantum or effects that's in the graphene so that's basically the message I was trying to address here so how can I prove that well experimentally actually I'll just show you here that fractional quantum effect appears only in the lowest Landau level and equal to zero Landau level so you see that there are fractions one-third, two-third, four-third and eight-fifth actually going on in that direction looking at this sequence just to look at the sequence we can immediately pick up the one interesting fact we are seeing one-third four-third but we are missing the five-third we are seeing that only one-third, four-third but nothing five-third already good enough to give us some of these scenarios should hold than the others let's assume that instead of arguing that I start with SU4 type of this Landau level I start with somehow there are different scenarios possible so that such that say G-man splitting is strong enough so that I start with spin-split Landau level so spin-up and spin-down is split or maybe you can argue that well, you put your sample onto boron nitride which actually tends to break the AB sublattice symmetry so in the worst case that I may actually break up all the symmetry by just single particle regions so awesome that that's kind of another scenario there is no degeneracy I started with in fact I started with all symmetry broken states like the 1, 2, 3, 4 type of the integer quantum of state I'm seeing I will argue that this and that is not a possible solution possible the case that if I just kind of match with this experimental the fact that I'm seeing the 1, 3, and 4, 3 but not 5, 3 where each Landau level has particle or symmetries which means, for example if this is a right scenario that if I see the 1, 3 I should be able to see the 2, 3 about the similar strengths and be able to see the 5, 3 well that's not the case I'm seeing the 4, 3 but no 5, 3 so this scenario is gone how about that so you too same thing for the particle or symmetry across here if I see the 1, 3 I expect to see the 5, 3 but that's not the case so we should eliminate that so by eliminations only viable solutions viable case initial Landau level I start with should be a 4 type of symmetry well because of this the underlying interesting symmetry only do exist in the graphing case not for the the conventional 2-dimensional electron system in fact this system start to give us some different behavior I will just give you one more example here that I just show you here the 4, 3rd diffractions at different temperatures because the the activations across the composite phenomena Landau level by just measuring that this RNS plots say even different magnetic field I can just show you how the gap actually scale for this the fractional quantum state of 4, 3 turns out gap scales more or less the scale type of the behavior which is expected but what is interesting thing is the size of the gap is fairly large in this case one of the strongest fractions the gap size is about 20 Kelvin bear comparison with the Gardner-Massonade case this is the effect of the 5 larger than what you see in the Gardner-Massonade so the fraction is fairly robust the other thing is that oh by the way those kind of gap is actually matching with some of the calculations based on the spin polar lies but value on polar lies ground state correspond to 4, 3rd descriptions but besides that in fact if you just do this gap measurement for all other fractions that I just mentioned we clearly see start to see some of the interesting trend for example the first of all we are seeing that all this black point which is 4, 3rd, 8, 3rd, 10, 3rd of the gap size at the 35 Tesla they are all larger than open circle which corresponds 7, 3rd, 11, 3rd and 13, 3rd in other words if I have the even numerator in 1, 3rd state their gap is larger than odd numerator states and also there is an interesting trend as you go to the higher fractions size of gap decreases especially these even numerator states and those kind of structures in fact related with that SCU-4 structures and the inside of SCU-4 spin structures I am going to argue in a moment but nevertheless I think this give us that kind of the rich flavor that what generate by this SCU-4 type of the spin structures in each lambda levels and there are also of course some of the unanswered questions that basically the questions drawn to the theorist that why actually 1, 30 is so much larger than 5, 3rd and those kind of things now this structures of the SCU-4 is in fact you don't even have to go for diffractions in fact these structures can be also seen so called this broken symmetry the integer quantum states here I am showing you low field measurement for all these integer quantum states 6, 10, 14 but in between you see all the steps correspond 7, 8, 9 11, 10, 12 and those kind of broken symmetry states one thing that we also notice here is if you just do the gap measurement again for all these broken symmetry integer quantum states we are seeing that even state such as 4 and 8 is much larger in terms of the gap than the other even the odd the integer quantum states such as 3 and 5 at least in fact over 6 larger so it's a very similar flavor that what I just showed you in the fractional quantum state for the even numeral state versus the odd numeral states we can actually do this better we can take these even numeral states and I just measure this gap at the different magnetic field now what we do here is we just tilt to the magnetic field so that I fix the perpendicular direction of magnetic field so orbital part of the energy is fixed then I try to tune the changes here in a sense the perpendicular magnetic field is fixed but changing total magnetic field just tune these spins sectors of the energies so ideally if the gap here is just a spin gap we expect that this gap is linearly scales with this total magnetic field because the perpendicular magnetic field orbital part is fixed but what you are seeing is we are seeing but not linearly and with a different slope if you just measure the slope part this the higher magnetic field part the slope is close to g-factor is equal to like the smell is like the spin but as you go down to