 Can you see the screen? Very good. Let me just fix the laser Okay, I'll give you a signal after 25 minutes, and there will be five minutes to to the end of the talk Sure, sure. Okay, so I cannot find the laser. I'll just go on with the mouse All right, so hi everybody, it's really a great pleasure to to attend although remotely and I really Sorry that I couldn't attend that that was actually the planned and of course thank you the organizer for the Invitation and the opportunity to present our work So I'm a lot correct and I'm coming from the technique on the faculty of material science and engineering And I'll talk about interlateral transport in shield by layer Graphic systems, right? So first I would like to thank the people who are taking part my group at the technique on and collaborators from IBM Zurich and Tel Aviv University and of course for the funding agencies So I think electronically speaking One of the two in most intriguing examples of how the angular mismatch if you basically consider two layers of graphene Or two mesostructures that are stacked one on top of the other. I think the two most Intriguing examples of how the physics the underlying physics can be different as a function of the angular mismatch are shown here So on the left side you can see this very Pioneering work basically Discussing the fact that if you have a bio layer of system and you apply a vertical electric field You can open a band gap and already from 2009. That was a great promise For all kinds of logic applications because as you all know single graphene and doesn't have a band gap So it basically cannot function as an efficient logic switch And the story was actually interesting since it took three or four years to realize that this can only Happen when you have a banner stuck in so so the story was that many groups actually tried to follow this concept Trying to see this band gap opening, but in many cases they have a misfit angle And there were actually not aware of that and it took three or four years to realize that this can only stem for better stacking So I think this is probably the point where all these twisted graphene structures started the huge research that is still ongoing and then part of this effort realized in this very astonishing Publications We're a group from Colombia and MIT showed that Whenever you have a 1.1 angular mismatch, you can actually realize superconductivity They call it magic angle magic angle buyers and this really shows I think or emphasize the fact that you can get totally different physical aspects Depending on the angular mismatch. So this is basically what I'm going to talk about today And of course, not only the electronic properties Basically almost every other material properties like the mechanical friction You all know you can switch from high friction to low friction. You can basically tune the band gap You can use different interlayer coupling and interlayer conductivity You can also change the optical and optical Phone-on interaction like Raman coupling as function of the miss angular mismatch And you can also realize what is called van der Waas hetwa structure where you combine different materials Still playing with the angular mismatch angle and get very very unique and Superior properties like very high mobility Again tuning the band structure and also realizing Roba superlubricity, which was first Basically suggested by Odeb and was actually realized a few years back by one reason and probably one of the most intriguing fact is that you can actually tune all these properties in a very tunable Matter so you can get either Switching between different properties or also continuously changing the the material So just to make some order We are talking about twisted stacking configuration Let's see what are the different families that we can consider so Along with the banana stacking, which is you can see this in the left side, which of course is commensurate periodic Stacking configuration. This is when you have the two layers aligned You have the twisted stacking configuration and in general you consider the non commensurate structure Like for example 10 degrees and in essence, this happens when you have an irrational ratio between the superlattice structure and the single graph in lattice And then it turns out that you can have more exotic type of configuration For example, so the comments right where essentially the ratio between the superlattice structure and the single graph in System is rational and then you have a strictly periodic interaction and also you have more how to say exotic configuration like a quasi commensurate structure for example for 30 degrees and we have shown that this Stacking configuration has a distinct effect on the frictional properties For example, you would expect that along with the strictly commensurate configuration for the pseudo commensurate configuration You would have a linear scaling of the friction For us with area contact and for the quasi commensurate actually, there is a more intriguing periodicity you get the quasi periodic or self-similar Interaction between this Fractal like structure So the way we experimentally study the systems is actually very simple. We realize this nanostell metal Structures on top of HOPG this allows us to get very large arrays of systems and then we start to manipulate them with an AFM Already from the beginning we have seen this very interesting behavior So just by measuring the lateral forces, we could get an indication that there is a very small lateral force This is this force versus Displacement curve that you can see here essentially the trace and retrace are almost completely overlapping and there is a tiny Friction that is basically In this case, this is these are circular structures is coming from the mainly from the circumference And this was actually very nice Closer to a very Interesting and intriguing experiment done first by Quan Chi Zhang group. So you can see here this is a macroscopic probe a few micron square and While shearing this pillar, they could see that itself retracts and again This basically comes from the fact that the friction is extremely small compared to the addition So when we when we measure these forces We are basically governed by only adhesion forces and this basically tells us that we can come up with all kinds of Design rules we can essentially design the shape of the structure