 the afternoon session with Christian Ast from Stuttgart. And he will talk about superconducting quantum interference at the atomic scale. Okay, can you hear me? Yes, thank you. So, can I? Please point more towards there. I think it's got some connection problem. And the receiver is down there. Not really. I can, I'll just stay here. Okay, sorry about that. No, no, no, right. Okay, let me see. All right, so, yes, thank you for the introduction and also thank you to the organizers for the kind invitation to present our research here today. Yes, so I want to talk about superconducting quantum interference at the atomic scale which we investigate using scanning tunneling microscopy. So in a way this technique is quite a bit different from what we have heard in this workshop so far. But there's also very distinct similarities because in the end an STM is no more than a tunnel junction. Okay, before I start I want to acknowledge the people who are involved. This is my work in the department of Klaus Kern at the MPI for Solar States Research which always makes my daughter giggle because she's wondering what kind of research you can do with solids. But there are sort of things we can do, I guess. Then most of the work that I present has been done by Sujoy and Haonan and some of the work also by Piotr. And then I want to also acknowledge the invaluable theory support that we have received over the past years, most notably the group from Ulm, Joachim, Björn, and Ciprian who really have helped us understand everything a lot better than we could have hoped for. And also Carlos and Alfredo from Madrid. We've heard Alfredo before. And then also Anika who helped us out of a tight spot with the last paper. Those are the contributors to the research that I present today. Okay, so we have interference in the title and interference needs coherence and this is typically a problem in STM because the STM operates in the dynamical Coulomb blockade regime which implies sequential tunneling and makes coherence a little bit more difficult. So we have to account for phase fluctuations in the tunnel junction. However, these phase fluctuations are typically on a much longer time scale than individual tunneling events so that basically if we are happy with a short coherence time, then everything will work out. And this is basically what I want to show you in the following. So one example to also connect to the microwave theme of the workshop, we have started also using microwaves and shining them in our tunnel junction. These are some of the first experiments. We have here a reference junction. This is taken with a vanadium tip and a vanadium sample. So both are superconducting at 300 millikelvin. You see the coherence peaks here. This is our reference junction. Now if we turn on microwaves at 75 gigahertz, shine them into the junction at a very small amplitude, we see a slight reduction of the main peak and we see replica showing up. And if we increase the amplitude now, we see replica and the modulation of the intensity quite a bit. And if you put this on a more continuous scale, you actually see a nice fan of these two coherence peaks here from the bias voltage as a function of the microwave amplitude. You see the coherence peaks here and here as they fan out. And now you see the modulation of these peaks here and these are actually indications of coherent interference of the tunneling electrons with the microwaves. So there is some coherence in the tunneling event or in the tunnel junction. And then the superposition of the peaks here in the back show at higher frequencies, higher amplitudes shows an incoherent superposition of tunneling events so that we can basically say we have coherent behavior within one tunneling event and incoherent superposition between tunneling events. So okay, I don't think I have to motivate coherence and the importance of coherence in this audience really. So there have been, we're all looking for coherence in one way or another. And now we are also looking for coherent behavior in the STM and there's basically two topics for the shortness of time. I can only cover one of these topics maybe in the end if there's still time I can talk about this. What we've done two years ago here, this has been published in Nature Physics two years ago is we were able to actually show demonstrate tunneling between two individual quasi-particle energy levels namely Yushy Baruzinov states inside a super-connecting gap and by changing the tunnel coupling between these two, between the tip and the sample we were able to see some emergent coherent coupling in the quasi-particle tunneling. So what I do want to talk about in the following is the question if we can realize some at least some rudimentary phase sensitivity in the STM such that we would be able to detect for example a pi junction. Similar to what we have in a superconducting squid as you see here where we have the junction of interest with a quantum dot and the reference junction and then we can get the interference between the phase by basically superimposing the phases of the two junctions. And I will show you in the following that we can at least to some extent move that concept to the STM tunnel junction and at least detect a sign change in the phase. Okay, to do that let me start at the beginning. We operate a milli-Calvin STM in Stuttgart in a precision lab. This is essentially a low noise or noise-free environment. You see the dilution refrigerator here which