Andre Geim on Graphene

okay good morning everyone I wanted to discuss our latest results but Lawrence twisted my arm saying that not everyone is expert in this audience so I’ll I’ll start with a usual line the first and transparency’s how great graphene is and so on and xeno case which probably 80% of my talk will be the latest results from our group in Manchester so that’s the storyline so what what’s so special about so simple material which is just only carbon and the structure is one of probably most simple one could imagine yes seems to be not much to be gained but when you start looking for the properties okay some of you have already seen many times the list of superlatives which I compiled over the last couple of years it’s of course the thinnest material you can imagine and yet it covers a surface area with one gram you can cover a football pitch easily in Manchester we measure everything in football pitches as you know and it’s according to Columbia group it’s the strongest material ever measured and I do agree with with this statement although carbon nanotubes show similar similar strength strength of course probably more defective usually it’s stiffest material it’s stiffer than diamonds that’s for sure at the same time as you know it’s pliable material and you can elastically stretch it by 20% or several groups including our groups have shown it shows record thermal conductivity outperforming graphite on diamon unfortunately now we know that it has to be suspended graphene on the substrate flexural fan phonons are suppressed so conductivity is no longer records but still very high it shows it at room temperature can sustain current density million times of copper at room temperature it’s really the record it’s impermeable even for helium so so those rings you see on the screen there they’re so densely packed with electron wave functions that they do not allow with electron waves that they do not allow even helium atoms squeeze through and it shows pretty good electronic properties which I’m going mostly to concentrate in my research I thought what else to advance from time to time I get I get some people some other similarities for example there are groups who claim that it shows the best merit figure for some electrical conductance and recently MPL group has shown that it’s the best material for quantum Hall effect standard so okay out of those two our group and probably most people in the audience are interested in quality and electronics you know bility of the material let me remind what this is about you put graphene and on the substrate and make substrate conductive or top gate and you can change properties of the material by by sucking in or pulling out electrons and holes from the system usually for silicon and gallium arsenide you can sweep very small concentration of the carriers but in graphene you can do practically from ten to the thirteen very large nearly half electron volt concentration of electrons to the same concentration of holes if you try a little bit harder in suspended devices we could reach one electron or one hole per square micron which actually no other material allows to do remain in conductive at the same time and if you try liquid gate you can go to really high concentration Columbia

group and several other groups caption have shown that you can dope really high probably the most amazing property of graphene that despite being placed on a rough substrate and being covered with at the base and so on it’s shows quite remarkable electronic quality so electrons can shoot some micron distances routinely in the devices okay made by whatever technique it is either transfer from from metals or exfoliation of silicon carbide it’s still the same sub micron distances and already okay few years ago it was argued that if you eliminate those scatterers you get really a record intrinsic mobility in the material which all translates that you can study properties very nicely and can can find is a clean material they usually the more pronounced properties are so let me a little bit update on both currently current status of quality of graphene mostly its refers to exfoliated graphene which still a cut as a proof-of-concept devices and for fundamental studies it was known for quite some times that the problem is a substrate and up to date and we probably tired half a dozen more than that of different substrate instead of silicon oxide the breakthrough came from Jim Jones and Philippi Kim’s group who used a specific type of boron nitride we also try highly oriented pyrolytic graphite but it didn’t show any improvement Bathory’s exact no mana crystals of boron nitride you can get from actually couple of different sources and it was a dramatic improvement it’s really really really very important achievement so that’s our data using this substrate graphene placed on boron nitride structure whole bar and as I will do usually we get mobilities around hundred thousand but sometimes we reach half-a-million mobility at low temperature and a couple of hundred thousand at room temperature another way of getting good graphene was demonstrated by even three if you leave diamond I mean you call this group it’s suspended graphene you you put those fingers and you etch away half of silicon oxide and it’s suspended and you need to anneal it in in liquid helium or in ultra-high vacuum and it shows good quality typically two hundred two hundred thousand we managed don’t know why but our devices sometimes shows a couple of millions mobility is this an example should make of the gas oscillation start at fifty girls and level degeneracy you see splitting already at 500 500 girls people sometimes in literature they mention that okay suspended devices are gives very high mobility at room temperature indeed Philip reported I think hundred fifty thousands of even 200,000 that room temperature there was for some time disagreement because our devices have showed very strong temperature dependence and at room temperature we typically see only 20,000 mobility 10 times or so wasn’t Philip so what we think this is actually intrinsic mobility for graphene is low at room temperature and this is due to flexural phonons due to this vibration out of plate like a drum vibrations and there is no disagreement because our samples actually also shows some spread in room temperature mobility and we attribute these differences between different samples to strain so if you pull your sample a little bit between those fingers and you suppress those flexural phonons and then you can get high mobility even at room temperature as another reminder of why

