 Hi, everyone. Good morning. My name is Marcin Kieszel from the University of Basel. I do my contribution. I would like to actually show you that dissipation signal atomic force microscope can couple, can sense, correlate and insulating states or phases of graphene at the magic angle. So the arms, I look sort of standard, at the beginning a few words of introduction, then a bit about technique. The results divided in three parts. First part I will explain our atomic force microscope dissipation spectra. Then I will tell about the local probe technique. I will tell a little bit about the determination of the twist angle. We can hear you. I will tell a bit about the determination of the twist angle distribution and then I will show some results that we maybe... Yeah, we're working on it, this energy dissipation on how correlated and insulating phases of twisted bilayer graphene responds to magnetic field. I will finish with conclusion. So what is twisted bilayer graphene? There are two sheets of graphene that are twisted with respect to each other and there is this magic angle twist, which is equal to 1.08 degree and the twist of the magic angle leads to creation of the supercell in the reciprocal space we have this twist leading to creation of the mini-brillian zone. Here below you see the energy structure as it depends on the angle twist and what is really characteristic for the system is that the angle which is equal to 1.08 we have really flat bands created at the Fermi level. So flat bands... Yeah, that's the moment there. So flat bands basically means the kinetic energy of electrons is negligible and the coolant interaction takes over and the system is driven by strongly correlated electrons so the physics can be quite exotic so we could enter phases like mode transition or even superconductivity in such a systems. This was already... That phenomenon was already demonstrated. Most of the results, if you look at the literature about twisted bilayer, if you just google it you will find out two types of techniques that sense as strongly correlated in the relating phases of twisted bilayer graphene. One is capacitive detection. So basically we have a layer of graphene. On top there is gate, which is more or less the size of several micrometer and if the capacity of the quantum capacitance of the twisted bilayer graphene changes we can basically detect this drop of the capacitor by this gate. Here in this example we see drop at half-filling. At half-filling we can exactly inject two electrons into mini-brewlands on maximum. We can have four electrons for the mini-brewlands on such a system. On the right side you see transport measurements data. This is resistance versus doping concentration. What you see on this graph that for the magic angle twist we have some rises of the resistance. For example, at CPD this is most probably to electron holes scattering but we also see some jumps for half-filling, a bit of... A lot of resistance for full-filling. In this particular case we inject two electrons into mini-brewlands on this is for n equal to or four electrons for full-filling. You see also that the spectrum depends very strongly on the twist angle so this is a bit smaller twist angle what you can see here and basically the charge concentration basically depends on the twist angle like twist angle to the power two and full-filling for the graphene is given with this formula A is the lattice constant of the graphene. What is our technique and why it's different from the techniques I showed you before? This is a pendulum force atomic force microscope so it's a cantilever that is suspended like a tiny pendulum over the surface so it oscillates parallel to the surface so it shares a tiny vacuum gap between the surface and the tip. The reason for the suspension is quite clear we use extremely soft cantilevers so if you just come with normal suspension like standard FM geometry we will just snap to the contact so we want to avoid the snapping. Quality factors are quite high even in the order of one million and on this graph I show you comparison of typical dissipated power of different technique versus its spatial resolution so I would like to draw your attention to this comparison between tuning fog you have seen yesterday by Remy show you that tuning fog due to its very high amplitude stability it offers you very high spatial resolution but it's several orders of magnitude less sensitive to the dissipative forces as compared to pendulum FM so pendulum of FM minimum dissipated power is in the order even of fraction of act of arts maybe it's not the best imaging tool you see that basically spatial resolution is few nanometers so what is this is our system once again the pendulum FM oscillating like oscillating cantilever gate we can apply voltage to it for most of the measurements I will show you today we keep those cantilever ground just for simplicity but you can independently apply voltage to it and play with the electric state of the tip what is important that we can apply voltage to the back gate electrode back gate electrode is the silicon p-doped silicon and you can tune doping of this silicon this silicon there is an oxide on this silicon there is our twisted billiography device deposited and by changing this voltage gate you can tune doping you can do basically our twisted billiography with electrons or holes as you want it we have also saw the drain for most of the measurement I show you today we keep them grounded what you can see here measurements will also perform in ultra high vacuum and low temperatures what you see here it is the formula I wrote this is formula for dual dissipated power for mechanical oscillator basically and you see that dual dissipation or FM dissipation pendulum dissipation should be proportional to resistivity this is raw this is not so easy this is not so difficult to understand basically you can imagine you have some static charges at the end of the tip then you oscillate this static charge creates image charge in your sample and when you oscillate you create some oscillating current in the sample if the resistance of the sample rises dual dissipation rises that leads to rise of dissipation you see also that there is also capacitance gradients in the formula that means the quantum capacitance the device