 Thank you Mr. Chairman, thank you organizers, thank you boarders for inviting me to join the party. And it's my pleasure to give you an update on the experiments that we've done on one dimensional semiconductor nanowires, and in particular with a focus on revealing the properties of Majorana fermions in these systems. So this is work done over the past two years or so, so it's a collection of experimental results from the past two years. From the group, our group in Delft, we collaborate already for a decade with Ilik Bakkers, his group who's a material scientist, so he grows all these nanowires, and supports theoretical support besides people like Carlo Benek, who are very nearby, Juli Nazarov, we have a direct help and interaction with Michal Wimmer. So Lady Glossman already gives you the introduction on these topological systems, Majorana fermions, et cetera, and a very simple picture that I would like to start from is a picture where we have bands that have a different order on the outside compared to the inside. So for instance the valence band in red and the conduction band in blue are normally oriented on the outside, but on the inside it is inverted, and that is sort of the pictorial characteristic of a topological system. If you connect this system to a superconductor, then under the right circumstances you can have interesting states at these crossing points. These crossing points, these quantum states, they are composed of sort of loosely speaking half an electron and half a hole, and these are supposed to be the Majorana fermions that we're looking for. This system, the system that we're looking for, you can look at these iron atoms on lead, but we've been using a semiconductor nanowire, this is here in green, we're at the end points now, at the end points you expect these special states. So what do you need to do? In 2010 there were two papers with very specific recipes on what to do in order to get into the right regime, such as these Majorana states emerge from all the other properties. Two papers, 2010, Mutschendal and Oregadal, they had a recipe that has four ingredients. First of all, you need this one-dimensional semiconductor system, you need spin-orbit interaction, somehow superconductivity has to be induced, and you have to tune the chemical potential and the magnetic field at the right values. And this should be a phase that is extended in this parameter space where you are in a topological superconducting regime, including the Majoranas. 2012, so about two years after the first, not the first prediction, the first predictions were from Gitaev in around 2000, but from this specific recipe, two years after there were several experiments reported, one from our group in Delft, but also from Lund, Weitzman, Urbana, Harvett, Copenhagen, and you will hear more from Charlie Marcus about the Harvett, Copenhagen results. So what has happened since? And in order to discuss it, I would like to go through each of these ingredients first separately before we bring them together to get to the topological phase. So first of all, the one-dimensional systems are starting point, the semiconducting nanowires. So one-dimensional system, the first thing you expect is if the transporter is one-dimensional system is ballistic, and you have discrete one-dimensional modes, then you can expect things like a quantized conductance. So for that, we know, and actually it's a pleasure to have Michael Pepper as our chairman because we know since 1988 where his group, together with our group in Delft, discovered that in a small, in a narrow constriction at that time confined in a two-dimensional system shows quantized conductance. And this quantized conductance was actually fairly robust against scattering. What you need is a ballistic motion in the region around the constriction, but if scattering occurs at a little distance away from the constriction, then the opening angle to actually go back through the constriction is very small, so the probability to go back and destruct the quantized conductance is small in this two-dimensional system. It's much more likely that you scatter off and then end up in the right contact. In a nanowire system, this is different. In a nanowire system, if you induce a small extra confinement, for instance here in the middle, even if you've passed the constriction but hit the interface with human telecontact, you can still return, basically it's a large probability to return through the constriction and have, you know, break down the nice quantization of the plateaus. So very important, besides having high mobility one-dimensional semiconductor wires, is the interface with the metal, crucially important. Now we've been working on these metals, it's half chemistry what you have to do to make the surface between the semiconductor and the metallic contact as clean as possible. And here, for instance, the high resolution picture, it's a cross cut through the sample where you see the substrate, it's actually a silica substrate here at the bottom, it's always black stuff. On top there's a dielectric layer, this gray stuff. Here you see a cross plane through the nanowire covered by the gold contact over here. If you look very closely then you can still see at the bottom of the nanowire a hexagonal structure, that is the facets of the wire as Eric Buckers gives us the wires after growth. But before putting down the gold, we've been cleaning the surface because there's always a little bit of an oxide layer on the surface, you have to clean it with some chemicals, and what you see in this picture is that the top surface is much more rounded in comparison to the bottom surface. The