we are interested in graphene okay of course it’s electronic structure practically everyone has seen this picture I believe it’s in graphene it’s not shredding electrons it’s okay Dirac link equation is what what is used to describe low-energy dynamics of of charge carriers in graphene instead of spin you have pseudo spin which is coupled to orbital motion it’s essentially the weight of the wave function on one of those carbon sublet it isn’t in bilayer graphene you get another very interesting matrix-like equation which is a mixture of Schrodinger equation and Dirac like equation and who knows what’s happening in trial I am try lights it’s already a rather complicated story so all this sort of this picture allows you to think how we can compete with with another branch of physics like particle physics nuclear physics and there are phenomena and two of them shown on this transparency which have been known for seventy years like klein tunneling or relativistic fall on the center which would imp by particle physicists or nuclear physicists not to be accessible in any reasonable experiment for the next century in graphene those phenomena at least client tunneling is routine and this hopefully supercritical regime when coupling is really strong between impurity and electron hopefully micro me one day will report there are phenomena which also contradict to what we know from condensed matter physics usually it’s still badly understood phenomena of minimal metallic conductivity why with such high resistivity of the order of H of a square graphene is still metal in this regime I will discuss it later in my talk there are new results to contribute to this one but it’s very unusual that you can go all the way from electrons to holes for a metallic regime and conductivity and or at optical frequencies is considered to be Universal with some many body Corrections so when you look through the graphene USS not only its audacity by your I US s5 structure constant because it’s a distance given by PI multiplied it by alpha which is given by this universal conductivity so it’s sort of examples of the phenomena you can study in graphene it’s the main interest of probably graphene community there is also interesting applications everyone who is doing graphene is sort of thinking what sort of applications could come from particular assertion each superlative of course offers an idea what to think about and there is a huge potential for applications and I’m not going to discuss those except showing this one transparency applications or ideas of applications range from something which can be called only dreams like graphene as the next silicon or DNA sequences to quite reasonable applications high frequency of the electronics and electronics belief hidden we’ll be speaking about this graphene instead of IT or at least this is proven in academic answer in some industrial labs that it’s a feasible it’s still a long way to consumer products and some applications like inductive ins and batteries allegedly graphene already there are also people by graphene usually mean platelets of graphite so so as a moment okay we’re still gearing up to go into applications and don’t expect anything after five six years of interval of such intensive researches has been done so okay with this one I’ll give you I’ll overview some topics we were studying during the last year since okay since last summer I would say so the first subject is the question of this d-roc spectrum how linear is a spectrum actually a so okay

you saw the picture there are cones and so on so let’s remind you how we know that okay in good old times where there were few competitors okay like fill it on our selves okay we measured shunick after cars oscillations as as a carrier concentration measured the temperature dependence analyzed it extracted cyclotron Mars and from cyclotron Mass we found that cyclotron mass is function square function of concentration which actually translates into this d-roc light spectrum and the slope or Fermi be lost you which is confusingly called Fermi velocity actually it just velocity slope of the spectrum is this number with some accuracy both our groups reportedly there were many other measurements which essentially gave the same number for for velocity in this range of concentration 10 to the 12 now we have those suspended high mobility samples and what is most important that they allow us to go to really a very small range of gate voltages and concentration and study how this Fermi velocity or slope how the slope changes so that we did the same routine and the first thing we have found that experimental data and if Fermi velocity would remain the same as as typical numbers we extracted at high density that’s where we would expect it that corresponding curves to fit the data we need in this particular case twice – a velocity so and this is not marginally it’s okay a factor of two – differencing in slopes and in temperature dependence it’s it’s qualitatively large effect so Fermi velocity changes with concentration slope changes with concentration and that’s for one of the samples we we get these data that’s the previous value and that’s for high concentration for concentration like like here only scale would be and it’s it’s goes high so what what what’s the origin for this as the explanation has been long time in literature so electrons are usually metals layers they interact with each other and so only when you have a large concentration of electrons their screen enough by other electrons so you can you can use them as a single particle picture picture landau Fermi liquids here what’s happening in graphene here near the Dirac on neutrality point concentration goes down and interaction becomes extremely strong and that’s what we expect from previous series of renormalization of interaction one has to be careful how to interpret this picture because the spectrum doesn’t actually change itself it’s still linear spectrum the spectrum depends how many electrons or holes in your in your system each time you change your concentration the Fermi velocity changes but but it remains called a constant underneath underneath the Fermi surface so it’s sort of dynamic this slope is dynamic you see when you probe your spectrum each at each concentration you probe different Fermi velocity according to two theoretical predictions which go back to particle physics actually well before the first papers considering this theoretical well that’s a collection let’s see how its matches with with the series’s collection of data for four different samples for suspended devices and those two curves that’s where we expect it and previously measured for concentrations somewhere here that’s the slope I especially give this in logarithmic scale because of the scatter answer to cover three orders of magnitude changes in concentration and this is where our lowest concentration data goes three times higher so it’s a shacks but only as you change your

