 Right, for our last talk of the session we have John Saunders from Royal Holloway. So thank you indeed to the organizers for inviting me here. So the point of my talk is that helium is a material and it's simple. So how can we manipulate helium and do something interesting? And also we know how to get to temperatures in the micro-covine regime. So how can we work with people from this community to advance the cause? So I'm from Royal Holloway. So first a few words about Piers and Royal Holloway. So I'm I think in the century 2000 to 2010 in the classification. So Piers was instrumental in starting the theory of condensed matter group at Royal Holloway which is small and perfectly formed. In some sense then this is one of Piers' second homes. You see it's rather stately in appearance. He founded the Hub of Theory Consortium which is a collaboration among theory groups in the London area and with experimentalists on the Rutherford-Aberton laboratory site. He initiated condensed metaphysics in the city which runs sex in the city a close second I guess. I'd like to personally thank him for scientific collaboration and support over the years and helping to make contact between the helium community and this community and particularly its theorists as well as experimentalists. So this is an experimental talk so here's some cryostats. These produce temperatures down in the few hundred microcarbon range. So we have one that's concentrated on looking at helium from the bottom up as it were. So we have an atomically flat surface of graphite and we grow a layered helium film on that surface and that gives us a lot of flexibility. The other approach is top-down so we engineer a nanofluidic cavity and we fill it with superfluid helium-3 and we see what the confinement does to the superfluid. And then we have a third nuclear demagnetization cryostat which we've dedicated to working on strongly correlated electron physics. So the two things we've been doing most recently are to try and solve the problem of cooling a two-dimensional electron gas to blow one milliculving which is important for studies of the fractional quantum Hall effect. And we've succeeded in getting a world record temperature of around one milliculving by actually borrowing techniques from the cubic community as to how to reduce power input into your samples. And most recently we've been working on the silicon activity of the helium-2 silicon 2 that was referred to briefly by Jimmy earlier. So maybe I'll start off with that then. So I'm going to skim over the surface of many of these topics just to give a flavor of the kind of things that are possible in this temperature regime. So there was this report in 2016 then that the canonical heavy fermion superconductor with an in-plane quantum critical field of about 16 millitesima underwent a superconductor heating transition at a couple of milliculving and you can see that there's a clear Meissner effect that was observed in low magnetic fields. Also what was observed was a heat capacity peak that was attributed to nuclear spin order. So there's an interplay between nuclear magnetism and superconductivity. And the problem was that there was no transport evidence of superconductivity and transport was perceived to be a difficult thing to do. So our approach then was to use squid amplifier-based techniques to measure the resistance. So what do you do? You can do Ohm's law or you can measure the noise across a resistor. And so here's the circuit. So this is a single crystal sample. The technique allows us to measure a single crystal sample, which has got a resistance of typically a millio. And so in this mode, the noise mode, you get Nyquist-Johnson noise and that. So if you get the red stuff for a minute and that drives the current through the input inductance of a squid and you measure that current. And from that you can and it's frequency dependence. You can that noise spectrum, you can determine both the temperature of your sample, which is handy because knowing that your cold is important. And you can also determine the resistance of the sample. Alternatively, you could do an AC drive and then you can decompose then the really imaginary parts of the current that you measure here in terms of the sample resistance, which is dominated by this is the C axis. So it's dominated by the resistance in the AB plane. And the contact resistance, which is currently leaking out of the sample through the contacts, through these leads and into the input circuit of the squid. So both the contact resistance and the sample resistance then show the well-known transition from T linear to T square behavior at the antiferromagnetic ordering temperature. So this is what happens is you go to lower temperatures so the blue dots and noise measurements, they show this kink at this feature B, which was seen in the magnetization data. And then the total resistance, which is now the sample resistance plus the contact resistance. The sample resistance has got a strong contribution, is dominated by the resistivity in the AB plane. And the contact resistance has got a strong piece that's coming from the resistivity along the C axis. That sort of meanders down to zero. And then in the driven measurements, we can separate out the sample