 je to početniko vsega vsega predikšnja, je to početniko vsega ekonomijne malosti, v 2008. S tem, da je vsega vsega, vsega vsega vsega, na kočanju, vsega vsega, na kočanju. To je tako početniko, da ne boš, ali početnimo do L.A. v 1998. And Boris told me a short story. I'm sure many of you know so I'll be very quick about it. The story is how Rochal became so rich, and he was a young man in Paris, and he used to go to the south of Paris, to the poor people's market, and buy one apple for one cent, and it was dirty and not very appealing, so he cleaned it and polished it, Išlo v nordnju delu Pares, kako malo vših boši, in so bi se za 2 sveti. And then he drove back to the south part of Paris and bought two apples. Do the same thing, so we did it for two weeks, and his father died and left him a billion dollars. So that's the story. And I think it sums up everything we know about capitalism now. And I don't know about you, this I found on the Internet. To je tukaj fotograf in imač nekaj Nathan Rothschildov. Vsih je tukaj nekaj... Tako, tako početno, da imam tukaj kolaboratori, da mi je pomočil na tukaj tukaj tukaj. izmeni mnega grupa. In da... Tako, tudi, vi svoj sem v tom vrste pravnozakovljeni izvrstavnozakovljeni, in do vsev svoj temo tako, da bo inzitri inzitri, ne zelo prezijen. V tem sej križen, in Jelen Goldmann, kod svoj izvrstav, svoj izvrstav ni nezimnozakovljeni in ne zelo vse začen, vzlušaj na vsega izgleda. Tako, če je vsega parametri v sistemu, ki je zelo način, kaj je koncentručnje, nekaj nekaj zelo način, in vsega vsega, ki je vsega vsega v magnetu. Vsega je bilo vsega tako zelo način. Vsega je, kaj je, nekaj je, kaj je izgleda Netko še superglibne stavy, s takimi rečenimi stavami, da je večga danes naprejfaom magnetica. Po enim dežen' sinstavu je bila však ješnja neko je nožilja, nič nožilja, da vse očvarje bolj jezva, je začala, da inzulatorji ne neč neč neč nekaj nebo tega magnetica. Inzala, da vse zelo postido vse tak je neč nekaj nezaprejfa magnetica. v semom mače. Teoretično, ki jih so naredil v 90-jih, je, da je vzvečnja izgleda je nekajけれgo superkondaktivitij. Vzvečnja superkondaktivitja je pravda režimna, in vsečenje na razrednji stup. Na kaj je površene teoretike vseč, da počutno vsečenje, je bilo vsečenje, na kaj je bilo zdaj, da je to vseč način. Kaj pa vsi vsečenje, kajne in vsečenje, vsečenje, vsičenje, načinjati, da je krupiče vsečenje, Tudi, ki se nespešnimo, ki se veče skupnili, nespešnimo, ki se nešto veče skupnili, je ta način, da zelo vsečimo všeške, kako sem potrebnimo vsečino vsečino vsečino način. Tudi, ki se nešto veče skupnili, je to način, da nešto veče, nespešnimo, ki se nešto veče, in v superkondakcij stah, kaj je taj sempli, bo resistenja je zelo zelo zelo. Oselječenje je tudi ljudi oselječenje, in prejudicitje korresponde v požavljenju kubej. Zato, kako jaz vse insulati, tudi je tudi ljudi kubej, tudi je tudi ljudi eksperiment, in jaz sempli vse zelo zelo. Kako jaz vse insulati sempli, hen »Red« š frame, you can see that even though the resistosion is much higher you still have, this is on a log scale you still have oscillation at the same frequency as your do in the superconducting. If the frequency of oscillation represents, or corresponds to a charge of 2e in the Returnnu conductor, it is also true in our insulator. Yea, you can see it here. It's a photograph of ourünems rifle. It's just a small section, it's just an array. Rather this order, an array of holes. naredite, kar je, da si se je nekočen, kaj je superkonduktor in očen in vsega insulatora, je lahko se več nekočen del, da je zelo, ki objevno, očen in insulator, sve sem zelo, da je transporter na izgledanje sprem i nekočen. Tudi je to in očen od toga izgleda, da so, da smo v svetu početiti, vzelo na čednjih vzelo. Zato zelo, da se vsega insulatora vsega insulatora, kako jestovate iz nekaj bolj čovpivcičnih sk awakened. Kako očelijo vse meseče, da se pravimo naživamo všega transprvokrizati data. Pizera je začudovat, če je jezini. Zato vznešte mi. In je več vzljubil na prejzistu, da je zelo ta del, ki se odrečila, na tega začinil na odljubil, na jazda, da je dobro vzljubil na pojah. Se pri pukajte na vzljubil strah, da je to tako vzljubil. To je vzljubil zelo. Očal, kaj mi to dobro vzljubil. Kaj je ozljubil vzljubil na dobro vzljubil na dobro vzljubil. Zelo je dobro vzljubil na dobro vzljubil. vsega izgleda in insolatora, in v superkondaktorji, ki jih se plovila na log-logškej skale, vse ga se zelo, da je data izgleda. If you put a ruler to your data, it follows it quite nicely over all the temperature range and over several orders of magnitude in resistance and in magnetic field. This is another type of ruler. We have this straight line behavior. If you're talking about superkondaktors, this is not surprising. We have a power law dependence. The only thing that changes between temperatures