concentration by three orders of magnitude those supreme curves that sir ethical predictions from this 90s paper because there is a fitting parameter in those series which is self screening at a dielectric constant of graphene we don’t see any anomalies its behaves as it should be in this case and what we did a little bit more seriously in this work here and we incorporate itself consistently into into this theory that graphene self screening changes with concentration so it’s reasonably good fit to all to all the data one thing I have to mention there were couple of papers 2008 and recent paper which worked in this regime largest intenders as well and they reported deviations from a constant Fermi velocity by 25% and if you extrapolate those deviations they they would go much much a big effect that we observed so in our case it’s it’s how it should be not big not small one might notice that we do not reach in our suspended samples the value 10 to the 6 which is we certainly know that happens for graphene on silicon oxide and in other systems we know the origin this is described in this paper that’s because we have suspended graphene when we put graphene on boron nitride will see that Fermi velocity actually moves upwards due to dielectric extraneous again in very good agreement we we Siri so message to take away from from this particular researcher that there are renormalization effects that they’re modest on one can call them weak but if you go to concentration less than ten to eleven they become quite clear and pronounced as these densities near the drop point and should be taken into account lawrence asked me to make it more interactive so if someone wants to get any questions concerning this bottle research you’re welcome to ask now or at any moment you just can shout rubbish I’m happy to confront you in order to see to see shooting up the glass oscillations the sample should be bigger than cyclotron over automatically when we see unique of the gas oscillations we are in the regime when the sample is larger than cyclotron orbit otherwise we will see anything and if you estimate that in some cases we do see cut off of shunick of the gas by the size of the sample but so far the quality is not as good to go into this regime yeah that’s what Nelson Mandela would call I have a dream so okay so that’s what what I like to to share with you okay so somewhere okay five six years ago we reported that it’s not only graphene that I have shown this transparency ad nauseam for for some people for many many years so I’ve seen many other materials are LED and a single layer can be extracted or few layers boron nitride disco die Calcutta night and so on that was at this very slow burner for quite some time only recently boron nitride has come into play and a few papers on other dye Kalka neither were published but okay not not as popular as graphene so what Allah I always pointed out that some of those materials are insulators of metals of semiconductors some superconductors some ferromagnets so there is a huge range of of different materials you can play with so the dream is something like that okay to make and you add compounds on demands and see what would what would happen how do we do that how could we do this in principles of what already people in