operates at the base temperature of 10 milli-Calvin. The STM sits about here. It's a scan head that's just the size of my fist. We have a prep chamber down here and the periphery of the dilfridge. Then we have a huge concrete slab that weighs about 100 tons to decouple vibrationally from the environment so that we can have really very low noise environment for the STM. And the theme in my group is basically to look for new quantum limits and one of the inherent quantum limits in the STM is to have atomic resolution and this is probably one of the defining differences compared to other tunnel junctions. Here you see an aluminum surface which has nothing to do with the rest of the talk. It just looks nice. You see atoms, the aluminum atoms in Lysli's arrangement of square letters and some defects, some of them are oxygen, some of them are carbon, and some of them are subsurface and you see these standing waves emanating to the surface. And then as we lower the temperature, we get all kinds of quantization effects. We get charge quantization. We were able to see this in the dynamic coulomb blockade. To do this, we have actually pulled one aluminum atom out of the surface and placed it onto the surface so that we can create a tunnel junction between two aluminum atoms which actually turn out to feature just one transport channel and the other transport channels are at least an order of magnitude smaller in transmission so that we were able to demonstrate these charge quantization effects here and also single channel transport through a Josephson junction. And this connects very nicely to, for example, the work that has been done in Sakhle and other places. So from this point of view, the STM is just another tunnel junction. Okay, so how do we create a pi junction? Let's start out with a quantum dot. We have a quantum dot that is connected to superconducting leads here and now if we place a single spin onto a quantum dot, then, well, the short version is we exchange the formionic operators across the junction and then we create a sign change which leads to a supercurrent reversal. So in the STM, we basically have a very asymmetric quantum dot, if you will, because we place a magnetic impurity on the tip or on the sample and this is usually strongly coupled to one side and then we have the tunnel junction here on the other side. And now if we place a magnetic impurity onto a superconducting substrate, we induce a so-called Ushiba-Ruzinov state and this is basically what we want to work with. So what happens now? We have a clean superconductor. The density of states features a BCS gap. We have a vanadium substrate, for example, and we see coherence peaks. Now we place our magnetic impurity on top. The magnetic impurity has some exchange coupling with the substrate and this induces a so-called Ushiba-Ruzinov state inside the gap. So the Ushiba-Ruzinov state is a bogeyube of quasi-particle which is a superposition of electrons and holes and if you plot that in the density of states, you project this bogeyube of quasi-particle onto the electrons and holes and this is why you always see two peaks at plus minus the energy inside the gap here. And what I would also like to point out is that the coherence peaks are actually suppressed. So this will become later on important just as a comment now that you see this here. Okay, so what happens now? We can actually change the exchange coupling. So from the magnetic impurity to the substrate and if we start with a weak coupling, the Ushiba state moves from the gap edge towards zero, both peaks move towards zero and in the weak coupling regime, the impurity spin is free. So that total spin of the system is the impurity spin in this case of spin one-half and the superconductor has a spin zero so we have a total spin of one-half. Now across zero here, we have a quantum phase transition. The ground state changes. You can think of it as a Cooper pair breaking and then occupying the Shiba state so that in the ground state, the Shiba state is now occupied and in the excited state, it's empty. But in the ground state now, the Cooper pair, the Boko-Ljubov-Quasi particle that occupies the Shiba state now screens the spin such that the total spin of the system becomes zero. So and yeah, now we want to investigate that with STM. So it's a local technique. We have a local perturbation. So it's an ideal technique to show that. There's a lot of work has been done starting in 1997 with Ali Astani for example and then continue on later on. Katarina Franke has done a lot of nice work on that and in the past few years, more and more people got interested in this work and so did we. So and our favorite superconductor to do this is actually vanadium. You see this here. We have a vanadium one zero zero surface with nice square terraces. When you see that the surface is not so nice and clean. We, for example, as in the aluminum surface, if you zoom in, you see an oxygen reconstruction. This is part of the preparation process. This is very difficult to get vanadium clean. However, we can turn this nuisance into a virtue because it turns out that a few of these defects actually feature a very nice Shiba state because they have a free spin. And the nice thing about these Shiba states compared to I would say 95% of all other Shiba states that have been prepared so far is that they actually feature a single Shiba state inside the gap that you can see here. And they are, for all we know, very nice spin one and a half