Okay. Thanks very much, Steve. Thank you all for coming. Well, I've had a wonderful week.
Too much hospitality, but everything else was perfect. Okay.
Now. All right. So I'm not sure which one of these things to look at.
Let me look at this one. I want to talk about kind of two things.
One thing is techniques and approaches for visualising electronic quantum matter.
Whichever kind of quantum matter you like, that's that's one side of the coin.
The other side of the coin is my own specific interest has been in working on the problem of high temperature superconductivity.
So in fact,
many of the examples that I'll show you of how we develop and use these different techniques are focussed on solving the problem of high tech.
So those are two different sides of the coin. If you couldn't care less about high temperature superconductivity, of course that's hard to imagine.
But if it were possible,
then just concentrate on thinking about how you could address some problem of interest to you by using these these techniques.
Many of them are still quite new. They haven't spread out into the world yet.
However,
I can tell by looking at your beautiful new building under construction across the way that these techniques will be in use in Oxford quite soon.
So this is a wonderful opportunity for me to introduce them to you.
Okay. Here's my present affiliation. Cornell University.
For the students, post-docs in the audience. If you're interested in a stint in the U.S., please consider Cornell.
It's a wonderful university. It's about 250 miles from New York.
So you have to like living in the country, but probably anybody who can survive Oxford can survive Ithaca.
And and we have we have very large physics operation for departments, about 150 active faculty, about 500 graduate students and postdocs.
So it's really a wonderful and very active place. Okay.
All right. So let's define our terms a little bit.
So conventional electronic matter is the stuff that we are all familiar with and have been familiar with in some cases for millennia,
in some cases only for 100 years. And it's the basis of our technology set at present and also of our so-called civilisation.
And we understand it rather well. Conductors.
That's Shawshank Farrow, Shawshank Signet Ring.
It was found outside Jerusalem. So that's a pretty old piece of metal.
So conductors, insulators, magnets, semiconductors, we've known about those for about 140 years, many.
Active electric materials are a key part of our technology set and I regard conventional
superconductivity 100 year old superconductivity in the same light as these well understood questions.
So how do they work? Well, we all know how they work. You have elementary particles, they're called electrons,
and they have a momentum which is related to their wave vector or one over their wavelength via the de broglie relation.
And we're dealing with non relativistic particles usually. So energy goes as a wave vector squared, p squared.
So that's the dispersion relation. If you put these objects in a crystal which has a periodic boundary,
so that defines a new wave vector pi over the distance between the atoms in the crystal and the interaction between these electrons and the nuclei.
And the crystal opens the famous band gaps. Then, depending on how many free electrons you put per unit cells,
you fill up these states because electrons are fermions, as you know, and you fill them up to the Fermi energy.
That's the energy separating the empty from the filled states. And also you fill them up from zero with vector out to the Fermi wave.
In real space. You have to think a little bit.
You have to think in both spaces now because this thing is a very tiny web vector, but it's an enormous wave length.
Okay. And this thing is a large wave vector, but it's a very tiny wavelength.
And you have to consider both things. Okay. So now, you know, it's based on our control of this set of ideas and the material science which uses it,
that we know that a very large fraction of our economy and society is based on.
Now we can for many types of materials, we can find out whether the elements will go together stably to make the materials.
We can predict using band structure or quantum mechanics what the bands will be in the material and where the gaps are.
And then by chemical or electrostatic doping, we can alter the number of carriers and then we can get those things and make active devices.
Transistor being the most famous. So this is based on using Schrodinger equation and independent electrons.
It's often said that we're going to reach some limits of that technology base quite soon.
And, you know, as a matter of fact, when it comes to shrinking devices, that statement is trivially obvious.
And in fact, the truth is, we already reached it quite a while ago.
The device frequency stopped changing. Device performance stopped changing all around or four or five.
Your new computers now are not based on devices which are somewhat which are smaller than they were ten or 12 years ago.
What they're based on is having more and more cores.
That's more and more chips are CPU's onboard each computer.
The next generation of computer that you buy now will have like 18 core sorry, 16 cores it.
So the device size barrier has already been reached or we're very, very close to it.
There's no point in pretending that it isn't there. All that's happening now is we're just putting more chips in each box.
We need new we need some way to get out of this trap. And one of the things we need are new materials.