and by that it gives different lateral Forces, so this is essentially coming from the fact that the adhesion is simply proportional to the area and The lateral force will be proportional to the derivative of the area change And this is what you would get from a circular flakes for more complicated structure, you can see here this Green curve you get some non-linear response and then you can get a constant force and you can see also zero force Which is basically buried Within this profile and then of course this scales with the radius as you can see from here, which allows also one to very efficiently extract the binding energy Graphite and in all kinds of other two-dimensional layer materials and By designing these rules one can also come up with some other Type of devices for example by step structure And this is what we call rotational bearing structure when one can induce a single Interfacial twist defect buried More or less the middle of this structure And we have used these to measure how they conductivity the intellect on the activities Changing as function of the angular mismatch. So this is basically measuring of the current as we continuously rotate the structures and this allows us to get really unprecedented angular resolution Which allowed to see for the first time this very abrupt and narrow conductivity peaks So basically explaining all these profiles This my modulation this bathtub like shape. It's basically induced by a phonon made in the interlayer company So this is the case space schematic illustration. You can see that when you want it Flakes in real space. There is also rotation in case space and your static You're starting to have this momentum mismatch when it turns out there is a phonon branch that can mediate this This transport and and this is basically probing this the population of this momentum Sorry, it's phonon branch and this very sharp conductivity peaks Especially with the help of dead and student. I we could explain These peaks by cell documents read periodic superlative structures They can come with two different symmetries like you can see here These are the arrangement of the atoms and actually you see this superlatives pen structure that is associated with this with this Stacking configuration and you can see actually why for one a symmetry you would get Triangular shape for example like here and for the other symmetry you get the double peak shape You see the pen structure here. So this really give the essence of how this electronic arrangement is playing a role here So then moving a bit forward and we probed how the current is modulated as function of the lateral distance and In the beginning we naively considered that the current will be proportional to the overlap Area so essentially you have two systems of this graphite structure you slide with AFM You measure the force, but you also measure the current and If you consider that only the area plays a role at the best fit that you can get is this blue Solid line this town 3d explain very well the measure experiment and Then it turns out that only if we add another channel that is essentially proportional to the circumference of these structures We can get a very good fit and this gives the first indication that the circumference or ad states are playing a very strong role in the electronic transport between the the top and the bottom as up and Another indication was here. So when whenever we changed applied bias be so different contributions So I didn't mention but this electric circuit and the fitting procedures allow us to extract the different Contributions for bulk and edge and this is what you can see here. So these lines basically add up the blue line is is the completion of the bulk and the green is the edges and Summing summing them up together and we get the total response But the interesting part was that what we saw is that whenever we use a local applied bias But this is the applied bias. It's it's the applied potential that is dropped Across the interface is about three times lower We see dramatic reduction in the contribution of the bulk and this again brought us to the Seminal work by Breselhaus considering the transport or the chronic band structure of graphene Flakes and graphene algorithms essentially what they show there is that Whenever you have zigzag states, you have a very sharp density of states or even you can call it topologically Protected at states which are localized and the zigzag edges and this is really corresponding to this very sharp density of state peak and then when you increase the the Fermi window The applied bias you probe more and more the bulk states. So this can essentially explain why when we probe or when we apply a small bias we We probe more and the contribution of these at states So in order to get the full response the full current voltage characteristics We apply this Technique we take the full IV and then we slide five nanometer and then we take another IV and Just making a long story short. This allows us to expect for all the applied bias conditions a separate contribution essentially the current voltage curve for edges and bulk and this is what you can see here So these are just two sets of profiles taking from here And the most interesting part is that if you compare the the IV curve of the bulk and Against the transport of the edges you see that for the edges you get rather a more linear response But for the bulk you see this Insulating behavior at the lower bias regime, but when you increase the bias you see even actually in the section and the bulk transport takes over So again with the help of the dead and And we wanted to explain this also from a theoretical point of view And what you can see here These are very nice calculation of the wave function distribution. You see that for perfectly hexagonal flakes You get a very strong amplitude of the wave function just at the zigzag edges. So these are perfectly hexagonal Flakes terminated only by zigzag edges and if you calculate the transmittance You see this indication of this strong density of state of state of state peaks that are associated with with the zigzag termination Then if you do the same calculation for armchamp terminated flakes, you see this typical Transmission and this against in agreement with the density of states that is associated with the bulk states So whenever we have a circular flakes, we actually