picture on the screen has more contrast than this big screen, but the bottom has fastest and the top is rounded off because of the edging. And this is something that you don't want, because here you're actually changing the properties at the surface exactly at the point where you have transmission from your gold contact into your semiconductor. So thinking about a little bit more and thinking about what kind of system do we actually have, indium and timonite, it grows in the 1-1-1 direction, the facets are all in these planes of 1-1-0, and at these planes indium and timonite is actually quite special. It's a non-polar facet, meaning that the indium and the intimonite atoms stick out equally much, so there's not more positive charge compared to negative charge, it is non-polar at the surface. Of course until the moment you start chemically treating the surface, then you maybe rip out these antimony atoms and leave extra indium atoms or vice versa. So this you have to prevent. So if you make your contact, for instance schematically here there's in green the semiconductor nanowires and in yellow the gold contacts, then before you put down the gold contacts you clean it, and one way to clean it doesn't matter what you actually do, one way to clean it is this plasma edge. And it turns out that if you do a plasma edge on this indium and timonite, then you get some band bending at the surface where you do this cleaning step, and the band bending is upwards. So even if you have a nice metal and a nice semiconductor at the surface, there's a little upward band bending that gives you a reflection of the electrons at the interface. It's a tunnel barrier. On the other hand, if you use a sulfur edge, then actually it turns out there's an accumulation layer at this very surface. So in this case the electrons experience, don't experience a tunnel barrier when they go from the gold into the semiconductor. They could just, you know, there's a much higher probability to go in. So it's very important besides having, you know, good wires that you have good contacts and this one, you should not take this argon plasma edge but instead, you know, another recipe. If we do that, we make these devices. We have a long few micrometer long indium and timonite nanowires. Here you see a very simple device of gold contacts. There's a gate buried in the substrate in the back of this plane so you can change the potential. And if you measure the conductance through the system, you see very clearly that the conductance here in units of 2 square over 8 as a function of gate voltage. If there are no electrons at all in this intermediate section, so it's completely pinched off the conductance, of course, zero. But if you open up the constriction, let electrons in there, then the conductance increases to the quantized value, 2 square over 8, second plateau, et cetera. Also if you, you know, if you look at this finite bias measurement from this finite bias measurement, you can also extract the sub end spacing between these one dimensional sub ends and various samples give different numbers but it's always more than 10 millilectron volt. Between 10 and 20, 30 millilectron volt, these are the typical numbers for the orbital sub end spacing. This data is not typical data. This is the best data we've ever measured. But if I show you some typical data, it still looks okay. Here you see six samples that were all fabricated on the same wafer. They were all measured. And they all show features at the quantized plateau level. Sometimes nicer, sometimes less nice, but they all have that characteristic feature. So what it means is that at this stage with this new sort of focusing on the interface, we not only have quantized conductance in the wire, but you can also measure it from the outside. This is all taken in zero magnetic field. If you now look at magnetic field dependence, you get this color scale graph where dark blue in this case means no conductance. Red is high conductance. And here you see these regions of constant conductance in between. And these are again the plateaus. To show you some line cuts, here at zero Tesla, this light blue region is the first plateau at two weeks quite over age. And here you see a little bit of a darker blue region. That's the first spin-split plateau, which grows if you increase the field to four Tesla. So from this data, if you look at this difference here, you can extract the Zaman energy, as well as the g-factor in this material. And this is very special about indium and timonite. It has a g-factor of around 50, which you should realize is 100 times larger than we're used to in gallium arsenide. So this is actually one of the reasons that we choose indium and timonite for these studies. So that's a large number. So this is a large energy scale. And we should keep that in mind. So first ingredient, one-dimensional wires, they show quantized ballistic transport. Second is spin-over interaction. And the simple idea is that we have a wire on the substrate. We have an electric field asymmetry between substrate and the outside vacuum. That field is perpendicular to the momentum of the electrons in the wire. If you take this out of product, you get effectively a spin-orbit magnetic field, meaning that if electrons travel through the wire, they rotate about this axis of the spin-orbit field so they go from up to down, et cetera, et cetera. And the length over which they change their spin by pi, that is what we know as the spin-orbit length. Now can we probe the effect of the spin-orbit energy in these indium and timonite nanowires? Again, in simple transport. Complicated slide, but the pictures are actually