We also need new ideas like quantum computing. But I'm not going to address that.
But we do need new materials. So what other possible states of electronic matter could exist?
Usually when you read a classic textbook on solid state physics, let's say Steve's textbook or Ashcroft or Merman or something like that.
You're you're taught about these states and it's implied that there are no other states.
What other states could there be? But of course, there is no barrier against having other exotic kinds of electronic matter.
There could be all kinds. And how can that happen? Well, many different ways, but one way is correlations.
So I wanted to talk about correlations. Since you live here in the south of England, you know what this is?
It's a traffic jam. And the reason why eventually the traffic comes to a halt if there's no accident,
is the correlations that are being enforced by the drivers and the position of each vehicle.
So, you know, your insurance company certainly wants digital or no double occupancy and your.
And for your own safety, so do you. So. So so you have a two dimensional plane with identical particles in it, but no double occupancy.
And that produces a traffic jam, as you know.
And in fact, if you put a small number of vacancies into a traffic jam, as you all know as well, it can suddenly free up.
Okay.
So the number of vacancies you have to put into a traffic jam to suddenly get it to move is actually a very tiny fraction of the particle density.
And the other thing, you know, is it's virtually impossible to predict and control these things.
And this is a piece of classic classical physics.
Just well-defined square boxes on a two dimensional play, but very difficult to understand and control because of the correlations.
Now, in quantum mechanics, you face the same thing.
So, for example, in several high tech superconductors, you can have a material, let's say, which has one active electron that's a vehicle per site.
And if there's no double occupancy, they get frozen in position in the Mott, the famous Mott insulating state.
So that's a complete quantum mechanical traffic jam. And we do understand the quantum mechanics of this object reasonably well.
So electron no double occupancy produces this traffic jam.
But if you put a small number of vacancies into this system,
suddenly the electronic fluid starts to flow in many materials in a way which has proven extremely difficult to understand.
Actually, decades of work have gone into understanding this situation.
And of course, the reason is that you're trying to solve a correlated quantum mechanical problem.
The state of every electron depends on the state of every other electron and their interactions and the
solution of all those simultaneous Schrödinger equations the diagonal ization of an enormous Hilbert space.
Even for this tiny little patch of material, that's an unsolved problem.
One thing we do know about this situation, though, is that when you make materials that have these properties,
you get astonishing surprises about what can happen.
So you have some very complex interplay locally between charge and spin and also orbital and indeed sometimes the lattice.
And from this situation emerges high temperature superconductivity and colossal magneto resistance and thermal electricity.
Multi ferro x very strange superconductors, very strange electronic states,
new order states that I'm going to talk about and new ways to address the fundamentals of quantum mechanics.
These this set of ideas, this motivation has tremendous potential in many fields of solid state physics and materials science.
But the truth is, it's still poorly understood. And one of the reasons why it's poorly understood is that that experimental technology set,
which had been used to understand metals and semiconductors up into the 1970s and 1980s,
is completely mismatched to the question being addressed here.
And what has happened over the last ten, 15, 20 years is the invention of many new tools, which are what's necessary to solve this problem.
The other thing impression you get from a Ashcroft Merryman style book is that,
you know, virtually the materials we can work with are already established.
And that fact is also around. There's an enormous number of materials that can be made either thermodynamically or nowadays by
molecular beam epitaxy artificial materials which can't exist thermodynamically but can still be made.
And they obviously there's untold possibilities for new materials with exotic new electronic properties.
What we'd really like to have is a predictive theory of correlated electronic material.
Then we could probably design and build many new types of materials and devices.
Okay, now here's the specific example I want to tell you about.
Of new electronic states of matter. These are called electronic liquid crystals.
So you all know, I think what this is, it's a vapour, it's called steam.
And it's made of H2O molecules and it's translational the rotational invariant.
It's isotropic. It has no stranger our internal properties.
If you increase the interactions between the molecules, you get this very mysterious state.
Some of you are familiar with this. It's called water, and it's one of the most difficult to understand states.
It's really a difficult problem to understand water because the interactions are strong.
If you increase the interactions a little bit more and if you live in Ithaca, you get ice.
But that's not the state that I want to talk about, because there's an intermediate state, which is the liquid crystal state.