is the slope of those power laws. And so you can concisely describe the transport data by this formula here, where the temperature dependence come only in the power. This can be explained by some vortex physics, if you like. It's all in the 260, 5 pages review. The nice thing is that this power law continues beyond the crossing point into the insulating state, some ways. And so again, showing a relationship between the transport in the superconductor and in the insulator. But what we find is that if you go to lower temperature, and this is what I would like to focus on today, what happens when you go to lower temperature, say below 0.2 degrees, that the deviation begins to develop, but those deviations are only on the insulating side. You can see it quite clearly here. The superconductor side follows the power law quite nicely all the way down to our noise, and the deviation begins to develop in the insulator. Let me show you this again. So on the right bottom side you can see the temperature scale, 0.2 to 0.9, and I will add more and more lower temperature, frame by frame, so you can follow. This is the same. Now I switch to two terminal measurements so the superconducting side kind of disappears. But just so that you can easily measure in the insulator, and now we begin to lower the temperature. And you can see that not much is happening in the superconducting side, although as I said we haven't been showing you this here, but you can see that the resistance traces, this is 33 mili degrees, this is 13 mili degrees, the resistance traces just become sharper and sharper, as we go to lower and lower temperature. If you want you can still try to fit a power law there, and the power is 1,009 for this particular. So let's see, 1,009. So two is from phase space consideration. Three you get from electron phonon population, and so that leaves 1,004 to go. So obviously this seems almost discontinued, but we didn't pay attention to that in the beginning. This was 2005, 2004 when we were starting to work on this. We really didn't pay attention to this low temperature, data that much. What we did do is we measured the current voltage characteristics in our sample, that's what you want to do if you have a sample where you measure in transport, one of the things you want to do. And so you take one of those insulating states, this is a particular sample, and you fix your magnetic field value and you measure the current voltage characteristics, this is the current versus voltage, and so you have insulating like strongly nonlinear behavior, but nothing radical, not different from any insulator you usually see. If you plot it on a log scale, this is not the derivative, but it's basically not very different. You can see that at 150 mili degrees, that depends on the sample, I guess, the data is still continuous, but once you go to 50 mili degrees, suddenly the data becomes discontinuous. This is not a change of the conductivity as a function of voltage, it's a given voltage threshold. This is newer data, but the same thing you see, you have hysteresis, this is on log scale, so you increase, initially you follow the black ohmic line, and then the small deviation, and suddenly a big jump into a different conductive branch at much higher current. These jumps can exceed the five orders of magnitude. This seems interesting to us, so we published this paper, and then it was also seen in titanium nitride. We called it collective insulating state, I don't even know why, it didn't, you know, something was needed, but then this was taken even further, I guess, and Vinokur and Baturina explained this with some sort of super insulating state that is mirroring the superconducting states in some way which I don't really understand. You can read it. Around the same time when we were making our measurements, three theorists, A, B, B and A, B, C, were working on something else altogether. Where is it, Dennis? And they published this very interesting paper, which I read very carefully. This is page 32. They realized rather quickly that it's not going to be very approachable to experimentally, so they wrote this paper for the experiment, and there are also pictures, so you could try to read that even though we didn't. So what they say in this paper is that if you look for experiment and manifestation of many body localization, you want to see that even in presence of weak coupling phonons, meaning that not totally zero, transition will manifest itself in nonlinear conductance to bistable IV curve. And they also pointed out in that paper that this similar stuff has been observed in etiomsilanine, which have nothing to do with superconductivity. And a year later we sort of got together, and they wrote this paper ensuring to our work in which they looked at those discontinuities in the IV in a different view from what