quite simple. These are the spin degenerate one-dimensional subbands, the lowest subband. They are, in this case, degenerate because spin-orbit interaction is still taken to be zero right here. And if you change your Fermi energy from below here into the subband region, you make a transition in the conductance from zero to one time to e squared over h. Now if you add spin-orbit interaction, the picture over here, what you do is you horizontally shift the two parabolas so you have a separate blue curve for, let's say, spin-up and a red curve for spin-down. But if you look at transport in this picture, then still if you go from below here, if your Fermi energy into the subband region, you immediately hit all the states, the same number of states as you hit in the last picture. So again, you go from zero to a value of two e squared over h. So simply by measuring the transport from the case of no spin-orbit interaction to the case with spin-orbit interaction, you wouldn't see any difference. If you now start applying a magnetic field and we zoom in on these lower curves in the magnetic field, first of all, a magnetic field that is along the axis of the spin-orbit field. In that case, the external field just adds up to the spin-orbit field and you just shift the two parabolas without making any mixing, introducing any mixing between them. It just adds up to the spin-orbit field. If you apply the spin-orbit field perpendicular, so the external field perpendicular to the spin-orbit field, in that case, you start to mix up the states at zero energy where they crossed without an external field. You open up a gap of size to Zeeman energy. And this is an interesting system because in this case, if these vertically shifted parabola, if you change the Fermi energy from no conductance below, you start to hit the first sub-bent, you have one single spin-resolved sub-bent, so now you go from zero to half two e squared over h before you hit both sub-bents right there and you go up to one times two e squared over h. In this case, there's an extra dip introduced that below no conductance, first, if you hit it right here, you go to two e squared over h, but if you go into this gap, you have less states that contribute to transport and you drop down to half the value. And this particular gap, what people call the helical gap, is actually called helical because the right movers with positive momentum have predominantly a spin-up state whereas the left movers with left momentum, they have the opposite spin. And so spin and direction motion is now strongly coupled. Now, the third case is sort of in between where the external field is actually under some angle, not perpendicular, but under some other angle with the spin-orbit field, and in that case, you get the mixture between these two cases, so one shifts more down, but nevertheless, you also open up a gap, so first you get the spin-resolved plateau if you hit the Fermi energy right there, then there's a small region in energy where you have all the states, so you go to two e squared over h before you get into the helical gap and you drop down to half the value. So these are sort of the, you know, what you can expect if you apply your external field in the presence of a spin-orbit field. Now these pictures are hand-drawn and they look good, but Daniel Lawson, his student Diego Vainise, has indicated if you do numerics on a system, it is actually not as simple. There's sort of a complication. And the complication is such that if you model your system with a extra confinement in the middle, then you have your bands, which let's say are, let's say in the point with largest confinement are in this case, in this particular where the Fermi energy hits, let's say these lower energy states. If you move outward towards your contact, then at some point your potential goes down or your bands go down, and this will be the case in the contact. Now the difficulty is that there's no smooth adiabatic connection between this case in the constriction and this case outside the constriction. At these states, if you move them out, they actually have to zener tunnel into the higher band in order to end up there. So by optimizing parameters like the smoothness of the potential, et cetera, you can still get features, but the features are not so, you know, not as stepwise nice as I showed you in the schematic diagram, but there are these additional oscillations, fiber perotide oscillations, but you can sort of still see sort of that there's this region over here where the conductance is suppressed. On top of these fiber perot oscillations, there's still this region of suppressed conductance. These are line cuts at zero magnetic field, and it actually helps if you also use the magnetic field as an additional parameter, because if you do that, you can create again these two dimensional plots and maybe your eye can sort of smooth out all the oscillations and still see a pattern. Now the pattern that we see in the measurements is this panel of gate voltage and magnetic field up to five Tesla. Again, these colors of dark, no conductance, blue, quantized plateau at half the quantized value, then there's more light color that's a higher conductance, but then there's this region where you go back to the dark blue color. Now this, you can extend down your simulations to a two-dimensional graph, which was done by Michel Wimmer. And also here in this case, you see this region, the split region, where the conductance goes down, and in the numerics, you actually know what you're doing, so you can extract the associated spin orbit energy if this is really the helical gap. Now from comparing, you find a