Manchester in a Colombia have been doing them in several other places okay you prepare graphene okay that’s one of techniques we are using okay on double-layer PMMA with release Linea there are variants of this technique you can use and lift it off then place face down aligned with another layer on the substrate dissolve and you get two layer systems consisting of different different and different monoliths for example a few layers of different materials to make this stack of course you have to repeat this procedure many many times and this procedure is not simple simple and straightforward but we know if we one day find say room-temperature superconductor let’s for for the sake of gravitylight sake putting those materials together and someone like from Samsung like beyond he next day will make roll on production of this material so unfortunately this dream is sort of a little bit difficult because certainly we know that boron nitrite and bisko’s those two stable materials not superconducting at one layer sickness but less table enough other materials are less stable some sometimes quality is not that good so you have to deal with few layers of those materials so if you wear go to singular we’re mostly limited to insulators why do we need insulators okay for those who are in semiconductor physics they know that insulators can be used in a variety of structures in tunneling and resonant tunneling device especially put here for Lawrence Eve’s who is an expert in this sort of devices spin tunneling is also another important application for for tunneling devices so the question is okay usually due to evaporation and so on why we won’t use one of those insulators as atomically thin barrier something what ambi can’t do that what we have done last year we learned how to isolate one nitrite in in single boil and other qualities that’s way more complicated and difficult than doing the same with with graphene where the contrast is extremely weak its enhanced and it’s in grayscale and so on but but we can do it reasonably reliably reliably in our experiments so what we started with is making gold finger footing boron nitride say single layer of you layer put contents on top so you we try to assess properties of boron nitride as a as a barrier if you put graphene here you don’t see anything which right before the resistance is it’s incredibly small you can’t you can’t see a barrier but with boron nitride lay seven seven layers it’s about three nanometers it’s an insulators and you start seeing tunnel current at ligh voltage at high voltages before it’s down down for two as you start no longer see any insulating state it’s just high resistivity everywhere we’re not exactly sure about this number because interfaces might contribute because we do not know the exact area because interface of gold is roughish and for single layer from mega ohms we go 2 kilo ohm shanthi it’s linear weekly temperature dependence dependent ID characteristics and what they can be translated in high Gap and effective thickness actually larger than what you expect three lines we don’t who are not sure why it is so but it requires ok first principle probably analysis what effective thickness of one mono layer and but most importantly what we learn from this one is that there are no pinholes in the system which is very good news for for the material to use as a tunnel barrier we can do a little bit better use conductive F that’s cautious

resolve results here with his post dogs and we measure if we put at a particular point we measure IV characteristics which are nonlinear again it’s room temperature measurements and you can see that okay it’s tunnel kind of behavior which is dependent on the number of the last and we can scan reasonably large areas many many microns and again we do not find any pinholes which brings me to conclusion to this part that boron nitride can be used not only as a substrate which is currently using but as a high quality tunneling barrier and then you can start thinking what people have done in 2 5 8 to 6 3 5 semiconductor physics about thinking about vertical various vertical devices as well going out of playing transistors but doing something else that the simplest case I’m trying to because those okay futuristic devices are too complicated for the moment so the first example you might think of this one is encapsulating graphene in boron nitride actually there are advantages with respect to putting in on top of boron nitride as Phillip Diamond Jim Coan did recently we carry it with another graphite layer and it turns out not to be a marginal advantage because really for those who work with graphene know that each thermal cycle exposure to air changes the device you need to anneal under certain so we find those lines really protected they’re much much better and more stable and in addition there is a an advantage you can put a gate on the top if you have more than three layers and control concentration from the top so it’s a pretty good top gate dialectic so that’s an example of one of Maestro our structures that’s okay boron nitride substrate and Mesa edge the weight in graphene and this line indicates that here there is a ciggy Schleyer I don’t remember 10 20 nanometers thick boron nitride on the top in some cases we put a gate top gate on top of this structure so usually we get for those devices way they show pretty nice characteristics mobility up to 150 I would say say at concentration 10 to 11 similar to water the Columbia groups reported and and but in some devices it goes better those devices are usually characterized as square root dependence on gate voltage rather than linear voltage so in those devices okay also the call although mobility is still sort of hundred hundred fifty okay as in other devices many of those okay say we started tens of them well twenty devices by by the moment her for the moments okay we in those devices we use our favorite band geometry putting currents through these two electrodes and measure voltage here and then we’ll find out that resistance for for terminal resistance becomes negative which tells you that electrons from this contact can go all the way through and reach this contact and then the chair’s a reversal of sign that’s besieged up to 250 and probably a room temperature in some devices and devices and we know how to interpret this it’s negative band resistances and responses to magnetic field as it should be by applying magnetic fields you quench this negative resistance so every seen what has been seen what 1020 years ago in gulley aluminium arsenite two-dimensional electron gas is what what you can do from this negative resistance and it behavior you can estimate reasonably accurate within say 50 percent you can estimate mean free path and extract mobility for typical concentration and it’s girls at low temperature took half a million of those we’re now pretty sure that this is the case because we do see devices with the