changes the density of states of this device changes this should also lead to the rise of dissipation if you remember those two measurements I show you at the beginning these transport measurements when we measure resistance and the capacitive measure when we measure capacitance it's not so surprising that we should actually the pendulum I FM should detect just looking at the formula should detect these oscillating phases of twisted billiography so this is our device so first I told you before that it's not maybe the best imaging device but basically that's our sample you have to find it so you can imagine you have a 5 by 5 millimeter sample and you have one on this sample surface of one device which is few by few microns and you have to find it so it depends on your experience and on your motivation it takes from two days to two weeks so this device this is this rectangle it's protected with eight wires so you have four at the bottom this is five, six, seven, eight and this is how it looks like again, schematics so back gate voltage is applied to p-doped silicon there is 300 nanometers silicon oxide that couples our twisted billiography into the back gate the sample is capped with 10 nanometers of HBN just to protect we have our cantilever that we can apply voltage to it but most of the cases as I told you before we keep it grounded so the drain we keep grounded at all times so we have our gate that is coupled capacitively to the underlying twisted billiography through the 10 nanometers of HBN this HBN for us is equivalent to 40 nanometers of vacuum because dielectric constant of HBN is 4 thickness of this HBN is 10 nanometers so 4 times 10 is like 40 nanometers of vacuum so we can see or we can detect the phenomena that literally exists below the surface and this is raw data our spectrum so what you see on the y-axis is the dissipation on the x-axis is back gate voltage so this is the voltage that we can apply to this p-doped silicon we have electron side as you can see this is above zero on the whole side but you can see you see series of dissipation peaks so there is one here small one there is quite big one here and very big one there and if you look carefully you see that on the whole side it's kind of mirrored but it's kind of stretched this is due to creation of the depletion zone for the negative voltage applied to the back gate so it's easy to correct just simple transformation I'll check for that what we see also that there is some small from the zero point so symmetry point is shifted by so cpd shift is shifted by 8V this is due to the disorder density that is present in the sample so now our task is to convert this back gate voltage into doping concentration this is extremely easy if you know back gate capacitance or because you know the electric constant of silicon dioxide you know the oxide thickness you can easily calculate the back gate capacitance and then by this simple linear transformation you convert your back gate voltage into doping concentration Q is the elementary charge we notice by doing that that our graphene is not exactly 1.08 degree twisted the angle is roughly like 1.1 degree and for the full feeling the charge density is equal to this value so when you make this linear when you convert back gate voltage into doping concentration your spectra's look like this you also take care about this depletion layer creation on the whole side so you see everything is symmetric everything is bring to zero and we have series of peaks exactly corresponds to fractional feeling of the correlated isolating states of twisted billiard graphene so at 1.4 feeling when you have one electron for many balloons injected into flat bands there is a small peak at half feeling when you have two electrons many balloons injected into flat bands we have a peak for three electrons and for full feeling we also have a series of dissipation peaks from this cpd shift we can easily determine the dissolved density and this is in the the numbers 5, 10, 2, 12 I guess 10 per centimeter square if you compare this with the literature it's pretty much corresponding to the values that were already reported in the literature again I told you before that we kept the pt grounded but the spectra which you show here on this map is actually dissipation map so the contrast is the excitation so red line red contrast is the high dissipation on the x axis you have back gate voltage on the y axis you have voltage applied to the tip so the spectrum which is shown here this is for the tip voltage grounded it's just a profile along this white dashed line so what you see on this graph is that when we apply voltage to the tip we just introduce this placement electric field from the tip and this shifts our position of our dissipation peak this is an extremely practical graph to know extremely important graph to know for practical reasons because if you know the slope of this dissipation peak you can quantify the lever arm between back gate capacitance to the tip sample capacitance and if you want to say something quantitatively about the system you have to know these things you have to know these quantities like tip sample capacitance or back gate capacitance so as I say our method is local so we can actually determine the twist angle at any spot of our device so we basically came to this left top corner of our device and we acquire spectras for different points across this line and if we now match the position of the dissipation peaks to the super lattice density we can determine the twist angle for every single spot of the device this is the histogram of this twist angle so you see that our it's quite a pretty good device I have to say so the main twist angle is 1.06 plus minus 3 to 4% error for 50 different spectra so we have some relaxation I mean nothing is perfect and of course this twist angle also relaxes so there is some angle relaxation from place to place this angle relaxation we can actually map so there is another way to basically track this angle distribution is to perform the constant high dissipation images so basically we position our tip roughly on 100 nanometers above the sample surface and we adjust the voltage to fractional feeling like 1.4 filling or half filling and we acquire this contract dissipation map so what we expect is that we cross the