 who will speak non-contact dissipation in quantum graphene. Thank you, so welcome back. So today we talk about free-standing graphene membranes. And in our measurements we are doing non-contact AFM, so it's a non-contact dissipation or non-contact friction. And we are interested in what we call quantum graphene. So basically we are looking at objects in graphene that behave as quantum dots, so it can be defect or it can be surface deformation. And we are using a scanning probe. And what is interesting is that with a scanning tunneling microscopy or STM, it has been shown that surface deformation, like here a puddle, can behave as quantum dots. So we can charge and discharge this surface deformation. So basically the measurements, it's the IDV. So here you have the density of state. Here you have the energy. And every peak you see in the spectroscopy is a charging event that occurs in this quantum dot. And this behavior, they can explain with these two capacitance model. In atomic force microscope, it's also possible to charge and discharge quantum dots. So here you have a semiconductor quantum dot, a channel barrier, and an electron gas. And the oscillation of the conciliver on top of the quantum dot is putting in and out the electrons in the quantum dot. And the system can also be described with this simple capacitance model. So in the AFM spectroscopy, the charging and discharging event looks like this. So here you have the force. Here you have the dissipation. And here you have the bias voltage. And what you see is that at certain bias voltage, you have a drop in the frequency shift that is followed with a peak in dissipation. And this is characteristic to electron charging in quantum dots with AFM. And when you do real space imaging, so x and y, you see that those peaks, they look like column rings. So this brings me to my outlook. So I will make a small introduction about our system and the sample. And then I will explain you our measurement. So first, the typical dissipation experiment, and then how they behave in the magnetic field. And then I will do a small conclusion. So our system is an atomic force microscope, but our geometry is different. So we call it pendulum because the conti-level is perpendicular to the sample surface and it's oscillating like a small pendulum over the sample surface. And this geometry is to avoid the snapping of the tip onto the sample surface. And this enables us to use conti-level with low stiffness, so very small spring constant. So basically it's a contact conti-level that we use to do non-contact measurements and we have high quality factor. And these two parameters, they are the main parameters we can change to increase our sensibility. And if we compare it to different techniques, you can see that here it's the dissipation and here is the spatial resolution. In terms of spatial resolution, we are okay. And in terms of dissipated power, we can be very sensitive. So our system looks like this. So it's a beam deflection AFM. We operate in UHV and the measurements that we show you today are made at low temperature. And basically what we call dissipation or friction is the evolution of the oscillation of our conti-level depending the tip sample distance. So we set our conti-level to a fixed amplitude. So in this case it was two nanometer. So we make it oscillate to two nanometer and when we approach it to the sample surface, the interaction between the tip and the sample surface are dumping the conti-level, yes. And then we use an electronic circuit, the phase lock loop to keep this oscillation constant. So what she's doing is that it's applying an excitation to the conti-level to keep this oscillation constant. And then due to that we can get the frequency shift and the dissipation with this expression. And in real life it looks like that. So here you have the conti-level and here you have the sample. So our sample is a copper substrate patterned with holes of 6.5 microns of diameter where a film of graphene, a monolayer graphene was deposited on top of it in order to have a circular freestanding graphene sheet just like this. So before to do the experiments we wanted to characterize our sample. So we did STM imaging on the graphene that is supported on the copper substrate and on the freestanding graphene. So this is the typical image we got on the supported graphene. So you see that we are able to reconstruct the honeycomb lattice of the graphene just like this. And on the freestanding graphene, we can guess a structure underneath on the graphene but the main structure that we saw it's some surface deformation and the more prominent ones are these wrinkles and nano-ribbon-like structure with a width of two nanometer, yes, of two nanometer. And again we can describe our system with these two capacitance model. So this is the typical dissipation spectrum that we got. So the tip was 300 nanometer away from the freestanding graphene and then we apply a bias voltage and we looked at the frequency shift and the dissipation. So here you can see that on the frequency shift at certain biases we have a drop in the frequency shift that's are followed with peaks in the dissipation