same mobility measured my normal way but they do not show this negative band resistance so and numbers okay for room temperature are so pretty pretty pretty pretty large so it’s probably we don’t know okay some devices only shows this behavior but it’s gives you an idea that for that sort of structures mobility can be really high and we believe encapsulation is really helps at least it’s makes more comfortable to work with this sort of devices since I mentioned the top gate okay that’s an example that top gate does work okay it changes the bench resistance some electrons no longer go into this contact by reflected weakly by reflected and so it’s you can see fabry-perot interference on to the gate hundred nanometers without any problems we didn’t investigate these but similar what and Angie Yan and Phillip Kim reported so it just tells you that that the gate does work pretty nicely one boron nitride is using the game my my last subject is a little bit more complicated structure along the same lines of compounds LED materials but in this case we use two as of graphene and they both every single K encapsulated okay maybe sometimes without the top layer but it’s boron nitride boron nitride boron nitride on top so it’s double a structure similar to those which were described in gali asana arsenide heterostructure business but okay let’s see what the difference graphene makes for that line of research so how to make it and here I to show that Israeli okay very involved in procedure so first we deposit on silicon oxide a crystal of boron nitride a Sikich say 20 nanometers and a layer of graphene h it into a whole bar structure we want then another layer of boron nitride with the chosen Cygnus a from one Nanami 420 nanometers whatever will warms and graphene age tag and the position of the context so it’s involves three dry crystal transfers okay with with crystallized are not touching and kneeling this at three hundred four rounds of electron beam lithography three plasma etching to metal deposition and hundred times of cleaning structure and three moving resistance so so good seen that it does work okay that’s an example of the structures we have made let’s look at this one for example that’s the bottom layer of boron nitride that’s the bottom line false color orange brownish color is the bottom layer here on top of this bottom layer is f like shaded here bias encounter that’s a flag of boron nitride finish sort of ten nanometers and another layer of graphene L line on top with accuracy ten nanometers or so on top of another another structure typically we get okay mobility is hundred thousands lowering top layer which remains usually exposed and actually a little dope in separation which writes three to twenty nanometers so far as its top layer usually deteriorates after after exposure to air on this bottom layer remain circuit pretty stable for very long period of time what we can do because those layers individually contact it and there is no for thick boron nitride there is no leakage between those two we can apply back gate from the substrate which is colossa around here okay we rat rod is missing okay so we can we can buy back gate with pump electrons mostly in the bottom layer and because of some screening in the top layer we’ll also get a small concentration when we apply

inter layer voltage we we push them in different direction electrons in one layer holes in another layer so we have we have control one has to be careful this is very unusual case because of finite screening of the system okay we can’t no we cannot relate all that’s better colors we we can we we cannot relate voltages to concentration by linear equation quantum capacitance which was looked for many many years actually a dominant phenomena here no screening at low concentration everything goes there and because of these distances relation between concentration and those voltages is strongly nonlinear so the first experiment you can do you can see how properties of your bottom layer influence what happening in the top layer let’s put it pretty large distance 10 nanometer for example and see how this layer changes properties of another way if you are 70 Kelvin or something like that and distances lives on okay that’s a typical curve which we usually measure change in concentration in the bottom layer and then we add something to the top layer and nothing happening what you as you see here as if the top layer doesn’t do any influence this is not the case at low temperatures what you see in what you find out that okay resistance in the high mobility lie usually diverges when you put carriers in the top layer it’s better seen here that high density in top layer and that’s our characteristics but now a different temperatures if you if you are at low essentially very low concentration no electrons here that’s a typical temperature dependence a little bit freeze out of electrons but then there is a metal insulator transition if you put a lot of electron screening in the top layer that’s better seen here on this picture on this picture when you put a spacer closer than the phenomena becomes diverging you can go to mega ohm regime but it’s difficult to work in this regime because because some specific to this double way structure phenomena occurring but what is it is it a gap state or is it an insulating metal insulator transition at this resistivity the answer is if you apply to this state here magnetic field you’ll find out that so that you quench this insulating state which is a clear indication that what we’re dealing is is sort of interference under some of strong localization regimes this is confirmed by the fact that these divergence between sort of quasi metallic to insulated regime happens when resistivity per karyotype is about a chi square or wary square it has nothing to do with the metallic resistivity which was discussed many times before in graphene that the number comes one usually people see metal insulating transition the transition in any system in graphene for example how do we explain this knowing that this is insulating state and this explanation is sense to volodia Falkor we know that in graphene whether it’s on silicon oxide in boron nitride there are puddles we have known list for many many years and it has been that within each puddle graphene remains metallic and conductivity of this complex system is just a percolating probe a problem between the electron and hole puddles from here here so conductivity is not given what’s happening within the puddle it’s given by this barrier between two puzzles and it happens to give a conductivity of the order of H over 40 square or something like that so within each puddle we have a matter so and it’s probably extends to boron nitrite where puddles are bigger and shallow but still have a pretty large density of the order of ten to eleven or something like that what we