It's a state which simultaneously is a fluid but brings some special breaks, some of the available symmetries.
So we understand this very well. Of course, it's now the basis of our it's it's how this projector works.
It's how you get your information everyday on your laptop and on your telephone.
Our ability to understand these phases and to control them has indeed revolutionised information technology in a most spectacular way.
And also, it's very good for business. Okay, now there's two types of liquid crystals.
So one is and the magic and the magic liquid crystal is where all the molecules are aligned in the same direction,
but they don't make any pattern in space. They don't break any symmetry.
A liquid crystal is a one where all the molecules are aligned in space and then they get patterned in space as well.
Their periodic density is changing along this direction.
So we say this smectite liquid crystal has a way vector to pi over the wavelength
and pointing in this direction it breaks both rotational and translational symmetry.
It was Piers Illusion who figured this out from the physics point of view in the early 1970s and for which he received the Nobel Prize subsequently.
And one of the key thing I mean, of course, the key thing he used to solve the liquid crystal problem is genius.
Okay. But the other thing he used is that in the early 1970s, visualisation of in phase contrast microscopy became possible.
And you could look at the liquid crystals and see what kinds of topological defects were occurring and what happened when phase transitions occurred,
etc. So actually the visualisation was a key part of the understanding of how the liquid crystals work.
Okay, so this is the classic liquid crystal.
Now in this state. This is a piece of copper wire. No doubt you're all familiar with it.
And inside it, there is a more or less isotropic fluid with weak interactions between the particles.
It's a fluid of electrons. If you increase the interactions between the electrons, you can get a heavy electron fluid,
which is a very exotic state of electronic matter that I don't have time to talk about today.
But it's where the electrons have really become strong and intimately interacting with each other.
And if you increase the interactions a little bit more, probably you would think we should get an insulator or a mat insulator.
But there's another possibility and you know what it is from analogy, it's that there are electronic liquid crystals.
So this idea was put forward by Vicki Emery, Eduardo Fradkin and Steve Gibson in the late 1990s.
And it was at this point that I got interested in this subject. I had been working well, of course,
I had been working on quantum mechanical liquid crystals because Superfluid Helium three is a very elegant quantum crystal.
But I suddenly realised there could be electronic versions of this exotic situation.
Now you see these cartoons here. Those are the actual figures in the nature paper.
It isn't larded with exotic mathematical theoretical statements.
This is the prediction that if you put electrons strongly interacting with each other into a correlated insulator,
they will first break rotational symmetry,
making a pneumatic phase, and secondly, they will break rotational and translational symmetry, making a symmetric phase.
That's the basic, you know, it's just well, I shouldn't say just intuition.
These colleagues have won a number of major prizes for making this proposal.
But but that's the basic idea.
If there can be strong interactions of particles making classical liquid crystals, why not quantum mechanics of liquid crystals?
Okay, now, kibbutzim. At that time I had I was visiting him in UCLA.
I was at a helium three meeting, but I, I took the opportunity to talk to Steve Wilson just when he had published this.
And he really he kind of he radicalised me, as they say now.
He just captured my attention to this problem and we started working on it.
Okay. So how do you visualise electronic matter? You take a scanning tunnelling microscope.
These are very common devices now. They work beautifully.
They have a sharp metal tip with one atom on the end, you scan over the surface, let's say about one angstrom.
From the surface, you apply a voltage between the conducting surface and the conducting tip.
And you and then you measure the current, the tunnel current, which goes through this tunnel junction.
Then by feeding back on that current to keep it constant, you can make an image of the feedback signal and that's called an image of the atoms.
Each dot here is a selenium atom in this complex. This is niobium diselenide.
Now. This is cool. It's very lovely. You can win the Nobel Prize for inventing this machine.
But this machine does not tell you where the electronic wave functions are.
It just tells you where the atoms are. Okay. And in fact, in this compound, this compound, this come this compound.
There there is there's a pneumatic, electronic phase in this one.
And that one there is this metallic electronic face. In this one, there's believed to be a pneumatic, electronic phase.
Conventional ASTM will not allow you to see that, because the thing which breaks the symmetries is not the atoms.
It's the wave functions of the electrons. So the way to visualise the way it functions is the following.
And this is a generalisation of tunnelling spectroscopy introduced by Javor
to for the study of superconductivity and for which he got the Nobel Prize.