spin orbit energy of four milli-electron volt, and that's actually a very good value. That's a larger value than we had thought of earlier. Now this is preliminary data, but at the moment we have another device that actually reproduces this data almost exactly. So the confidence is growing, and this is indeed the helical gap that we're looking for. Most importantly, actually, we wanna extract this number, which you could take from this graph that's being closed, medium of order, a milli-electron volt. I can comment on that. So this theory was done as a non-interacting theory, no self-consistency at all, and this is a real experiment, which is a self-consistent experiment, and it's really the, and it's really the, we're much more in a constant density regime in the experiment in comparison to this calculation. It's from the screening. This was under an angle, so it's under an angle, because you first go to half the plateau, then you go to a higher value, then you go back, so you have this region where you're under an angle. But now we have data. My chairman says that we have to have discussion later on because it is being recorded. But nevertheless I wanna answer your question is that, so the thing to do is to change the angle. If you change the angle, for instance, you go more perpendicular then this should decrease and this should grow, and that is what we've now seen in the new experiments. So let me move on. The helical gap is not so important. What we wanna know is what is the value for the spin-orbit energy, and we have some alternative measurements based on localization, weak localization, as well as weak anti-localization, where we also extract the spin-orbit energy, this ESO of a value, in this case somewhat smaller, but it's still close to a milli-electron volt. So conclusion is that the spin-orbit energy, the Rajba energy scale, is of order a milli-electron volt, and that corresponds to a length scale of about 15 nanometer. And kind of interesting, and actually it's important if you compare it to numerics, is that with these values, the spin-orbit energy is about the same as the Zeeman energy at one Tesla, which is more or less the magnetic field scale where we are going to look for these Majorana fermions. All right, so next is superconductivity. So for these, to test superconductivity in the system, we make various type of devices, including this one where we have a normal contact on the left, gold. Here you see the nanowire, and blue there is a gate, so we can actually change the potential in this region, make a tunnel barrier here, before the electrons go into the proximitized nanowire section underneath this purple color. Here we use the Jovi-Methanium nitride in order to sustain an external magnetic field. The first, we'll take away this barrier, so the voltage on the gate is very positive, and it's very easy for electrons to go from the normal metal into the superconductor. And in this case what you expect is that processes like Andreev reflection occurs. And Andreev reflection has a nice feature that incoming electrons form a Cooper pair, if they also grab an electron from below the firmacy, and this actually enhances the conductance by a factor of two, because instead of having one charge that is transported, we now have two. So the quantized value for plateaus is four e squared over h, instead of two e squared over h. Since our wires are nowadays, let's say wires and context, so quantized plateaus, we can actually do this comparison. So here again you see the differential conductance as a function of gate voltage. And the red curve is in the normal case, where only electrons or quasi-particles can go through, and this shows a quantized plateaus at two e squared over h. If we turn on superconductivity, and we actually do this by lowering the bias voltage, you see that there is an enhanced conductance in this region of the plateaus, and if you take this value somewhere around here as the enhancement, put it in the formula from Karla Behniker from a long time ago, you find that the transmission probability for an Andreev reflection is actually larger than 0.9 in that region, meaning for us that the contacts are very transparent. So very similar as this quantized conductance with the normal context, also the superconductive contact has a very high transparency, very close to one. So next, so this is the region for enhanced conductance where Andreev reflection contributes to the current. We now change our focus to this region, where we actually go close to the pinch-off regime so that we find more negative voltage to this gate, so now there's a tunnel barrier in between, suppress actually Andreev reflection, you see the black curve is below the red curve, and in this regime we can actually do spectroscopy on the states in the superconducting section. So here's a sample, we actually pinch off the, it's a new sample with more contacts, you can do more things, but we pinch off the upper gate here so the transport flows from this normal contact and out the superconductor into the electrical circuit, external circuit. These two gates, the big one underneath and the small one that forms a tunnel barrier are actually connected in this particular experiment. And if we change it, we see mostly the effect on the conductance from changing the tunnel barrier in the system. And we apply a field along the nanowire. So the color scale graph of magnetic field vertical and bias voltage horizontal looks like this, it's actually easier to look at line cuts. First of all, the line cut very close to zero magnetic field, it's a black curve which has these two BCS light looking coherence peak and a