and this is what I showed you before that it's characteristic to charging and discharging events on quantum dots using AFM. When we take back this simple model we can wonder what is the effect of every capacitance. So this is what I will try to discuss today. So first we investigate the tip capacitance. So it's easy to investigate because we just need to change the tip sample distance and look what is happening. And this is what you see here in this map. So here you have the tip sample distance, here you are far away from the sample and here you are at the surface. We applied a bias voltage and the contrast that you see is the dissipation. So the black color is for low dissipation and the yellow color is for high dissipation and the curve, the white line here is the curve I showed you before. So what we see is that when we change the tip capacitance we are shifting the peaks to lower biases and this shift is called the lever arm. So basically with that we understand that the tip sample distance or the tip capacitance is shifting the peaks into lower voltages when we get closer to the sample surface. So the second question is what is the effect then of the substrate capacitance? But to investigate it we need to consider two capacitance, one capacitance for the geometry and the environment and one capacitance that is the quantum capacitance that can lead to quantization if the system enables it. So this quantum capacitance is described with this formula so here you have a pre-factor, here you have the quantization and here you have the heavy side function for symmetrization and what you see is that this quantum capacitance is directly proportional to the density of states. So we try to model this capacitance so with a different size. So here in the quantization you see you have the W, so the size of your graphene that you're considering and here we plot it for two size. The blue size is for 100 nanometer graphene so like a big graphene fake and you see that you have the normal V shape of graphene without any peaks and when we lower this size so for the orange curve it's for a five nanometer ribbon graphene and you see that we start to see peaks and those peaks they are Van Hoof singularities. So this is a strong hint to tell us that the peaks that we are seeing in the dissipation they are due to these Van Hoof singularities. So in order to verify this we try to model our frequency shift, our frequency shift data to see if we are able to fit these peaks and this position with just this simple assumption and then we then decided to fit the frequency shift because it's easier to fit than the dissipation. The formula is a bit easier. So here we have again a pre-factor and then there is two parts. The first part is to describe the charge in the graphene and its image charge in the cantilever. The second part is the interaction between the charge in the graphene flake and the polarized charge in the tip and the third part is to describe the parabolic background and it's also describing the interaction between the polarized charge in the tip and the back gate electrode. So here you have again this frequency shift. Here you have the bias and the blue curve is the dissipation. The black curve is the data that we recorded and the red curve is the fitting using this formula and for the quantum capacitance we use a width equal to nanometer like we found on the STM. And what you can see is that we are able just with these simple assumptions to fit the position and the drops in the frequency shift. So this is a strong heat to say that the peaks we are seeing in the dissipation they're really due to these Van Hoof singularities. And another remark is that you see that the drops in the frequency shift they're very small but the peaks in dissipation are very big. So basically what that means is that we are more sensitive to with the dissipation channels to these Van Hoof singularities than in the frequency shift. So now that we know how they behave at zero magnetic field we wondered how they behave in the magnetic field. So we did the magnetic field measurements by applying a magnetic field from minus two Tesla to two Tesla with a step of 0.12 Tesla and we apply again the bias voltage and here the contrast is again the dissipation. So dark blue is low dissipation and yellow it's high dissipation. And the first thing that we observe is that the peaks they are shifting to lower energies. And this shift is linear. So to try to understand this we use the semi-classical Borsam-Muffet phase accumulation model. So basically when you are at zero magnetic field the system is behaving like a normal quantum well. So you can describe it with this formula. So the wave vector is proportional to two pi n. And when you start to apply a magnetic field you start to accumulate the election in due to this magnetic phase accumulation and then you have this phase here that is added to the formula that is called the payer phase. And for the linear shift we believe that it's due to the linear energy dispersion of graphene. So when you put this into the formula we found that the S, so the sample bias is linearly proportional to the magnetic field and