In the early 1970s. But now you use SDM tip, so you park your tip at this location.
And now turn off the feedback system so it's passively stable at this location and now change this bias voltage
that's this voltage here and measure the total current as a function of voltage and take the derivative.
That's the differential conductance as a function of voltage of this junction.
Now we know from theory that that function is proportional to the sum overall of the wave functions at that energy at this location.
So you're measuring something proportional to upside squared of the electronic wave functions at this location.
So now here's how you do it. You build one of these machines, put your system, tip over here,
measure the differential conductance spectrum at the first atom, at the second atom, at the third, at etc., etc., etc., etc.
The end of that process, you have a map of the differential conductance.
So if conductance is high, I use a light colour and if the conductance is very low, I use a dark colour.
And this tells me that this image is in this field of view.
The wave functions at that energy. But you have you have a map at all the energies where you measure it.
You can zoom through the energies of the electronic eigen states, and at each energy you visualise the spatial arrangement of the wave functions.
That's the great power of this technique.
And you can all see just by looking at this movie that a tremendous amount of information is contained in each one.
And that's true. It took us many years to discover how to extract the information.
And another thing, which is that many real correlated materials are very, very complicated in terms of their way functions.
So what you get is atomic resolution, energy resolved image of the electronic wave functions in the material of interest.
And this is hard to do. This was very hard to figure out how to do.
And here's the reason. So if you take five, 12 by five, 12 pixels and 200 data points, so that's 250,000.
So that's 50 million measurements to make this movie 50 million.
And there are serial measurements. We have to do them one after the other.
So 50 million serial measurements in 24 hours gives you about 2 milliseconds per measurement.
So you have to get a high signal to noise measurement of the current in a millisecond.
That's basically where we're at.
And that was really hard to figure out because when you look at the equations, it requires you to move the STM to the right location,
turn off the feedback, and then have the tip vibrate no more than a few centimetres.
Okay.
So the constraint is not to improve the spatial resolution, it's because the current noise is a function of where the tip is relative to the surface.
So to suppress the current noise and do the experiment quickly,
you have to clamp the tip in the right location with our mass motion of only a few centimetres.
And that was that's hard to do. So we introduced a way to do that, which is the so-called ultra low vibration lab.
You take an underground concrete vault, you put acoustic isolation inside the external vault,
and then inside you put your experimental chamber on a separate, massive slab.
First ones were around 30 tons. Second generation, my lab is about 100 tons.
It looks to me like some of the new ones in your building will be in the 100 ton range as well.
And then on this lab, you put an inner acoustic chamber,
and inside there you put an ultra low vibration refrigerator so that you're cooled down to a fraction of a kelvin.
So here so the arms motions on the floor here are in the micron range.
So in your lab, in your basement lab down here, they'll be in the few nanometre range.
When these isolators are working, the motion of this whole room will be in the few angstrom arm's range.
This isolator of the motion up here is a few peak metres and down inside the crash that we get rid of as well.
The motion goes down to a few centimetres if you don't make any mistakes.
Okay. Well, so. So that's cool, right?
So. Okay, so now this seems like an obvious idea.
And if you want to see one of these amazing things go over and take a tour of your
new building as soon as they're available because they're really impressive.
But when we first came up with this idea, you know, I went to see the dean at the institution where I was then working,
and I said, look, this is a really good idea, right? We'd be able to visualise electronic metal.
All we need is some of these labs. There is no precedent for it.
So the dean just laughed and said, You know, it's too expensive and we just can't take the risk.
You know, we're not going to invest in this. So it was at that stage I moved to Cornell because the Cornell audience were willing to take the risk.
They demolished one of their underground stores of charcoal, their famous low temperature building,
and into that demolished corridor, they dug down another story.
So they ended up two floors high and the whole length of the building, more or less like the design of your building.
And then into this space built for ultralow vibration labs, three of which are in use today for spectroscopic ASTM This one is online right now.
This one is is just gone offline and this one is under repair.
So one is working today, but typically they're all working and we have visitors working on these projects coming from all over the world.
Okay. And of course, the design does work.
That's the good part.
So one of the powerful techniques you can bring to bear now with this facility is the following thing crossing particle interference, imaging.