we were used to, and that is involving the heat balance equation. What is the heat balance equation? You assume that you have no equilibrium, you have a steady state, you apply external heat, this external heat goes to the electrons, the electrons transfer the heat to the phonons, and they transfer the heat to the substrate. That's basically what happens in our experiment. You put a lot of power into the electronic system, the power is dissipated to the phonons, and then to the substrate, which is connected to our fridge. You can write this mathematically with this heat balance equation, and there are several assumptions in the theoretical paper. Two of them I will mention here, because I think they are nice. The first one is that the IV is linear, which is kind of odd if you look at the data. And the parallel linearity comes from the fact that the electron can have a different temperature, a higher temperature than the phonon, quite significantly so. The second point is that r as a function of t is a fast function, and that if you put those two ingredients into the heat balance equation and you solve it numerically, you can get a regime at low enough phonon temperature, where there are two stable solutions for the electron temperature, for the same phonon temperature. And you write this equation a bit... This is an implicit equation relating the electron temperature and the phonon temperature, and you can solve it, and you get a nice graph like that, and you can see bounded inside the black curve is the regime where you cannot... is the excluded regime for temperature of the electrons. And from that assumption you can generate data, which one is ours, that one is ours, this is from the theory that mimics the experimental result quite well down to some even fine details. So they published... we beat them with one page for the publication. To make a better comparison you can try to... under the assumption of the... under those assumptions that we talked about, you can try to determine the electron temperature from your measured IV. So here's an example of how you do it. IV at a given phonon temperature. Oh, something is missing. Ok, so you take a point there and INV at a high temperature branch. It's missing from this graph. I don't know what. And you transfer it to your resistance to the function of temperature or inverse temperature which you measure in the ohmic regime. Ok, so now this is your thermometer. It's the measurement of the electronic system in the ohmic regime. And so you take a V over I and the value over there you transfer it here. It comes 2 times 10 to the 7. You find this value on this graph and then you can determine the electron temperature at the high voltage measurement by comparing the V and I V divided by I value to those that you measure in the ohmic regime. So using the ohmic regime as a thermometer and this is the data that is converted to electron temperature and in our experiment you can actually see quite clearly this excluded region and I'm going fast here I know but there's a lot to say but you can see the theoretical excluded region and in our experiment really the electron temperature don't, you cannot find temperatures in this region similar to what has been predicted. So we've been looking at it for some years and maybe it would be it has been, it is obvious but the physical picture is rather simple. So since we have this very strong nonlinear very strong temperature dependent of the resistance and the electron and phonons are weakly coupled you can have a situation where the electron is at elevated temperature above the phonons and it so turns out that if you solve this heat balance equation there's a bistable region the temperature can abruptly change so to me that means that the entire electron system have their own temperature because the electrons are interacting with each other they can sustain their own temperature separate from the phonon temperature in a non-equilibrium situation maintained by the voltage but the power that experimentalist is applied so does heat flow into the electrons and it's quite strong because the electron can be at 300 mD when the crystal is at 10 and the heat flows from the electron to the phonons but I can still define a temperature for the electrons and a separate temperature for the phonons so this is basically again the same data we're just removing some d-axis here and let me show you if you turn it over move it to the side it looks very much like the graph on the left even the same colors the graph on the left is a solution, is a mathematical solution to the van der Waals equation for the liquid gas mixture don't need to remind you that including the Maxwell construction here is pressure versus density for a liquid gas mixture and again you can see the striking similarity between the two system one is measured