resistance, that's AB, and the contact resistance, that's along C. And features of this that are worthy of note, then, are that the sample resistance shows a transition to supernativity down here, where there's action along the C axis at some much higher temperature. And if you add this curve here, with this curve here, they should sum to the red curve, and that agrees with the noise data, so everything is internally consistent. And then the other neat thing about this technique is a bonus is when this entire loop, including the sample, is supernatting, then the flux within that loop should be quantized. And so that's the definite proof of macroscopic quantum coherence in that loop. So we see that in this blue region here. So there is absolutely no question that this material is supernatting, but it's doing it in a very interesting way. It's a three-dimensional metal, but the supernatting response seems to have some anisotropic character to it. And if you look at the poster by Jan Asedel from Dresden on Serium Rhodium Indium V, that's the material that I can see around in the literature that most closely resembles this kind of action, the difference in the behavior along the C-axis and on the sample. So when we first saw this kink, we identified that as it just felt that it had to be a phase transition. There was discussion in the earlier paper that this was supernatting fluctuations, but we think there's a genuine phase transition here. And this is some kind of dissipative supernatal. So then when we apply a magnetic field, now we're looking at essentially the sample resistance. You see two things. The transition temperature is pushed down a bit. And in the larger fields, we see re-entrance of the normal state. And this curve here is looking at resistance as a function of temperature on a logarithmic scale. So you can see this corresponds to a fraction, about 0.3 of a miliome, and this is about 15, 20 nano-ohms. So we've got a factor of more than three orders of magnitude change in resistance. So to the man in the street, that's a supernatal. And in field, we've got some dissipation here. We've also got some interesting signature here at just below 2 mili Kelvin, which we think is the magnetic transition in the sample. So if we summarize that on this, this is the most honest and therefore the most confusing phase diagram that I could plot. There are results here from two samples. On sample three, the blue sample, we did both the noise measurements and the driven measurements. And sample one was the first sample where we just had noise measurements. And this is showing various features and their dependence on magnetic field. So this feature here is in the driven measurements, the resistance going to zero. And so this slope tells you that you're talking about heavy fermion superconductivity. The coherence length is huge. It's 300 nanometers. The effective mass is like 100, something like this. This is a heavy fermion superconductive that's emerging from a normal fermi liquid state with some kind of as yet unknown anti-ferromagnetic order. The putative electroneuclear ordering temperature, which is around 2 mili Kelvin, we also see in the data that's down here somewhere. So we think the quantum critical origin of superconductivity proposed by Schubert L is unlikely. Sorry, Chi-Miao, but that's what the evidence is telling us. I can't go into detail, because I want to talk about helium in a minute, but this is evidence for multiple superconducting phases. We're wondering whether it's spin triplet, because YRS has got known to have strong ferromagnetic fluctuations. And talking with Gil, ferromagnetic spin fluctuations tend to lead to relatively low TC, so that might tie in with why is it in the terbium compounds that TC's are so low? If it's a spin triplet, hey, maybe it's a topological superconductor. It's something to make you go into work the next day. So at this low temperature, there's evidence for a transition, this electroneuclear transition, which is influencing the superconductivity. And this TC against field line looks like a powerly limited line, so that may be also indicative of a spin triplet phase where the d-vector, the direction of spin projection zero is by spin orbit coupling confined to the AB plane. What's the origin of the intrinsic and isotropy of the superconducting response? What's the origin of this dissipation? If this is a dissipative superconductor, it's a dissipative superconductor in zero magnetic field. So what are the topological defects then that are moving around that are causing that dissipation? So it's very exciting material that we want to pursue. So in my role now as the ambassador for helium, I'm going to switch to helium if you don't mind. So we have a fermion and we have a boson and the idea is to manipulate these isotopes, this material in 2D and quasi 2D to create new materials. The advantage in comparison, for example, with the penictydes is that they're simple, maybe they're model systems, they're probably not really quantum simulators because we can't dial up a Hamiltonian like the cold atoms people can. But the advantage of that also is they're going to get surprises. We're going to get emergent new quantum states. And the history of the subject is quite promising. After all, we