Every material has it has impurity atoms in it.
An incoming electron is in a fluid of electrons and incoming electron with this wave
vector will scatter from the impurity atom and make an outgoing wave function.
If you add these two wave functions together to get the interference pattern and then square to get the probability density of the electrons,
the q vector of this modulation, the wave length is half because you added and squared.
So that means the Q is twice the Q of the original electronic state.
So you can take the for your transform of that image. And measure the Q vector of all these oscillations.
Super. This is reasonably easy to do, of course.
It wasn't easy to think of, but it's easy to do. So now you know the Q vector is related to the vector by a factor of two.
So you can just divide and that's plus minus K, it's plus K scattering to minus K.
So you get two pieces of information about the energy, momentum relationship of the electrons here.
But now if you have an energy resolved movie of this process, you can do that as a function of energy.
This is called QPR. If you look up QPR on Google now, you'll find hundreds and hundreds of papers about it because it is a very powerful technique.
You can image the empty states as well as the failed states.
You can do this. And ultra low temperatures, we do it down to about 50 milli kelvin and you can do it in very high magnetic fields.
The record is not in my lab. It's in Japan. It's about 18 Tesla.
But we hope to recover the record again next year by going to about 20 Tesla.
Very powerful technique.
So with this technique, we were able to make the first visualisation of the electronic structure of many classes of materials.
So this one I already showed you, it's the copper based high temperature superconductor.
It's a bit of a mess, of course, but before you transform of that mess.
Oh. Is. Very ordered because there's only a small number of island states which are undergoing this scattering interference.
We can undo this Fourier transform movie to determine a very complicated band structure.
Let's start again. So these are the cue vectors of the scattering interference related to all the momentum space states.
So we were also able to reveal the equivalent thing for the arm superconductors.
Horrible. It's interesting. I discovered that in real space, you know, wave functions don't look beautiful.
I suppose Mother Nature is in charge of that.
God is in charge of that. But in momentum space, in reciprocal space, they're beautifully ordered.
You can see three bands and three energy gaps. We were able to unscramble the electronic structure of our own superconductors.
These were the first heavy fermion wave function movies. They look like crap.
But before your transform looks beautiful, it contains exactly what's predicted for heavy firmly on cue vectors.
These were to diagnose the first measurement of the superconducting energy gap of a heavy Fermi on compound.
Last year we were able to see the wave functions of our gapped topological insulator for the first time.
They are cooled. You see that this is the direct service state.
It's a six Ford symmetric cone.
It's approaching not it's known, but the gap from below you enter the gap surface state is completely gapped, doesn't exist.
Then you exit at the top edge of the gap and the direct surface state reappears and heads off the way.
It's very beautiful. Okay. All right.
Now I want to talk about superconductivity. Let's see. How are we doing for time?
Good. Okay. Great. Superconductivity, my own.
I suppose passion would be a polite word for it. Obsession might be more honest.
So as you all know, you know, superconductivity is the appearance of perfectly dissipation, this electrical transport,
and also would be perfectly dissipation, less electronics if you use the correct the correct devices.
And it's a bit over 100 years old now. It occurs because in a metro these states here.
A plus and minus. Q are susceptible to of forming a new quantum mechanical object, which is a bound pair.
And that pair of plus minus K is called a Cooper pair.
That those Cooper pairs condense into a new quantum mechanical state and they leave behind some single particle excitations,
which are the signature of the existence of the Cooper pair of condensate.
The superfluid of Cooper pairs. So that's our classic understanding of this problem.
The Cooper pair of binding energy.
In the simplest case you can think of this energy gap here at this is an energy scale where a gap opens in the spectrum at the chemical potential.
It's the Cooper pair finding energy per particle. We also have the classic theory of how that works.
If there's some interaction between the electrons and you solve the species gap equation,
if it's solvable, then the gap structure contains the information.
So this is the momentum space structure of this energy gap.
It may be different in different directions, so it contains the information about the mechanism of the parent.
So the critical temperature is the temperature below which the material will superconductor.
And for classic superconductors, of course it's very low below 20 Kelvin, even up to the 1980s.
You know, at this rate it would have taken until the year 3500 to get to room temperature superconductivity.
But we need room temperature superconductivity part of my.