domain of different angle relaxation we expect the change of the dissipation contrast this is in fact what you see so what you see I mark these domains by the dotted lines so you see domains that are more or less few hundred nanometers in size what you also see you see some features which is characteristic for Coulomb ring so we have something on the sample which could be like a defect or in fact due to manufacturing process is pretty common but when the guys manufacture device there are some out of plane deformation and we know that they can effectively act as a quantum dot so this is from the single electron charging most probably but you have to remember that we have domains of few hundred nanometers these domains are most probably domains of different angle relaxation we also notice that from domain to domain the domains they have they could have those so different different charge concentration because we notice that we have some changes of contact potential difference from domain to domain which is on the twist angle relaxation but also charge relaxation now the magnetic fields come to enter so we are now at half feeling so again similar image of domains of different angle relaxation with most probably some Coulomb rings this is for magnetic field zero for half feeling and now when we apply magnetic field which is two tesla we observe complete disappearance of the domain contrast we attribute this phenomena to magnetic field polarizing of the charge states via spin so magnetic field basically induces some Zeeman splitting so for magnetic field zero we have this we strongly created the energy gap we can call it mod gap and when magnetic field is different than zero this gap is closed due to Zeeman shift and the domains disappear we have still some remnants of the single Coulomb blockade similar phenomena was also similar closing of the gap was also observed in transport a bit filled that were reported were slightly larger like full tesla now it comes the feeling which is a bit larger which is three four feeling also fractional ok almost my end so feeling which is three four so between three four and full feeling we observe well oscillations so you see dissipation versus magnetic field starts to oscillate we have this moustache of the oscillations at the beginning we were thinking that this could be characteristic like shubnikov has oscillations but there are two problems if that shubnikov has would require magnetic Fermi surface and this is in fact insulating state so it can the Fermi surface cannot be magnetic and the periodicity distribution has to have a special special behavior like one over b so this is also not the case here especially at magnetic field equals zero we should see no oscillations if it would be shubnikov has and we see that even for magnetic field equals zero we see oscillations so we talk to our ok this is again the we try to determine this periodicity of this magnetic field oscillations so you see that we have some distribution of periodicity so we have periodicity from 5 milli tesla to 15 milli tesla so we talk to our colleagues from transport community and they told us that actually similar periodicity distribution observe already in transport and this is related to magnetos magnetos oscillations in graphene p-enjunctions so basically when you have domains of different of different church church state let's say endowed and p-doped different doping magnetic field drives the charges in opposite direction if the magnetic field is big enough this charges can interfere the currents of wave functions actually it's quantum quantum mechanical interference can interfere leads to oscillations in the conduct like here or here with periods which are pretty close to ours and these oscillations are known as a boron of bomb oscillations so the only thing that the period of a boron of bomb oscillations should be given by this formula the magnetic flux which is enclosed by this domain of different charge it must be equal to magnetic field magnetic field quanta and if we know our periodicity and we know it we have it from our FFT we can actually estimate s so the effective size of a magnetic domain and compare with the image that we measured and if we do that we finish with the numbers which is like 500 by 500 nanometers which is pretty much in correspondence with what we observe in our images so we indeed have domains of few hundred by few hundred nanometers and that would pretty much correspond to boron of type of scenario so that brings me to the conclusion sorry for being a bit late so there are several conclusions maybe I would just stick to the most important so it's possible to couple mechanical oscillate to the quantum device and this have some some consequences for example Akash is now working on the qubit of the whole qubits so if you want to detect the qubit or change the charge state of the qubit you have to have a possibility to somehow come with something from macroscopic world to this quantum device and be able to sense or change the charge state and I believe pendulum AFM or actually AFM in general gives you this possibility if you compare the methods these local probe methods with let's say transport you see that the spectra's are much cleaner we are basically free from parasitic resistance effects so we are free from all the contacts imperfections all the short key junctions so basically transport people they have to have really clean devices in order to measure something sometimes in order to measure something they need to even dope the system to be able to detect any current and if you already dope the system too much all the physics that you expect at low doping can be just gone so this is advantage of the scanning probe approach so that's the system I thank you for your attention and I thank also several people that contributed to the work especially Alexina Olja this is a big part of this result is us who actually have Ph.D. project of course and Akash and thank you for your attention glad to take your questions we've run quite a bit over time so my suggestion is since now it's a coffee break back much in about his talk during the coffee break the next session we will move by 10 minutes so we'll start at 11 20 and the coffee will be served on the terrace outside so thank you and I'll see you in 25 minutes