have a combination and this is calculation for 15 nanometer diameter 15 nanometer 15 degrees angular mismatch and you can see how this wave function is strongly localized as zigzag edges and then it was important to Describe how this wave function decaying the bulk for two reasons Essentially, we wanted to use this computational analysis to explain experimental results And we wanted to show that this wave function fully decayed into the bulk already from sizes of about 15 to 20 nanometer and this basically tells us that we can essentially use this And the wave function characteristics or transport in order to explain bigger Flakes by essentially just scaling up according to the geometry in a simple manner and Basically, the second important point is that we can associate the main transport that is related to the edges Just for the first two nanometers. So we get almost two orders of magnitude decay Across the first two nanometer and basically the theoretical approach is to separate the contribution of the transport and the wave functions and First for the first two nanometer around certain firms and Compared with the transport at the bulk regions. So we scale this just in a simple geometric manner. This is what we get What in principle we see is that when we have a better stacking configuration We are completely for the size of the next step System which is 300 nanometer in diameter. We are completely dominated by bulk Transport but if we induce rotation Miss much of 15 degrees we start to be dominated by edge Across the low bias regime and then only if we apply a larger and larger bias Voltage we start to be dominated by the edges. So we can also Integrate essentially These curves and get the current and we get the same trends for the current voltage curves Then it was also interesting to do the scaling analysis and what we've done here We basically calculate the transport for a bulk and edges Separately as function of the radial distance for different applied bias conditions and essentially We would expect that as we increase the size of the contact essentially the bulk will win just because of the geometric scaling and Then we could basically consider this intersection. So these points where bulk transport Takes over and we could basically plot these intersections as function of the voltage And this basically allows us to get this sort of a phase diagram or transition from Edge transport to bulk transport. So for each and every angular mismatch below the curve We are dominated by edge transport and above We are dominated by bulk transport and what was interesting to see is that whenever we increase this angular mismatch We can get at the low bias regime. We can still be dominated by edges at the pretty large Diameters up to 2 microns And if we basically want to compare this with experimental results of experimental We know the diameter of the radius in this case and we can take this intersection basically the point where the bulk takes over which is At about 0.3 volts if we consider the potential drop across the interface and this Indicates that the angular mismatch Experimentally is between 5 and 15 degrees and this is actually a good agreement with the previous came Analysis that we've done considering how the friction scales with size. So this is more or less in Good agreement with what we think that is the angular mismatch in the experimental system and This is a another interesting Experiment so in this case we we have done the same kind of experiment we slide These two measures structures and we measure the current and it turns out that if we focus just across the five nanometer last five nanometer Distance we see a non-set of very strong confluations So if we just remove the background, this is what we see and And Many we see contribution of two different periodicities One is about five answer pick to pick distance and another is to answer me so just considering the registry or the the lattice and structure of the two Graffiti systems. We actually would expect to see these two answer and fluctuations basically whenever we have a large carbon carbon overlap and we would Expect to see this Increase in conductivity, but the other essentially longer period is he was more unexpected and actually this was in pretty good agreement with some Experiments done two years ago in this case. They use great junction graphene system So they break it and Essentially bring it back to contact many many times Integrating and they could also see this essentially larger periodicities at about six five to six answer In this case, they're they're using only bare man stacking. So they start with Essentially a single graphene flake and then they Do this experiment So again with the apple for dead and by an umbrella wanted to explain And how we can basically a sign or what what could the sign What is the fundamental Origin of this longer periodicity? So the first calculation of the current was actually showing us that Experimentally what we would expect is again this larger periodicity. So this is the calculation of the current as function of the sliding And then we also consider and compare it with the registry index which essentially again Describe how the carbon out albums are essentially coming into greater and lower Interaction and again expected here. We saw this to answer them fluctuation So we wanted to again find the essence of this last fluctuation. So we consider how they get the wave function and And That are localized at the zigzag edges and basically come into interaction as function of the sliding Conditions and I think this movie will explain the best what is really going on So in the calculation what we do is sign a Gaussian Function that describes their wave function aptitude atop the carbon atom So even from the calculation itself, we would expect This to answer I'm overla, but essentially when you do this this lighting and you look over the Wave function aptitude, you see that is dramatically changing as function of the position Which tells us that there is some additional interference or coupling Behavior as function of this Motion and coupling essentially what you can see especially Across the last few nanometers you can see this very very strong fluctuations and turns out that this really is The underlying mechanism for the larger periodicity that we that we see And then and then we basically wanted to complete the