suppressed conductance in the middle. If you apply a magnetic field at this red dash line, that's at half a Tesla, you pretty much see the same thing, the gap has not decreased very much, and the sub-cap conductance is still strongly suppressed. So these are just two values and you see if you look at the colors that even up to, I don't know, a Tesla or so, you still have an induced gap in the indium or in the induced gap in the indium at the nanowire. So if you put these ingredients together, that's a 1D conductance, large maneuvered energy, there's superconductivity that you can see in this Andreev enhancement as well as a hard disk gap. And we can now put all these things together and you put them together actually also tuning the gate voltage or tuning the chemical potential in the right region where you have this helical gap. Okay, so this is the picture. We have our nanowire, there's a gate to change the potential, that gate allows you to use a tunnel barrier, you fill all the electron states up to the Fermi energy. If you add a superconductor to the system, it opens up a gap in the nanowire section and this gap will actually necessarily go to zero near the end of the nanowire. So there's a decreased gap here as well as on that side. And at these two points, you have space, at least in this lower, let's say in these regions of lower gap values, where you can have bound states. It's basically a particle in a box bound state and these are the Andreev bound states. What is nice about these Andreev bound states is that they always come in pairs and it's symmetric around zero energy. So if you find one at positive energy, it should also be one at negative energy and that's how you can identify a resonance as being an Andreev bound state. If you make the transition to a topological regime by including spin-over interaction as well as applying an external magnetic field, then this actually superconducting gap gets a different type of pairing. It becomes a P wave pairing and now these Andreev bound states which came in pairs on one end now come in pairs on the two opposite ends. So this state is now split non-locally where one occurs on the left and one occurs on the right. They're now taking apart and put at a large distance away from each other. And these states are the ones that everybody's looking for because these are these Myerana bound states, zero energy states. We take these samples. We again pinch off the upper part so we have a very simple geometry from N to S and we change the potential on these two blue gates. We measure transport. This is again in the panel of field, magnetic field bias voltage. Here you see already the first curve near zero magnetic field. If you increase the field along the nano wire, you see that all these colors change. Dark, for instance dark here, it's very low conductance. Also here, blue is intermediate, red is high conductance. And you see if you follow the zero bias line you see that there's suppression here, there's a peak there and then it's suppressed again. Now if you take two line cuts again, then at zero magnetic field we have the black curve and inside the black curve, there's the PCS coherence peaks, you see extra resonances but they come in pairs. These are the Andrea bound states that come in pairs. If you change the magnetic field further, these pairs, these states sort of at least the inner ones merge leading to a single peak at zero bias. Now this is a measurement where we have a certain gate voltage and now we're changing the magnetic field and get this spectrum. Next thing you can do is can we actually extend this zero bias region if we play a bit more with the gate voltage. If we play with the gate voltage we may be more centered inside the helical gap, extending the region over which you have a zero bias peak. First of all let me show you because this is actually the sort of a big peak. If you could tune a little bit of the gate voltage and sometimes you have a very nice curve. This is a very nice curve and it's nice in the sense that the height of the peak here exceeds the normal state conductance outside the gap by about a factor of two or more than a factor of two. So it's not always a peak that is sort of hidden inside the gap, it can come out and be the dominant peak in the spectrum. So if we start changing gate voltage and we have a magnetic field in this case in the x direction so that's actually perpendicular to the plane sample then this is a typical spectrum. You have the bias voltage increasing to both ends, gate voltage becoming more positive so you're adding electrons in the system if you go up and there's a sub gap resonance symmetric around zero that you see with these two lines. If you increase the magnetic field now but take the same graph in terms of gate voltage and bias voltage then you see that these two states come closer together, they start touching each other, if you continue they really overlap and of course the next question is if you continue with increasing the magnetic field do they move right through each other or do they stick, keep sticking to each other? And they stick, still at 360 and also at 450 they still stick and now they stick at a range in gate voltage which you can read off here which is 100, 150 millivolts. And so here we've optimized also the gate voltage range over which this magnetic field or over which this zero bias peak is stable. So there was another feature of spin orbit interaction that is important and one way to test if spin orbit interaction is indeed a crucial ingredient is by actually rotating the magnetic field. So you keep the amplitude fixed, you sit on your zero bias peak, you