very far from equilibrium in a system which is quantum near t equals zero and another one is a liquid gas transition for which van der Waals won a Nobel prize 100 years ago so what does it mean? it means that we may be able to define an order parameter I'll go quickly because we haven't done the experiment properly so far you can measure a critical exponent if you want because you have a critical point second order like critical point movie this is the critical point I forgot with methane I think or some mixture of liquid and gas and what nice about that if you are at the critical point and you do an experiment slowly you take two fluids gas and a liquid they are intermixed above Tc and you lower the temperature both of them are transparent but near the critical point they become opaque this is called the critical opalence now you can see miniscuse forming and the reason they become opaque of course is that because we have intermixture of the different densities over all length scale that's what it means to be near a second order phase transition so if you take this point of view and you believe the similarity between the appearance of the graphs or RIVs and the van der Waals solution is not accidental you have to take into account that something similar is happening in our system meaning that you no longer can think about the electron as being at one temperature there has to be a mixture of many different temperatures perhaps in the sample which if you want to think in terms of currents rather than temperatures you can do that too because the current path in a sample when you undergone this continuous jump which is like lightning basically if you want to think about it it cannot be uniformly affected throughout all the electrons there are going to be some weak links that are going to be hotter quicker than other places where the higher resistance is so we must have we must be able to accommodate somehow I think a way to incorporate this into the alright so the last bit I have some time left Omicransport and this is again after several years of thinking and again coming from the collaboration with the theoretical group we began to put a lot of effort into extending our ability to measure resistances into high value at low temperature so we can follow and this is an example of 10 to 12 ohms and even higher in some cases this is not continuous measurement these are measurements that you fix the temperature in the magnetic field and you scan your IV and you extrapolate your IV as best as you can to V equals 0 to obtain the value of the resistance and again you see this sharp rise near BC near the critical point this is some sort of semi-observation of the arena group where the resistance is also increasing rather rapidly but let me show you our data this is the summary of the data that we have plotted on an Arrhenius plot and you can see that the dash line is a straight line but almost none of the curves are straight so we have two types of behavior so let's see what's what so this is activation behavior it's a straight line on this graph if you go to lower fields near the critical point in superconductive integrated transition you get something that is much faster than activation but if you go to 12 Tesla which is our highest field in this experiment you get something that is slower than activation so let's start with that let's start with the high field 12 Tesla in this regime where the insulating peak is already becoming weaker we see something that looks like Efros Szlowski hopping over several orders of magnitude now you go to the other extreme and again this is going faster than exponential this is the low field if you plot conductivity you see that it's sort of indecided it goes rather weakly with temperature until you get to 0.1 degrees and then the resistance drops very sharply approaching some temperature you try to fit it to an exponential it's not working what does work is some sort of an exponential with the shifted temperature scale T star you can see here now this is please note the number of orders of magnitude of this and you can see comparison between the 12 Tesla data of conductance and the 0.75 Tesla data and you can see how sharp it is this is all below 0.3 degrees so when you get to 0.1 there is four orders of magnitude separate them but by 0.4 they are equal 0.04 so this is a parameter ok so the question is whether this apparent disappearance of the conductance is indication of the many body localization this is a graph from their paper and again we are not sure and this is a comparing superconductivity transition in one of our cleaner samples with a TC of a little bit more than two to this transition of conductance so this is resistance and that is conductance and you can judge for yourself this is published yesterday after two years of so thank you for your attention