have the first BEC, the first topological clear evidence of a topological phase transition. Landau established the standard model of interacting fermions with liquid helium-3. We have superfluid helium-3, which is the first unconventional superconductor and it's also topological. As I'll say in a minute. So if we look at the bottom-up approach, then here's the atomically flat surface of graphite. And my assertion then is these are the classes of system that we can study. Two-dimensional Fermi liquids, what Hubbard transitions quantum spin liquid, heavy fermion system with quantum criticality that I learned a lot about actually thanks to Pierce saying I could come to this meeting in 2006 and I met with Katerine and she had all the great ideas about this and so on. And an important future goal is to try to achieve a monolayer two-dimensional P-wave superfluid. How is it that we can get that variety of systems just by growing helium films on graphite? Two ingredients. The first is that the films are atomically layered and the second is that we can pre-plate. So we can take the graphite and if we just grow a helium-3 film on top of it, then we'll have a solid paramagnetic helium-3 layer and then a fluid layer. But we could do something else. We could take the graphite and we could put two layers of solid helium-4 or two layers of solid hydrogen or two layers of solid helium-4 and two superfluid layers. And each of those, each time we pre-plate in this way, we get to different physics, the kind of different physics that I'm describing. So what about the top-down approach then? So the idea then is this is the phase diagram of bulk superfluid helium-3. We have two phases, A and B. A is chiral and it breaks time reversal invariance and B is a time reversal invariant superfluid. So the contention then is that in the periodic table of topological quantum matter, arguably the missing element is a topological superconductor and superfluid helium-3 provides a neutral version of that. So let's try to use that and ultimately gain access to the surface and edge excitations that emerge through bulk edge correspondence. And on the surface of the B phase, for example, those will be myeranolite linearly dispersing excitations. And so we're gonna do that by confining the superfluid in some engineered slab geometry. Technically to do this, we had to develop very sensitive NMR techniques to see the very small amount of helium confined in these slabs and we had to develop the nanofluidic cell technique. And I'm gonna call this topological mesoscopic superfluidity because the length scale that governs the height of cavity of interest is the coherence length which is pressure tunable in superfluid helium-3. It's about 80 nanometers at zero pressure going down to 20 nanometers of the melting curve. So what we can do is we can take a cavity with fixed physical confinement, then the effective confinement is the height of the cavity divided by this characteristic length scale, the coherence length, and we can tune that simply by tuning the pressure. So that's nice and flexible. And this is a boring list of the cavities that we've studied. Most recently we've gone down to 100 nanometers because what we're interested in doing is accessing the region where the height of the cavity is less than the coherence length. And in order to do that, we have to ask ourselves the question, what is it that suppresses superfluidity? Now normally it's going to be a disorder within the material, but we're talking about liquid helium-3. So there is no disorder within the material. So the suppression comes from surface scattering. But we can tune the surface scattering by putting a superfluid helium-4 film on the surface. And when we do that, the quasi-particle scatters specularly. And we've demonstrated in the 200 and 100 nanometer cell that we can achieve specular scattering, eliminate TC suppression. And so that will then allow us, by the top-down method, to access the quasi-2D limit, to get to a regime where in the normal state, the liquid has size quantization because of the finite dimension in the Z direction and move over into a two-dimensional superfluid regime. And then more generally, you might imagine this idea of that justifies me putting three buzzwords on the top or even four. So now height is the new tuning parameter. So by just tuning the height of our nanofluidic cavity, if the height is very small and we had rough walls, then we would have normal liquid here. The height is larger and we'd have superfluids. So we can make an SNS junction. If this were B phase, then we would have a very clean interface between S and N. It's almost like making a PN junction in silicon. It's the cleanest interface that you could possibly imagine. And at that interface, you're going to have Majorana fermions. How would that affect the tunneling transport between these two superfluid regions? You could create, let's call it a quantum dot or a mesa of superfluid. You could create interconnected cavities which could have the same height or different height. So I can, this is the buzzword slide. I could call that superfluid mesa materials. I could break rotational symmetry by having a series of posts in which I will, that breaking of rotational symmetry will induce new