the low magnetic field low total magnetic field that corresponds to the larger g-factor in other words you start to flip more spins and then one spins here in fact this behavior was seen in Gali-Marsena case actually this was taken as evidence of the spin scumions that excitations basically what you are seeing here is in the low magnetic field you excite the scumions with many flips of the spins but as you increase the total magnetic field the spin splitting becomes expensive because of the exchange interactions so you start to flip just one spin and your scumions size becomes small and those kinds of things that claim in the Gali-Marsena case what you are seeing here basically give us a similar flavor that in the New York full states is basically a spin polarized state in the ground state and excitations coming from presumably these spin flipped scumions now these same stories as you are fulfilling or in other words all the integer quantum states basically completely changes their energy gap is small and not only small if you just do the same experiment changing the in-plane magnetic field and see how the gap scales well many cases gap does not depend on the in-plane magnetic field indicating that it must be some sort of the valence spins which actually does not care what this is in fact the gap actually do decrease as in the in-plane magnetic field showing that this is much more rich and much more complicated that is simply just a valence splitting what is the real nature over here yes I like that in this case it has a minimum but not always some samples some filling fractions actually they don't some sample with a different thermal cycle they don't show the minimum so in a sense that it also depends on the disorder contents in the sample more importantly it actually depends on what is your perpendicular field so certainly this is not as simple as a spin splitting versus valence splitting but in this case the elementary excitation can be quite complicated might be this SU4 spins scumions in some areas and so on but I don't know but simply just showing that much rich physics in just gallium arsenide where you have the SU2 SU2 type of spins here so the shown message here is basically we have awfully complicated systems or for the theorists maybe more interesting systems but I know that already this becomes too much esoteric so maybe I should kind of stop to talk you about the detail of the discussions and move on something else but at least this shows a flavor of getting the better samples that there are much more rich physics and more interesting physics comes out now bilayer case is also interesting bilayer was discussed intensively this morning by Volodya and one of the really good thing about the bilane especially for the device application if you're interested you can actually control the gap by applying the electric field and one by many groups including the Feng Wang's group at the Berkeley they actually shows that how size of the gap changes applying the electric fields there and this optical measurement shows that the gap can be open up to say 200 millileft which is a sizeable gap and more of us is a tunable now the optical measurement is here is a kind of local measurement so you see that it makes up on the other hand all this transport measurements so far they're done on the bilayer sitting on the silicon oxide the gap they can measure either they cannot measure the gap because of this variable range hopping or if they did measure the gap such as the MIT group size of the gap is probably although many too smaller than what you measure in the optical gap and that's understandable in the kind of global sense so if you have the disorders basically disorder broadening that your size of the gap you are measuring is much smaller than what it should be now this type of the things again coming from the disorder substrate and the silicon oxide so if you go to the better sample if you go to the better substrate maybe we can get to the close the intrinsic gap you can open up indeed that's the case and I'm going to continue that a bilayer graphene sample sitting on the boron nitride and etched samples and so on your characteristic itself you see that this is kind of great I think this particular sample is one of the highest mobility samples we have seen on the boron nitride low temperature mobility of the 300,000 centimeter volt seconds and moreover if you look at this sharpness of pig I think this is kind of really needle sharp showing the surely that the quality of sample is great so such a sample we have put down these top gates to create this bottom and top gate dual gate device what we are seeing is indeed we open up the gap resistance increase and more importantly we can actually do the activation measurement in this sample and this activation gap we are seeing up to the levels before this dielectric breakdown happens so we open up the gap and if we improve this quality of the gate more we are pretty sure that we can actually increase even more but what you are seeing here is now the transport gap activation gap measured by transport is comparable size with what you are seeing in the optical gap showing that we are getting into the limits that really band gap is dictating what you are seeing in the transport as you see here the gap of the back gate is break down because there are only two data points there boron nitride itself the dielectric breakdown is fairly high I think that's... I forgot the numbers but something like the 2 volt per nanometer 1 or 2 volt per nanometers in this case in fact the device was break down because we didn't use a local gate underneath the boron nitride we use a silicon oxide as back gate and somehow when we unear the hydrogen argon the quality of the silicon oxide becomes worse so gate break down basically through the silicon oxide and that's why actually this device failed but boron nitride itself the quality of the dielectric breakdown is extremely good I think this is kind of important the case because I don't have the further data here but this actually allows us now we can actually deplete the carriers in the bilayer case so if you want to copy down some of the mesoscopic