keep the amplitude fixed but now you rotate the field. And there's various planes, this is the XZ plane which is this sort of a purplish plane which is perpendicular to the Y axis and the Y axis is our spin orbit field axis. If I change the angle in this plane and if you think about the spectrum, the gap spectrum inside the system, as long as you stay perpendicular to the spin orbit field the gap spectrum doesn't change very much. Indeed, if you take a measurement where you rotate over two pi, the zero bias peak stays at zero bias for all angles. There are small splittings for some angles but more or less it's a zero bias peak over two pi. If I now rotate in this blue plane, which, so if I rotate in this blue plane, it occasionally will actually be aligned with the spin orbit field. And pretty much everywhere it will have a component along the spin orbit field. If again you think about the spectrum, this component is along the spin orbit field will actually skew the bands. So you create some gap closing, it's an indirect gap closing, but if you do transport, you no longer have your gap if you start skewing the field. If you do that and look at the spectrum, then indeed the zero bias peak is basically not never visible, maybe there's some crossing points right there, but there's, for the other angles, it has disappeared. And this is actually at pi over two, we have the external field aligned with the spin orbit field, indeed you see no zero bias peak right there. Slightly different samples at different gate voltages, show you the same thing, zero bias peak in the plane where you're always perpendicular to the spin orbit field, but if you have components along the spin orbit field, the zero bias peak disappears. So this rotation is really important. Now in the remaining minutes, let me show you a few more measurements that actually are a little bit older, but sort of complete the picture of what can you expect from Mayuranas in this system. First of all, a prediction that was made by several groups, I just flashed the prediction or the paper from Zanko das Sarma, that if your system is not infinitely long, so the two Mayurans are not infinitely far away from each other, but they are at a finite distance, their wave functions have some overlap, and this means that the zero bias peak actually will start to, because of this overlap start to split to finite energy, and this splitting is another feature that one can look after. So here you see another panel where the zero bias peak, so you need a trained eye, but there's a zero bias peak, this red peak along here, which in the line cuts, so this is the same data, but now in terms of line cuts, you see very clearly coming up here in the middle. If now just change the voltage, sorry, if now just change the voltage underneath the section that is covered by the superconductor, then I effectively make this system smaller from this distance to this systems. So the two Mayurans are separated by this far at the upper panel, but if I change these voltages, I make the separation smaller, and you do see a splitting coming up in certain regions. And if you look again at the line cuts, you can clearly see the splitting. Sometimes the splitting is really very clear. For instance, in this particular, it's just another data set. In this particular graph where the zero bias peak extends over almost a Tesla, if I change the voltage here right in the middle, gate section, it splits up very clearly. So what it means in my remaining minute is that by changing something in the middle, you're doing something that does not affect the tunnel barrier, you're doing something in the middle. So whatever the zero bias peak is, it's not something from the outside or the tunnel barriers. And the picture is more like this, where you break the system into two pieces, and effectively you create a smaller distance between adjacent Mayurans. Now, let me, under a big pressure, and I respect your pressure, continue to the conclusion slides, where if you look at these recipes, what it really defines this recipe from Luchin and Oryk is that you can make an extended region in parameter space where you have this topological phase and where you should have Mayurans. And you should make it as big as possible. It's rigid over a large range in B and gate voltage. And these experiments, what they actually show is that even in other scenarios, if you have another alternative theory for these zero bias peaks, then that theory can no longer, because of these experimental data sets, can no longer be based on an effect from a tunnel barrier. It can no longer be based on Coulomb location because our transmissions at the interfaces are very large, close to one. The wires are ballistic, so your theory can no longer be based on localization effects. And it can also be not be based on Coulomb effect because of the data that I just skipped. You can show that we have an upper bound for the G factor, which is actually 100 times smaller than we have measured. Now, I cannot be taken, pushed away from the stage without my contribution to, and I have to flip through it, my contribution to Boris, because in early 2000s, 10 years ago, we had a very nice program with Boris and Daniel Loss and Charlie Marcus on qubits, on spin qubits. And I believe that also now the time has started for qubits, but in this case with my Iranas. And I think as with the spin qubits, I expect as many fine results that we can report at many nice conferences. And if you look at these pictures, you always have to look for a few seconds, hey, who are these people? Ah, okay. With one person, you always recognize immediately. Thank you very much.