this is in direct agreement, good agreement with the linear dispersion of graphene. So what we did is that we added this payer phase in the model I showed you before to see if we are able to fit again the position and the drops of the peak. So this is again the zero magnetic field so zero degree for the payer phase. So we were able, I already showed you that we were able to fit the position and the drop on the frequency shift. And now when we apply a magnetic field just by increasing this payer phase you see that we are able to fit the position of the drops in the frequency shift. Just like this. So this looks like to be also in great agreement with what we believe. So that we are accumulating the charge with this payer phase and then this shifting to lower energy the peaks. So the last part of the talk is to see how the peaks looks like in the real space. So we look at the bias voltage where we have this dissipation peak and we do constant height imaging on this specific bias on the sample. And this is what we got. So you see that they look like the Coulomb ranks but they are not circular like we can expect to Coulomb ranks. They are elongated and if you put the STM image on top of it you see that this elongation is in the same direction as the wrinkle we observe in the STM images. So what we think is that we are charging these wrinkles and the electrons are confined along these wrinkles. And when we apply a magnetic field you can see that they have the same behavior as in the map I showed you. So they have, they disappear by increasing the magnetic fields. So to try to understand better this linear shift we ask our colleague from CISA, so to Ali to do some tight binding calculation to try to understand better this linear motion and this is a simulation. So you have the black feature, it's like a different wrinkles and he did a calculation with different shape and what he taught us and what it looks like going in on is that we have small objects that confine the electrons but this linear shift is due to a bigger structure in the membrane. So it's completely independent to the wrinkles and he's able, so here you have magnetic field, here you have energy, this is a theoretical bounds and the red dot, sorry, they are our measurements and you can see that with a bigger structure than just these two nanometer wrinkles he's able to fit quite well the position of the motion of the speaks. So that means that we have bigger structure that needs to be taken in consideration. So with that I want to conclude, so I showed you the pendulum atomic force microscopy measurement of a freestanding graphene, so we saw formation of wrinkles in the membranes and when we do dissipation measurement we see that we have two peaks that are due to quantum capacitance and we also saw that the dissipation signal is more sensitive to the vanavent singularities as compared to the frequency shift and we are assuming that we are confining electrons into the surface deformation and in real space they looks like coulomb rings along this specific direction and the magnetic field, we are inducing a pair of phase that is shifting the peaks to lower energy, this peaks, this shift is linear due to the linear energy dissipation of graphene and the tight binding calculations show us that we have a distribution of length scale that have different properties, behavior on our dissipation peaks, so basically we have small structure that behave like quantum dots and bigger structure that are shifting the peaks on the magnetic field and then what we can say is that the wrinkles don't really alter this linear behavior. With that I want to thank our collaborator from CISA and Ernst Meyer for taking me as a PhD student and all the other members of the group and the founding, so the ERC and the SNI and you for your attention. Yeah, thank you for your very nice talk. I was wondering, when you showed this magnetic field dependence with positive and negative field perhaps slide 11 or something, yeah, that one, yeah, okay. Oh, well, the one, yeah, this one. I was wondering, positive and negative field, are they different because of some reason or is that experimental error? We have a different strength of the signal in the positive and negative reason. Yeah, you mean this bigger dissipation on negative side? Exactly. This, I don't really know where this asymmetry is coming from but we think it can be due to different symmetry because we have wrinkles, so we have distortion at some part of the wrinkles in the system and then this can behave differently with positive field. Yes, but we didn't really investigate it. I actually had the same question, so. Okay. Could it be that the film itself is not symmetric? Is that it mean, it could have a polarization, for example, and the negative and positive voltage would do something different? Maybe we have defected, I think, because it's a bigger layer, so we have. But you have the layer on a surface, right? No, this one is freestanding. Freestanding, yeah, thanks for the talk. I was wondering, does big samples, how do you actually produce them? We bought them, they're coming from a company. So they put it on the hole for you?