physics studies such as make the quantum dots what's mentioned there make the quantum point contacts and those kind of things we couldn't do that before for the single layer because we cannot deplete the carrier because of this client tunneling in bilayer now because we can create a sizeable gap something like 100 millilektric volt ranges if you go down to the low enough temperature just think about just bringing up all the quantum point contacts the quantum dots out of all this electrostatic kind of control so I think that's another interesting direction we can launch on starting from here alright this is just the beginning Andrea actually already showed that we can build up the kind of whatever structures there many of them start now with multiple stacks including this many many multiple for three or four the multiple stack of the tunneling junction device drag device and you see that kind of drag was kind of already mentioned before so I don't have to go through the details so this complicated device structure is indeed possible although this is painful because each steps you lose some of this you have the finite device here but nevertheless the method is there and we can actually build up the device we can actually go through some of the interesting the physics there I think that's kind of one of the the message I can leave at this point one thing about the distract device particularly we see that more or less this is the t-to-the-scale behavior what Andrea mentioned one thing we notice that is though the absolute questions versus what we are seeing is there is already about the factor of four or five difference we don't understand so that's one more point right I want to actually change the gears to some of the slightly different topics but related with this Borel-Nitri sample but this is according to Andre Guine that sometimes ago that this obscure corner of the physics the thermoelectric power right so thermoelectric power is in fact interesting physical phenomena that combine both the electrical transport and the thermal gradient basically the measurement is in a sense straightforward what you give if you have this channel that you want to measure or materials you want to measure thermal power simply just give it a temperature gradient and just measure the voltage across it so that's actually fairly straightforward measurement now it is interesting however such a phenomenological quantity in a sense that can be used for the thermocouples or peltated devices and so on actually hit some of the fundamental the thermodynamic quantity in fact if you use unsuggest relation this thermal power is directly related with peltated coefficients and the thermal energy transfer per charge actually happens in the system so although this one can be quickly measured that can kind of access some of the important transport quantities such as entropy, transfer, per charge now in typical system typical semiconductor, typical metal system in fact there is a well known the formula that relates thermal power especially diffusion part of the thermal power with its electrical conductivity which is known as a mod formula so basically if the system is dominated by the diffusion thermal power what it tells you is if you somehow measure electrical conductivity at different chemical potentials the information of the conductivity can be related with the thermal power and this has been one of the powerful relations that one can use for example tells you about why sine of the thermal power and why sine of the carriers you are dealing with so if you have positive thermal power your majority carrier that you are dealing with the holes and if it is negative you are dealing with the electron now this measurement in fact what can be done any samples including the graphene here is the kind of device the layout for example so again measurement is kind of straightforward what you need is you just contact the graphene on the top of that you just make the heaters by just sending the current through you heat it up temperature gradient sets up and you just measure how much actual voltage you are induced and if you just measure all these transport quantities such as conductivities and so on now you can actually see where the mod formula works simply by changing the measuring the conductivity at the different gate voltage which modulates the chemical potentials you can even check it out if it is a kind of good system you can even check whether this mod formula works now the experiments measuring the thermal power already was done a few years ago and this is one of the moments I realized how competitive the graphene research field I thought I was the only one that doing this obscure corner of the physics without any competitions as soon as I just we posted these papers in the connet soon after two papers followed and now it kind of just matter a few days so three groups actually doing the same thing here that's kind of an interesting part of the history of the graphene research now I don't want to go over all the details but the nutshell of this measurement is indeed whether the mod formula works so I tell you that indeed that works reasonably I'm showing you here that the resistance versus gate voltage and the temperature not much change is because this sample is sitting on the silicon oxide so it's a disorder and the substrate disorder is most of the things that govern this transport here we just do the measurement on the thermal power basically complete a different measurement give the temperature gradient and just measure the voltage across it with calibration of the temperature in the both side of the contact and the value of the thermal power as a function of the gate voltage and three different temperatures corresponding with the conductivity measurement now I told you that there is a mod formula that connects between this conductivity or the resistivity to the thermal power in fact if you know how much chemical potential changes are induced the thermal energy changes are induced by gate voltage I know how I can actually treat this part by taking the derivative and changing the relation between chemical potential to gate voltage is well known