kinds of superfluid helium-3 P wave-order parameter in a controlled way. I can make nano channels in which it's predicted that I will have a chiral phase, a polar phase, or in your language a pneumatic superfluid and maybe spatially modulated phases. And talking of spatially modulated phases, there's a prediction that at the boundary of the B phase and the A phase, a striped phase, a spatially modulated phase would appear. It's the analog of FFLO. And its origin comes from a domain wall between here's a piece of A phase and, sorry, B phase and here's another piece of B phase where we've just changed the sign of this component of the order parameter. And these domain walls have negative surface energy and this arises because you get de-pairing by, if the quasi-particles go through a scattering event that involves a sign change of the order parameter. And so if you have a domain wall, then you'll have a sign change when you scatter from the surface and you'll have a sign change which compensates that when you go through the domain wall. And so you get this negative domain wall energy. And so the beauty of Superfluid Helium 3 is you can determine the order parameter by nuclear magnetic resonance and that gains, under confinement, you get access to various averages of the order parameter. If we just look at this one in the striped phase, we have this plus minus minus, sorry, minus plus minus plus configuration. So this average is zero and what we find is something that's actually not zero so we can rule out stripes. And on the other hand though, we have something that deviates from a uniform phase so we claim that this is evidence for a two dimensional spatial modulation. So time is marching on. So I'm going to skip, I think, to this topic which is something that peers played a role in. Just quickly through, we can see mass diverging mock transitions in the two dimensional Helium 3 layer where the Landau parameter F naught A is more or less a constant so that's consistent with your most localized fermion model. And we believe then that this mock transition which is happening at significantly smaller fillings than one half corresponds to actually a Vigna mock hub of transition. So this is a density wave in stability in two dimensional Helium 3 and that's related to these other systems listed down here. This is the work on condel breakdown quantum criticality which emerged from this meeting in 2006 with Catherine. We can look, I'll bring this up actually at coupled fermion boson systems. So here we have two solid layers of Helium 4, two super fluid layers, and we're forming a two dimensional Fermi liquid in a surface state on the super fluid Helium 4 and we can tune its density. So we have the possibility there of coupling between the Helium 3 via surface excitations and probably the most interesting question is going to be what happens if we can tune the Fermi velocity through the sound velocity. And this is quite an interesting paper on coupled fermion boson systems that I would recommend. So we see a remarkable dependence of the Landau parameters on two dimensional density. I think I'm gonna try and say this because I think I have time. Roughly speaking, these two Landau parameters F1S and F0A are of equal magnitude and opposite sign. That was a very surprising result. If you just have S wave scattering, this is what you would expect. G is the interaction parameter that has this logarithmic form in two dimensions. So you can see F0A is first ordering G and F1S is second ordering G. So clearly S wave scattering doesn't work. We have to have at least S wave and P wave scattering. And then if we take the analysis of this Chupacoff and Sokol paper and follow it through, the conclusion that we arrive at is that back scattering is dominating. So we have a two dimensional helium three system where probably it's characterization in terms of Landau parameters is not useful because the dominant scattering term is back scattering which would have to be represented by an infinite series of Landau parameters. So it'd be worth redoing the theory for that. And so here is the super solid idea. So super solids in bulk, solid helium four have, to put it mildly, a checkered history. So what we have in two dimensional helium four monolayer as we tune the density through is by over a relatively narrow range is this family of curves. This is the mass decoupling of the helium four film from the surface. So effectively think of this as super fluid density. And Derek Lee at Imperial pointed out to us that we could describe this by some single parameter scaling formula where there's one energy scale that determines the characteristic temperature dependence and also the size of the super fluid density at T equals zero. And this data scales on two families of curves quite beautifully and to explain the linearity of the temperature dependence at low temperatures then we invoke an excitation spectrum that has a very soft minimum. That soft minimum according to the fame and Cohen argument implies that the structure factor is strongly peaked. And so Piers suggested this quasi condensate wave function. So that's like a macroscopic shirting a cat state. If solid is dead and super fluid is alive this is an entangled state of dead and alive. The end.