Task when I wear my working for The Daily Hat is to think about, you know, what will be the implications of having room temperature superconductivity.
We need very greatly increased efficiency and capacity and stability in our power network.
Certainly in North America, we need that desperately. And, you know, a superconducting power network could do that.
Here's a problem which is certainly occurring in the UK and it's known to be occurring in the US.
It's that as people move back into the city centres and they are doing so,
the energy density which is being required to be delivered to each major city is going up very rapidly and
there are many big cities in the world where we won't be able to deliver enough energy by around 2050.
One thing you could do, of course, is dig up every city and put in many more copper wires, but nobody wants that.
So an alternative would be to pull out the copper wire network and put in a superconducting network.
Then we could increase the capacity in basically every network by a factor of around 30.
So this is the important thing. We need room temperature superconductivity to accommodate renewables, to make efficient harvesting of energy.
You know, devices that don't waste a lot of the energy they harvest.
We need it desperately for information technology. We're using a huge amount of energy now for our information technology.
And most of it is going to heat or to air conditioning to get rid of the heat so that the CPUs keep working.
But a room temperature, superconducting information technology wouldn't generate any heat like that.
It would be largely non dissipative. We need it for high energy physics.
We need it for high energy physics. We need it for medicine. We need it for transport.
We have two candidate classes of materials, copper oxide and iron arsenide based compounds, and they have a number of characteristics in common.
There are two dimensional, quasi two dimensional, and they are strongly antiferromagnetic.
Those are the basic things. It's these two families which are discovered starting in the eighties and again in the 2000s whose critical
temperatures are rising such that it's not implausible that we could reach room temperature superconductivity.
In fact, there is one other family. There's the famous hydrogen.
It's too easy compound, which doesn't superconductive at ambient pressure, but also its critical temperature is above this line.
Well, it's perfectly plausible that we can reach room temperature superconductivity.
But we need to understand how do these compounds work?
So there are strong two dimensional antiferromagnetic there phase diagrams are somewhat the same when used.
The parent state is an antiferromagnetic antiferromagnetic insulator or antiferromagnetic correlated metal.
You introduce the holes antiferromagnetic and disappear as the superconductivity appears.
And if our magnetism disappears, superconductivity appears.
But in both of these classes of materials, an exotic phase has been more than one exotic phase has been discovered in this part of the phase.
Diamond unexpected. And so here is a cartoon of the situation.
We believe that if we could destroy the long range antiferromagnetic ism but keep the antiferromagnetic spin interactions,
then we could reach the point of having very robust, cool preparing and high temperature superconductivity to go from here to there.
But apparently in real materials, when you're going from here to there, you must pass through some other exotic correlated electronic phase.
And one of the proposals for what this phase is is the famous Fradkin and Kim Wilson proposal that it's electronic liquid
crystals that you have to pass through on your way from the correlated insulator to the high temperature superconductor.
They imply in this paper that it's even unavoidable. I don't know if it's unavoidable, but the prediction is pretty clear that it should be there.
All right. So we started to look for those states.
So in the iron based superconductors with two primary questions what is the mechanism of the superconductivity and what is this exotic state?
Is it an electronic liquid crystal? So in those compounds, two calcium ion, two arsenic, two dose with cobalt.
The surface is very clean, stable and nice.
We were able to visualise this was the first visualisation of the wave functions in the non superconducting states
of an iron based materials and the wave functions we immediately saw are all dispersing in only one direction.
Looks a little bit subtle there, but if I show you the Q space version, these are the wave vectors of the scattering, interference versus energy.
They're all just dispersing in one direction.
All the states, which you would imagine should be travelling in the other direction and scattering, interference and so on don't seem to be there.
We were able to visualise the static breaking of rotational symmetry and luckily or in fact
unavoidably we were able to find some twin boundaries because this crystal is our ceramic.
And at those twin boundaries we could see that the static breaking of rotational symmetry and the dynamic making of rotational symmetry rotates.
So actually in 2020 or nine, we first tried to report that the parent phase of the iron based superconductors is an electronic mimetic.
The first paper was difficult to publish. It took until the middle of 2010 to convince the referees.
But but luckily for us, this was the first observation of that state.
Okay. Now, the other thing we can do, equivalent materials, is look at the superconductivity.
How is the superconductivity? What is the interplay of the superconductivity with the electronic pneumatic state?