as long as you know what the capacity is coupling so there is no fitting parameter needed I can just take this data take the derivative, multiply these numbers and compare with experimental data indeed if you just do that without any fitting parameter it's completely two different measurements overlaps pretty well I think not only positional peak but at the different temperature we have the reasonable kind of overlaps with each other so tells us indeed multi-grade man actually it works great now you can actually do even better you can apply the magnetic field and just measure all these different conductivities whole conductivity, longitudinal conductivity there is a well developed theory already 20 years ago that in quantum regions then you can also measure all these and connect the longitudinal component transverse component of thermal power and connect with all these transport quantities and basically in the graphine it beautifully works you see that this is measured value and this dark one is the calculated value from all these transport quantities more or less reasonably matched not only the positions but also size so this extended multi-formula also works so this tells us that well these things should work as they should in single particle picture sounds good but it's a little bit boring but let me just go back to this slide and ask is this real hold now if you have peaky eyes if you have peaky eyes then this works but look at this, what is temperature this one is 200 Kelvin I'm seeing some difference here so in a sense it kind of develops up now why actually I show you 200 Kelvin only I can do also experiment with 300 Kelvin there's a reason I didn't show you because if we just kind of bring up the 300 Kelvin deviation becomes really noticeable so although I cheated you by some mumbling there's a reasonable matching here but if you go to the higher temperature it's clear that there is a deviation from multi-formula so one thing that we know here is as you go to the higher temperature we start to see the deviation from multi-formula well in a sense you can see that that is expected because multi-formula if you just go back to all the Boltzmann transport calculations basically assume that your electron gas is degenerate and as you go to the higher temperature degeneracy can be a problem well that's not the case because here maybe degeneracy is a kind of big issue but as you go to the higher gate voltage the 10 volt of the gate voltage already corresponds to the the Fermi energy corresponds to 1000 Kelvin in this case so degeneracy is not an issue here still the electron gas is degenerated but multi-formula doesn't work out well so what is really going on here? one thing we can realize is as you go to the higher temperature we can easily pick up that basically inelastic scattering time between the electron becomes higher basically inelastic scattering between the electrons that rate becomes higher over the temperature it actually depends on the temperature scale so go to the higher temperature we expect the more of the inelastic scattering scattering between electrons now I argue that this actually promotes many body interactions in terms of this thermal power especially if this inelastic scattering time is inelastic scattering rate between the electron is greater than the electron to impurity scattering elastic scattering basically you can quickly equilibrate the electron gas all the times and you can go to so-called hydrodynamic regions now in the graphene turns out that's the region that's a region that's already calculated by the few theorists including the Schatzdeff group showing that in the graphene this region is quite interesting because it's not only hydrodynamic regions but also the dispersion relation you have is linear dispersion relation basically this one really starts mimicking so-called relativistic hydrodynamic limits kind of plasma physics type of flavor except that you can actually designate this plasma one of the important conclusion out of this theory which is very difficult so I cannot send this one but I can at least copy down what is the result there is actually they expect that many of the thermodynamic quantity got changes including the thermal power for example in this the hydrodynamic limits in degenerate case the thermal power becomes universal does not depend on any disorders and those kinds of things and in fact this thermal power is expected to be larger than what is expected from mode formula now in a sense this is understandable in simple pictures simply because if the electron-electron interaction becomes dominant and say the hydrodynamic interaction becomes dominant one basically most of the entropy of the electron gas is governed by their own scattering and they don't start kind of thinking they don't care about what happened with the electron to the other impurity scattering so it becomes universal and it really depends on the thermodynamic energies and it becomes large because you are dealing with in and out many body states many body interactions here right is this really kind of working out well to test these things out we have to drive the system deep into the hydrodynamic limits basically these limits higher temperature now if the sample has strongly disordered you have to go to thousands of cabins to see this one reachable range is before now having this sample the graphene sample sitting on the boron nitride suppressing the disorder in the sample now we should be able to reach some of these regions in the sample on the boron nitride indeed that's the case so here that sample sitting on the boron nitride make this thermoelectric type of the device geometry we particularly choose this device we could have we have even better device but this device I like it because somehow this device after all this device fabrication you see that whole side is much better than the electron side as you see the resistivity is much smaller here right in a sense using this device I'm showing you that when you have the lower impurity then higher impurities in the same device how this thermal power do changes indeed if you just calculate the mobilities and all the scattering rates