impurities. So which makes the theory behind it a lot easier to calculate. So blue is the data, red is a fit and the Shiba state is shown here nice and sharp. And what you see here is also a coherence peak. Now remembering from before that the spectrum on the Shiba state does not feature a coherence peak, we conclude that we have here actually at least two transport channels, one going through the Shiba state and one going through an empty BCS gap, which is a straightforward conclusion because the spectral features are so decidedly different. Okay, so we keep that in mind for later. Just to characterize the Shiba state a little bit more or this impurity, we have turned on the magnetic field here for example, this is not a linear scale here on the Y axis, we have the bias voltage on the X axis and the DIDV signal on the, as the color scale here, this is the coherence peak here and here and then we have the Shiba state and as we turn on the magnetic field and increase the field, the gap closes and eventually quenches and then we see a very nice condo feature here which as we increase the field further splits up into two peaks and this is already a nice indication that we have a spin one half impurity because the two peaks, if you extend that to zero they cross at the finite magnetic field which also indicates the condo temperature of about one Kelvin in this case. Okay, another advantage of these vanadium impurities is that they are extremely flexible because they depend very much on the local environment, some other defects or structural defects in the vicinity so that we find them actually throughout the energy gap here. This is a histogram of Shiba states that we found on the sample and also on the tip, it turns out that the PhD student Haunan, who did these measurements initially he found that by dipping the tip into the sample he can pick up or modify the tip such that we get a Shiba state in the tip apex and he can do it so reproducibly and flexibly that he wrote a code where he can say I want a Shiba state at that energy so that the algorithm goes and dips the tip until we get a Shiba state at this certain energy and then this takes about 10 to 100 minutes and then we're done and we have a Shiba state at the tip. So now the trick is now to demonstrate a pi junction or even a zero pi transition is that we want to get these measurements with exactly the same tunnel junction to verify that nothing else changes. So now the capabilities of changing the parameters in the STM are quite a bit more limited than in other tunnel junctions because we cannot just slap on a gate voltage somewhere or and tune the parameters this way because it's simply too small. So there's other tricks that we have to do and it turns out that there is a nice trick that we can do here in the tunnel junction. So we have here basically our quantum dot we have the impurity here and we have the bath on this side on the tunnel junction on the other side and so what happens now is if you think about this in terms of the end of the impurity model we have an impurity substrate coupling gamma here and because the distance between the impurity and the substrate is just a couple of angstroms there are atomic forces pulling, attractive atomic forces pulling the impurity away from the tip. So if we now move the tip closer which we can do very easily we change the atomic forces between the impurity and the substrate such that we pull more and more on the tip impurity by moving the tip closer such that we change the impurity substrate coupling as we move the tip closer. So this is our way of changing the coupling. So this has been done, there's a number of publications that came out in the also from us in the past few years. So this is actually quite a general effect and we all studied not just on Shiba states but in tunnel junctions in general. So and now the trick is now to find an impurity that moves across the quantum phase transition while we are changing the tip sample distance and we have to be able to measure the Josephson effect at the same time. So and luckily we found several such impurities and what you see here is the collection of spectra where we have the bias voltage on the X axis and the conductance which is the tip sample distance on the Y axis and what you see here is the Shiba state here changing energy on the left and the right and moving through a quantum phase transition here. The Josephson effect in the center you cannot see because it's small. Yeah, we'll zoom into that region later. So now you see that the Shiba state moves and has a minimum here basically closest to zero and moves away. So it does not cross zero because we have a superconducting tip and a superconducting sample so that the zero point is actually offset by the delta of the sample. Okay, so now let's look at the Josephson effect. This is what the Josephson effect looks like in our STM. So we have dynamic aculin blockade and we can actually describe this very nicely with the P of E theory. The spectrum looks slightly noisy because we are very far away. So the current is also not very strong here. We have just a few hundred femto amps here but now we move closer. Yeah, you see the conductance on the X axis and the spectrum from last slide is actually this spectrum and then we move closer and we increase in amplitude and you see a strange behavior already here across the quantum phase transition. The Josephson effect does not increase monotonically but it actually