So this is a different compound. But these this is the superconducting energy gap.
If we image the wave functions here, they're a mess. There's a lot of scattering interference.
But as I said, if we image, if we take the four year transform and do the QPR analysis, we're able to find three bands, a central band here.
So that's the scattering interference signal from one of the primary bands.
And from that, we're able to determine determine the exotic structure of the superconducting energy gap.
So now you don't have to remember all that. I just put the key facts here for you on one slide.
In the army superconductors. You have a fairly simple Fermi surface.
You have an exotic superconducting energy gap there.
There's no density wave phase. There's no spectacle phase as far as we can tell.
But there is a pneumatic phase which now plays a vivid role in the study of those complex OC like this.
So in here there is an electronic pneumatic in the R&B superconductors.
All right. How about copper based? So in the copper based superconductors, same.
Two questions. What's the mechanism? What is this strange face?
Is it an electronic liquid crystal? So here's an image of the crystalline surface of one of the copper superconductors.
Okay, now I'm going to show you an image, a simultaneously take an image of the wave functions.
Oops. You see, the wave function image is very dense and looks quite different.
It's taken us a long time to diagnose it, but it looks quite different. Looks like a bad tweet.
Well, what it is is bad quantum mechanical tweet, I think.
In any case, you can diagnose what broken symmetries are in this image by taking the 40 and transform.
There are two key things in the for your transform. There are the Bragg peaks.
They're the ones periodic with the crystal.
And there are these broad peaks of incommensurate modulations which exist actually throughout the material, but only for a few periods.
So now I have to tell you a little bit about CO2, the unit sell of copper.
So inside each unit, sell of copper. Obviously there's one copper atom and two oxygen atoms.
If you just focussed on the copper atoms and took the for a transform of this pattern, it looks like this.
These are the Bragg peaks, you know, not of the orbital, but just of this periodic pattern.
These are the Bragg peaks and they have the same side. Let's just ignore this one for a moment.
This is what would happen if the two oxygens were equivalent. If the two oxygens are equivalent inside the unit cell.
Then when you take the four, you can transform this peak, and that peak will have opposite side.
The two modulations are opposite sine in the four year transform.
So now in the real material, suppose you have a combination of this,
plus that then you would add this to that this thing and this thing are the same sign.
This thing in this thing are opposite signs.
So the two brand peg should be in equivalent if there's a broken rotational symmetry inside the unit cell, which is what an electronic pneumatic is.
So when we did that experiment, the two Bragg picks are identical in the topographic image,
but they're quite different in the electronic structure image, about 40% different at low doping.
And so this and you can actually demonstrate in real space that the same thing is happening inside each unit.
So there there's a strong breaking of rotational symmetry.
So this constituted the discovery of an electronic pneumatic phase in the copper based superconductors, and people were very surprised about this one.
It's interesting.
Somehow the magic in the arm based superconductor seemed to be more acceptable than the the magic in the copper, evasive or inductive.
Now, the other thing is that the other thing we could look for is these incommensurate peaks.
Now we can look at those things, you know, with high spatial resolution.
So that's one, two, maybe three periods of this strange incommensurate modulation.
Of course,
it's not there in every energy because in quantum mechanics some energies are doing localised states and some energies are localised states.
And we were able to show that the same strange pattern of breaking of rotational
translational symmetry and rotational symmetry exists in multiple cuprates.
And then if you zoom in and look at this thing carefully,
you'll see that it's made of some very interesting and iconic object, a pattern we're not really familiar with.
It's unique directional. It's four unit cells wide.
Somehow it manages to break rotational symmetry inside every unit cell while still being periodic.
It took a long time to figure out what that pattern is. Specifically, what is this object which appears in the broken symmetry state of the Cuprates?
But now we know it's a D symmetry form factor density width.
So now I get to do my little dance to tell you what that is.
So a conventional density wave is supposed to charge on the two oxygen atoms inside the unit itself,
where modulating in space and their modulating in phase.
And the signal that the two copper sites would do this.
Sorry, the two oxygen sets. Let me do that again. Think of me as the copper.
These are the two oxygens, a conventional density wave, the charge modulation phase.
That's exactly what we all learned to expect. But it's not the only possibility.