picture so what you can see here This is sort of a master plot. It's the current as function of the angular Mismatch and the lateral shift just across the few last nanometer. This is the kind This is the registry index again. You see this different behaviors here. It's much more Flactuated and if we consider the Gaussian overlap functions, we basically get a very very Good agreement with the calculation for the console again, this seems to be quite robust For all the different angular configurations and I don't know how basically I'm with the time But I think this is the last slide. So with this I would like to thank you again for listening and of course If there are any questions You do it muted perfectly with time. Oh, thank you very much Thanks a lot questions comments Could I? Yes So thank you very much very very interesting what I probably Not understood Completely how you could separate from your measure data the contribution Coming from you what you are calling the bike and edge What is the what is the? Reason or or how you calculate that You mean I get there from the experimental data. Yes So this is actually Pretty simple. So you see the segment and electric circuit We have some constant resistances that we assign with the system and the top and the bottom Graphite method structures and we assign the changes only For the interface itself and then as we know the function of the area as function of the sliding distance we can basically Basically, you know go through this fitting procedure And extract the contribution. So what I was basically mentioning is that if we only consider a bulk Resistor a variable resistor that is proportional to the area overlap. We cannot really get a good feed This is the best week we can get this blue line and then if we assign another A resistor that is in this case is proportional to the circumference to the circumference So basically this this two different contribution change differently as function of the sliding position and Because of this difference you can actually separate between the two contributions So that means that you supposed to separate these two terms based on the apparent overlap volume Exactly, exactly That was my second question. How you know that that Assumption is Conformed to the reality So I don't fully understand the question So so that what so it is absolutely absolutely very cool what you did and and your model is Absolutely fine with me It has the basic assumption of the dependence of the apparent area, but We don't know in such a nano contact how How the contact takes place? So I mean What I can just say is that this is a strictly your medical analysis Exactly Exactly, and of course, this is why it was important for us to also complete the story You know in terms of theoretical Analysis and this is essentially what you see here and also in the theoretical Analysis we saw that we would expect very strong contribution Of the edges Particularly the zigzag edges that there are likely for example in this case you see this perfect hexagonal flakes You are completely dominated by the transmittance of these Estates, I mean, this is what we know from from the background the transmittance of these estates is Around the zero that this is just to speak around zero energy and this also in accordance to this wave function localization of the zigzag edges. So And this is in contrast for the option. So So there seems to be very different Contributions for the bulk and the estates Okay, okay fine with me. Thank you questions I Have one myself erud so in the last Example that you showed when you had the contact between two circular samples right and you showed These two different periodicities and you explain explain them out very nicely Wouldn't that depend on the relative angle of the two of the two circular things and what does that? Lead did you do it or? so, I mean experimentally we don't have actually Control when we do this experiment and we only did it theoretically. So this is what I was showing in the end So this is just the theoretical calculation. You have the current So this is the twist angle right zero thirty and this is the last This case three nanometers. I think yes. This is the current This is the resist the index and this is the gaussian overlap function right, so you see how it changes there are some some changes, but the periodicity seems to actually be quite robust and What you can nicely see is that as you increase the angular mismatch you are Basically more and more dominated by the edges, right? So you see that only when the two edges are really really aligned You start to see strong transport here. There is sort of a valley I see so the two zigzag edges are Touching when you are in the twist zero. Is that is that right? When is it? Exactly. Yeah, but what we also know from from the other calculation is that when you're close to zero angle You are actually dominated by bulk This is why you see strong transport Whenever you have more overlap And when you break the symmetry you see that actually transport through the bulk or you know I described it through the ball because here you have more overlap So you would expect more current, but it's actually lower You have this higher kind when the two edges are really one on top of the other Okay, well one other thing is In all of this does it matter how you passivate your edge your edges? I mean at the microscopic chemical level or do we have to assume as it Reasonable that these edge states are really so delocalized. They don't care what you do at the outer surface So so that I mean delocalized. I don't know exactly What this means I would say actually not not too much delocalized But from theoretical point of view and that was also part of some papers About even 10 years ago. They did the analysis of these edge states as function of the different chemical Modifications and they actually saw that this is extremely robust against many many different kind of chemical Modifications actually even in some cases they saw an enhancement of this edge states Which would agree with the topological nature which you alluded to exactly exactly there were other Papers that consider different toughness You know values and again also there they saw very very robust nature of this Of these states. Okay, if we have no more questions and we thank a lot Colin. Thank you very much Next speaker online is Nitya Goswami. Hello