believe that the top graphene acts as a metal plate and this metal plate screens all those puddles and push the system into its intrinsic regime which is where some okay yeah where is you exceed this value H away a square and you are becoming an artisan under Sun insulator so that’s okay conclusion from from this part of the resurgence and the only one thing I would like to add let me skip it is because I’m I’m running out of time time let me skip this transparency so what let’s take is this as a conclusion so you can do double layer maybe triple life whole layer ok hetero structures with graphene and boron I am nitrite an extra layer offers new flexibility an example is my last few slides is that you can do interaction experiments between those how influence of one gas goes on to another beyond metallic screening I discuss so in this case we typically get okay smaller separations for nanometers with Karin through the bottom or top layer and measure voltage induced on the top layer remember there is no any tunnel current so any current in use here is due to an interruption or coolant drag sometimes it’s called okay that’s how it’s typically behaved you measure resistance is its linear response drag resistance as a function of how you put electrons and holes in the system and when the system has the same sign of charges charges where the drag is negative it becomes positive where charges have opposite have the opposite sign and this sort of regime has recently somewhere here from here to here has been studied by a taxon group and using instead of boron nitride they use silicon oxide s and in C white and mobilities were low low and they couldn’t go into say from one AM be polar regime was not possible in the experiment it’s very easy achieved in our experiment and what we actually like to simplify the situation and study dragging in this symmetric regime when you put holes in one system electrons in another system and they have the same concentration so there is a beautiful behavior which shows that the drag the case when you have more charge carriers and it shows a dip at zero concentration as it should be whenever one of the systems goes so zero it has to be zero so qualitatively behavior is understood we don’t know how how it picks up here what the value is there and actually that so the theory has already been produced even for Dirac fermions not very different from the case of just electronic gas that as a simplified formula for this particular case of equal concentration in top bottom layer and since we do not know what’s happening here and this is most interesting situation but let’s try to understand what happening on this slope away from the neutrality point if you look for the temperature dependence concentration 10 to 11 to 10 to the 12 you’ll find out that it’s t-square behaviour essentially fluctuations in one gas give you T fluctuations in another gas give you t and it’s t-square behavior so as it should be the Dirac fermions are Schroedinger fermions doesn’t matter it’s simple if we go to concentration dependence how it decays here will we find out that it’s not that quick decay the decay is much slower like 1 over and Q sorry R square Squared highest concentration to less than 1 over and at low concentration a 1 over answer and it’s it’s for a big range of various temperatures what’s going on why Siri doesn’t work in this case it’s very simple in fact that the interaction between the two system is described separation between the the parameters separation divided over wavelengths of electrons in any of those systems so

usually people who studied two dimensional gases in conventional systems and sankar as well they thought okay it would be the same weakly interacting regime as has always been studied before but in our case we can go to low separation and even 400 nanometer separation we are no longer in this weekly interaction regime we are actually in strongly interacting regime and those different concentration dependency shows ok after we presented this at a couple of conferences of course several groups came up with predictions what we should have in our experiments and it’s pretty good agreement agreement we with with theory and so okay to finish this part okay you can do with graphene boron nitrite and other samples okay very complex heterostructures quantum Wells vertical devices not only imply devices what MBE can’t do it you can’t do a single layer continuous layer by and B or something like that and to conclude everything I think Akkad’s a general my view would be that after we can probably consider graphene research quite mature after seven years so many people at this conference and so many conferences every year but as for me I don’t see any sign of this gold mine being exhausted okay it says it’s really good and finally I like to acknowledge all collaborators especially Roma Gorbachev who who make all those hundred washes of all the structures three guys who measured the devices and other people who were involved in this particular research I talking today and finally thank you for listening me without interruptions for this very low-density regime that you can access that in the first part of the talk I’m just curious I’m not a big expert on these interacting systems but I’m just curious like I know that in sort of the gallium arsenite to take people they talk about creating big nerd crystals you know when you get into these very low-density regimes and the electrons start isolating forming these patterns these interactions is it possible to get into this kind of regime in these graphene I’m most certain that we’ll find all those phenomena okay usually Vigna crystals require low temperatures okay with we limited ourselves so far the temperatures although although okay high temperatures graphene man I take room temperature thank you for reminding yeah what what I we certainly see interlayer excitonic features so essentially electron in one layer couples with hole in another layer and this is what you can see interactions these features I did I I don’t have enough data to present those but they’re seen Vigna crystal with in suspended samples we didn’t see anything there is a paper we I presented it a year ago we it’s not on archive where we study by layer at a very at a very low density and we don’t see anything the crystals we see we see a construction of the spectra and so on but but nothing as reading the crystals but interaction if you have to become yes they become very strong and this is this would be one of the major topics I believe within the next 10 years I believe Jeremy good I’m trying the talked about the puddles and I didn’t quite understand the origin of the puddles was this from the substrate or where do the puddles come from yeah I think it’s I didn’t mention this because it’s sort of consensus in that would say even before Amelia Kobe mentioned by ASTM so there is saying silicon oxide or in any other substrate there is a distribution of charges and this distribution of charges created a random variant attend show and the electrons feel if you wish it’s a random gate sometimes it’s portal actor and sometimes call some places this is one