and so on this side beyond the fifth cabin you should drive the system into the hydrodynamic limits so how the data look like I'm showing you here thermal power as a function of gateboards I told you that this side is our good side higher mobility side and lower mobility side what you're seeing here is thermal power is greatly enhanced on the other side same device, same calibration there is no experimental artifact simply just changing gate voltage I'm seeing that much more enhanced the thermal power in that direction the other way that I can argue that is if you just try to compute the mod formula out of the conductancy measures and compare basically as you go to the higher temperatures the whole side actually deviation grows while this electron side more or less matches the mod formula that is there is a better way I can argue this if hydrodynamic limit isn't right basically we expect more or less universal thermal power which actually depends on the linear in the temperature which means if I just divide this thermal power I measure with the temperature I expect to collapse everything into these simple curves there if things in the hydrodynamic limit so I'm showing you the same data that I showed you before in the high temperatures and just compare with the whole side and electron side as you see here the most of the whole side especially going to the high temperature most of the curve is collapsed into the universal curve while this sort of dominated region where mod formula works basically that doesn't work so this is another indication that indeed as you go to the better samples that's another use of the better quality of the samples and so on so one of the topics that suffice up a few times was electron-phonon scattering electron-phonon interaction in the graphene this becomes an important issue especially if you want to make a device that works in the room temperature eventually ultimate the limit of these mobilities and scattering will be governed by electron-phonon scattering and it's important to understand how the electron-phonon scattering actually happens now the easy way that we can understand electron-phonon scattering is simply look at how the resistance changes with the temperature and here is a somewhat old data done by the micro-fuelers group that's showing that here is the resistivity of the electron side and the whole side I think it's a two different sample maybe just measuring how the resistance increases the temperature and the deformation potentials and so on now what you see here is though I just blocked it out some of the high temperature data only showing the temperature below 150 Kelvin and the reason is if you just look at the whole paper in fact higher temperature resistance actually increases rapidly and becomes quickly super linear well the reason why actually it increases super linear there are some issues like different stories maybe surface-polar-phonon scattering maybe quench repose and all of these different scenarios but nevertheless one thing important one thing interesting here is as you increase the electric field as you increase the density this super linearity actually starts to suppress so at least that's a good part whatever things it is probably comes from the the extrinsic region we can actually suppress that by just increasing the carrier density in fact we just repeat this experiment sample on the boron nitride we actually push up this temperature where the super linearity actually started out but nevertheless even for the sample on the boron nitride there is this super linearity appears so that's pretty much common things but again as we go to the higher density we can suppress those super linearity a lot and then we can probably can use this type of the behavior now so this actually tells us if you want to study the intrinsic electron-phonon interactions it's better that we just go for the higher density so that probably large carrier density starts to screens out all this extrinsic effect and try to pick up the intrinsic electron-phonon scattering so that's what we did we actually use electrolyte techniques which has been used by many other groups in many other different samples basically in this technique we just put the salt into the mixer with the polymer and supplying this voltage across those kind of ionic salt the liquid that basically you can put the charges extremely close to the channel that actually induce charges in the graphene up to the 10 to the 14 or actually record we went up to 6 times the 10 to the 14 a lot of charges we can put there now once we put a lot of charges what we see here is indeed as you go to the higher and higher densities by just applying the the charges onto the samples this super linearity starts to disappear it becomes straight so that's a good part we are seeing the more electron-phonon interactions but on the other hand what happens instead of going really sharply in the linear becomes a round-off and this round-off becomes more and more increased so we get rid of extrinsic high-temperature part of the super linearity but we are getting some sort of low-temperature part super linearity comes in so what is really going on in fact if you just compare the temperature-dependent part those rounding off is more or less a follow-up to the fourth behavior which is the low-temperature T in the linearity this behavior the low-temperature T to the fourth behavior is in fact what we expect when you have two-dimensional electron gas like the graphene like the two-dimensional electron gas especially this is what we call the Bloch-Glunasian temperature regime simply just considering that the electron-phonon scattering considering both of the phase space of the phonon phase space is nowhere so all the electron in the Fermi surface can be scattered but as you go down to the low- and low-temperature your phonon sphere becomes small because the phonon can be degenerate the only temperature below the KBT type of the energy scale of the phonon can be populated so only part of the Fermi surface can be the participate in the scattering events so it's not efficient that's why actually you just deviate from the linear T dependence and quickly