even decreases a little bit. So we have to look at this a little bit closer by plotting the current maximum that you see here as a function of conductance. In the dynamic aculin blockade regime, the whole spectrum is basically proportional to the square of the Josephson energy. So we can just take the maximum and plot that as a function of conductance. This is shown here in the blue trace here and you see far away from the quantum phase transition here, we see a square dependence on the conductance here and here and something happens across the quantum phase transition. The quantum phase transition is here. You see red is the position of the Schiba state. It has a minimum at the quantum phase transition and then we move across here. So we can rearrange this a little bit. We take the square root to get rid of the square dependence and then we divide by the conductance and we get something that is reminiscent of the ICRN product. This basically results in a step. So we have a maximum here and we move across the quantum phase transition and we have a small value here. So I can tell you already here that this is due to a zero junction on the left side which leads to a constructive interference between transport channels and a pi junction on the right side which leads to a destructive interference. And the slope here actually just depends on the temperature of the system which in this case in the fit turns out to be 75 millikelvin. Okay, how does this work? The STM, the sensitivity in the STM. As I've indicated before, we actually have more than one transport channel, one that goes through the Schiba state and another one that goes through the BCS channel with no Schiba state. This can be realized for example by having one orbital that has a free spin and another degenerate orbital they overlap and then we get, for example, two transport channels. Yeah, and they interfere now. If we plot the energy phase relation here in the tunneling regime, so there's not much amplitude here. We have the energy phase relation of a BCS junction and the Schiba junction here close to the quantum phase transition. If we zoom in here, we get an in phase situation on one side of the quantum phase transition and then the sum of the channels gives a larger amplitude. Now the Schiba side moves across the quantum phase transition and this means that the lower branch moves above zero and the upper branch moves below zero and this corresponds to a sign change in the energy phase relation here that you can see here and now the sum actually becomes a difference and the amplitude of the energy, the total energy phase relation is different. Now in the STM, we are not really sensitive to the sign because we measure the square of the Josephson energy but we're still sensitive to the magnitude and this is what we are actually measuring. To be a bit more quantitative, we have the current voltage characteristics in the dynamic equilibrium blockade regime which involves the P of E function here which gives the characteristic shape of the spectrum that we see and everything is proportional to the Josephson energy here to lowest order and the connection to the energy phase relation is simply a Fourier transform of the energy phase relation and to lowest order we get the cosine dependence and so E1 is basically the amplitude of the energy phase relation here and this is in the end what we are measuring. Yeah, okay, so and we have to still consider temperature so that we have a probability of having the Sheba set in the ground state or thermally excited, P is the probability to be thermally excited now and this leads to the situation where we have a constructive interference and destructive interference here and this is what gives the finite slope across the quantum phase transition and this is what you see here. The red line is a fit to the model that I just presented to you and this gives us a zero junction on the left side and the pi junction on the right side. Okay, and as I indicated before, the slope is given by the temperature. So now the zero junction would be the screen spin regime and the pi junction would be the free spin regime where we have the spin in the junction. The question now is do we have an independent means to verify that we have made the correct assignment and here we go back to the Kondo effect when we turn on the magnetic field and here we plot the full width or the half width at half maximum of the Kondo peak that we have measured with exactly the same junction in the magnetic field and you see that the coupling, so the width of the Kondo peak continuously decreases as we increase the conductance. This means that the Kondo temperature decreases and with a decreasing Kondo temperature we have a decreasing exchange coupling and the decreasing exchange coupling means that we are moving from a zero junction to a pi junction from the screen spin to the free spin regime and this basically verifies our assignment. And okay and with this we have demonstrated the super current reversal in Yushiba-Rusinov junction which is where we have exploited the interference between two transport channels very reminiscent of a squid except that now we have a squid with zero enclosed area because the two transport channels are basically in the same atom or in so closely located that we will not be able to pass any flux through it but still we can detect a sign change in this. Okay, how much time do I have left? Okay, I don't know. I wanted to, I can show