this is why we call nob Dirac point we call it neutrality point because it’s usually consist of puddles of different sizes of filaments electrostatic potential just to follow up on Jeremy’s point I have your time to apply magnetic field in this percolation crossover if you have what will that tell you in which well the bilayer in in double layer structures by the way it’s a difference yes we tried but it’s so complicated system so you see many things ok what they mean we’re focusing at the moment in in zero field regime we we do apply paddles are we see the Rockets increases which one of indications of interlayer accidents and so on ok something going on but in probably not related to puddles because Warren nitride is much nicer system and the size of the puddles is larger than the the inter layer separation ok the Philip came from Columbia the applications on on this industrial ecology means that when you have that pop gates it screens out what is the roar of the pseudo spin in that case say don’t we it’s kinda actually yeah no collision because the pseudo spin yeah that’s what’s a good that’s a good question so essentially what Phillip is referring to to get localization in the system you need to restore time reversal symmetry and for a long time one of the explanation for the absence of localization or weak localization was that we have a broken time reversal symmetry broken by the fact that two valleys do not speak to each other when they are completely separate then there is no localization so there is no localization in this case so to get localization you need to add some intervallic scatters for example we don’t see any sign of metal insulating transition in suspending devices they go straight to a finite conductivity in suspended devices stray to a finite conductivity because their ballistic but if there is a some minor number of scatterers which kick electrons between the valid present then you can can restore this localization regimes there has been argument we don’t know we can’t measure the concentration we have we can estimate is 10 to 11 from the transition behavior but for graphene on silicon oxide that’s a typical number of internally scatterers which are a minor contribution but still present there so the answer is you need to have internally scatters boron nitride is transparent it’s it’s a wide gap 5 electron volts we don’t see any of absorbance all those okay you can visualize just due to interference like phenomena rather than absorbance this is why it’s hard quantisation if you wish you can see one layer absorbs twice two layers absorbs twice three last try last three times in this case there is quantization the number pi alpha is reasonably accurate it seems to be there are corrections due to some I exit on ik phenomena at support or there are three at five evey and there is a tail goes to visible light but it’s in suspended devices it’s usually small on substrate it’s usually high but otherwise to three percent accuracy for this for this number you talked about tunneling and resonant tunneling for these hetero structures that you’re building but you have got this lattice mismatch between say bora-bora I tried and and the graphene yeah so you haven’t got translation symmetry across that interface as you would have in a in a lattice match three five hetero structure do you envisage any complications of that and then that’s going to presumably make them have you got it normally resonant tiling you’ve got momentum an engine and energy conservation yeah it’s a good point so

for example with reference to Philip Kim’s question about okay that you need to break down time reversal symmetry maybe this interaction with boron nitrite gives another channel for breaking the symmetry because it’s atomic scale potential of boron nitrite which can scatter we probably don’t need it but it might be important in inducing metal insulating transition on the other hand we know that this phenomena is pretty small people studied service strategy graphene okay where which is called confusingly epitaxial graphene where where planes are also randomly rotated and so we know if the Ango is reasonably large there is a very weak interaction between those those less and so even when you have a perfect match in the in the constant just rotation already two couples less efficiently and with the poor electric you haven’t the effect Mangal yes it’s your dream