the resistance decreases dropping into the T to the fourth behavior in fact those crossover happens when this phonon sphere is coincided with the electron spheres and those temperature range is what we call the Bloch-Glunasian temperatures and that can be controlled by just controlling this carrier density or the Fermi surface radius here so seeing this one is what is expected in fact just considering all the slopes and coefficient matching the theory which was developed by a few people including Dasama's group one can extract information such as what is the deformation potential and what is phonon velocities that we can use to parameterize these phonon spectrums turns out those kind of the deformation potentials is around 20 volt, electric volt which is well within this theoretically repeated the reported values and sound velocity is also kind of within the region of the regions showing that electron phonon intection is more or less what is aligned with known from graphite one more thing we can do here is following things in fact if you go back to some of the textbook so I just copied down this so original paper was published by the Meisner in 1935 what he did is he just plotted out how the resistance of metal changes over the temperature now what you see here is well first of all that it's normalized the resistivity and the temperature is normalized by the divide temperatures and beautifully all different metals sits on the universal curve here well in a sense that is expected because in this case since ferramid sphere and the phonon sphere is about the similar size what is a governing temperature is not the blue-grinded temperature which is much larger in this case so divide temperature is a characteristic temperature and if you go through the conventional argument typical argument how the electron phonon scattering appears you can quickly find out all the metals basically the resistivity versus temperature curve if it is simply enough metal we have this universal curve which is actually using so-called brilliant functions and beautifully shows up that all different metals sits in now of course in graphene this is a different story in graphene it's two dimensions and dispersion relation is linear and there's pseudo spins and so on and moreover the characteristic temperature we are dealing here is not the divide temperature because in the graphene divide temperature is much larger than the relatively small ferramid surface nevertheless very similar universal curve stories work of course formula is a little bit different because it's two-dimension because it has a linear dispersion relation but you can come up with this universal curve with normalized temperature with localized temperature now an interesting thing here is the localized temperature I can control by gate voltage so I just plotted out to correspond to different Brooklyn's temperatures in this case they like the different metal but nevertheless it more or less follows this universal curve why this is important such a good match of the universal curve for the electrons and holes and all these different densities tells us that such a simple theory that we use actually describes the electron and phonon scattering quite accurately during this linear dispersion relation but in a sense a bit boring but nevertheless the simple calculation that provides electron phonon scattering at least experimentally we don't see any anomalies here so the message I want to deliver is as you have the better quality of sample basically we are seeing the interesting physics there and also some of the new techniques such as the electrolytes and those kind of things we can actually start to push the sample to the front carrier density more extreme carrier density and so on so I believe I agree with Andre we haven't exhausted all this gold mine and maybe we have more of these interesting stories as we combine the better quality sample with the new tools available thank you very much again we expect the universal thermal power but the form is different that I just show you this is the device on the boron nitride we could in principle do the suspend device in fact the region that I didn't discuss but it's more interesting part is non-degenerate region so where you have now the electron hole normally populated so that's what you can think about really kind of interesting hydrodiming limits our sample on sitting on the boron nitride is still probably electron hole puddles there to hit those regions but suspense sample might be so could be interesting thing can be done another question what did you hide in those few transparencies those few what did you hide in the transparencies you didn't show I can show you later there's many intercalate systems there I think the highest intercalate graphite intercalate superconductor actually appears which actually Tc is 11 and we actually even use the particular salt contains the cautions and put into the single layer and biolayers and put up to the charge of 5 times 10 to the 14 down to 50 millikalibre we haven't seen any superconductivity is there any reason to believe that graphene could be made to help I think that's an interesting point so the thermal power the thermal power itself is actually not too bad especially if you just believe that all this hydrodynamic enhanced thermal power I'm getting something like 150 microvolt per kelvin at kind of closed room temperature which is respectable numbers and even better graphene in that decay range the conductivity is pretty good too so called the power factors that the numerator what Q is a graphene in thermal electric application is it has also damn good thermal conductivity so somehow if you kill thermal conductivity such as if you just imagine somehow somebody make this isotope mixtures of the C12 and C13 and mixed so to kill this thermal conductivity maybe there is a chance but I think that's highly speculative at this point I have to keep the electrical conductivity up yeah oh electric conductivity is pretty good though I know no but you kill the thermal conductivity yeah that's right that's why actually C12 and C13 is interesting because they do not touch the electronic part present