you just very briefly the tunnel junction, the Shiba-Shiba tunneling. When we do this with, we can do tunneling through individual quasi-particle levels by taking a Shiba set in the tip and the Shiba set in the sample. So very briefly we have, this is an empty junction with coherence peaks. We move over a Shiba state. We get the Shiba peak here and here. We place a Shiba state on the tip. We get a Shiba state. Now we take that exact Shiba state and move it over the previous impurity and we get an entirely new feature inside the gap here. You see this here, that this is an entirely new spectral feature which is related to tunneling between two individual quasi-particle levels. And this is basically the smallest tunnel junction that you can possibly create because if you take any of these components away, the tunneling current is gone. This is you see here. Anything is missing then the feature is gone. It is easier to see this feature actually as a current because then it's a peak. And if you zoom in, you see a nice peak and this is actually a direct measurement of the POV function because the intrinsic energy levels are roughly 100th of the width of the POV function. So we're basically mapping out the POV function and you see that we have zero current before and zero current after this. And so we basically demonstrate tunneling between two individual quasi-particle levels. So what we can do with this, just very briefly, we can measure this as a function of conductance. So tunnel coupling and we can plot the area of this peak. This is a very unique situation that we can actually have access to the area and this moves from linear regime to a sublinear regime. And this is basically, the sublinear regime is an indication of coherent coupling and the transition point here, linear sublinear indicates can actually be used to infer the lifetime of the Shiba state of about 48 nanoseconds. Now, in some ways this is a large number, in some ways this is a small number, we have done no optimization of the superconductor. So we are basically limited probably through quasi-particle interactions. But this actually shows that this tunneling is actually extremely efficient and allows us to go to the probably the largest tunneling resistance that we have ever measured of 22 tera ohms. The set point is 0.18 femto amps and we can measure a peak of about 1.2 femto amps. Here this is the Shiba-Shiba tunneling one side, Shiba-Tiba tunneling on the other side. And this shows how extremely efficient this is because you're basically tunneling through two singularities. And with this I conclude, thank you for your attention. So thank you for your interesting talk, are there questions? So this picture you presented in the first slides applied for classical impurities, this quantum phase transition. While in your case, if I understood properly, you are dealing with the spin one-half, right? Yes. These observed signatures of quantum effects. What would you describe? What would be a quantum signature in your? I mean, somehow you translate the zero, the s equals zero to the condo case. But condo is not exactly the same thing because condo is a true one-half model with the... Yes, okay, so we... Quantum, but while the other is classical. We use basically the mean field theory to describe everything, yes, but it actually turns out that we do see signatures of residual condo coupling in the superconducting state, yeah? This is, we're quite certain of that. I don't have a spectrum here to show this, but it would be present here as well, but you would have to look at the current voltage characteristic. It's not visible in the differential conductance, yeah? So you have to know what to look for, but it's basically there, and this in the end means that the spin is not entirely screened, free in the free-spin regime. It's partially screened, but it's always fully screened in the screen-spin regime because then the condo effect basically takes over. But we haven't, I mean, the model works so well in this sense, but for what we are doing, it works nicely, but you're right, it can be refined to include the condo effect also in the superconducting state, yes. Okay, any other question? Yes, I was curious about the final peak in which you see the POC imprinting in the IV curve. So there is a slight asymmetry, is that the finite, it's the detailed balance? Is there anything here? No, no, no, in the Shiba, Shiba. Oh, Shiba, Shiba, yes. Yes, there is, if you look closely, there is a slight asymmetry, yes. So that's the detailed balance of your energy. Yes, that we attribute to this. Yeah, and what kind of environment do you have in order to have this? Okay, part of the environment is vacuum, yeah? Which, if you want to call it an environment, but the most dominant part is actually the tip in the junction acting as an antenna, yeah? Okay. And we see, it's not obvious in these, but I don't know if we can see this in the Josephson spectra here. No, I cut off too early. But if you move a little bit further out here, we actually see resonances from the antenna resonances, yeah? And we can move them by changing the length of the tip, by changing the length of the tip, yeah? So the tip is a lambda quarter, quarter lambda resonator or a quarter lambda antenna, like a monopole antenna. And we can model this very nicely, even quantitatively, yes. So that's probably the biggest contribution to the environmental impedance. Okay, we need to move on. Let's thank the speaker again.