The other possibility is that the two oxygens could be equivalent, which they are, and the charge on them can modulate out of phase.
That's a D symmetry density, something predicted since the 1970s on symmetry principles.
Actually I've never seen before, so it's kind of surprising.
But we don't think it's a coincidence that this happens in the copper based superconductors.
We can also visualised superconducting wave functions, as I said before, by using QPR.
I see if this is working. Yeah. But by measuring the energy dependence of the of all these different wave vectors and having a model for their cause,
which is scattering interference due to impurities, we can measure the superconducting energy gap.
Now, this wasn't something new to the study and it had been done by photogrammetry, but nevertheless one can do it.
So here's a summary for what the package of information is in the copper based superconductors.
There's a very simple Fermi surface. It's got a relatively simple body symmetry, superconducting energy gap.
There's a vivid smectite electronic liquid, crystal, four unit cell periodicity.
And the degree of freedom which is modulated in this liquid crystal actually is the same degree of freedom,
which is whose symmetry, whose rotational symmetry is broken in the pneumatic phase.
And that's exactly what you would expect if you would read Macmillan or Daejeon papers about liquid crystals in the 1970s and early 1980s.
This is exactly what you would expect. There are some degree of freedom.
First, it breaks rotational symmetry and then it breaks translation of symmetry.
Well, that's exactly what's happening in the copper based superconductors and the pseudo graphics.
Okay. So there is both the pneumatic and the mechanic in this part of the phase done schematic phase diagram of the copper superconductors.
All right, so now I'll make a few comments about the consequences of that for the fundamental problem we're trying to solve,
which is I haven't forgotten it. It's what is the mechanism of how to see and how can we get to room temperature?
But I'm going to reserve those comments for a few minutes because one other really
interesting thing intervened at this point and really this only about two years.
There's another possible electronic crystal stake that can exist.
It's a cooper pair of crystal. It's a very different state than a density modulation in the charge.
It's a modulation in the Cooper pairing. So it's a it's a mathematically valid statement to say that in Ginsburg, Landau's theory of such a situation,
if you had an electronic liquid crystal like this and if it was coexisting with a superconductor,
let's say here, then a Cooper pair density wave, a cooper pair of crystal would be allowed.
Now that strong and such such cooper pair modulations actually have been predicted for more than 50 years, but never seen in any material.
They were predicted by Fulda Feller and Larkin and of Chillicothe in 1964.
So. And furthermore, there are good.
So the mechanism used in this proposal is different than the one which would exist in a doped instrument or in a correlated material,
but in advance theories of doped model insulators, specifically the cuprates.
There have been predictions that there should be a pair density wave,
a cooper pair of crystal appearing if this same type of broken translational and rotational symmetry occurs.
So. So the question is, could there be a there should be, but could we find if there is a Cooper pair density wave in the cuprates?
All right. So that involved developing a new technique.
The reason is that if you use a conventional SDM, your tip is made of, let's say, a normal metal like tungsten or iridium or something.
And the tunnelling from that normal metal tip is to states which have equivalent iron states, states which are single electron states.
So normal chips here in this cartoon will only detect a signal, you know, where it picks up an individual electron.
But if there are cooper pairs, it'll ignore it. There's no matrix element for a could prepare to tunnel into a regular chip.
However, if you had a superconducting chip, the opposite argument holds the superconducting chip.
If if we're working properly,
it's full of cooper pairs and at low temperature no normal electrons as it scans over the surface that the Josephson current.
Should tell you what the density of Cooper Pairs is as a function of location.
Now, of course, this is an old idea. This idea has been around for many years, 15, 20 years.
But nevertheless, the motivation really to try and implement it was brought forward by the Cooper problem.
So what's required is a scanned Josephson tunnelling microscope with Nanometre resolution.
This distance is 1.6 nanometres. So if you wanted to see this object, you need to have nanometre resolution.
Furthermore, when you look at the equations, you need the superconducting gap in the tip to be as high as possible.
And it turns out you need the Josephson Energy, which couples the tip,
the superconducting tip to the superconducting sample to exceed the thermal fluctuations.
And that means you need to be at a miller Kelvin temperature.
So what we had to make is a milli Kelvin dilution fringe based a scan Josephson tunnelling microscope which we did.
And we can tell that the chip has sufficient resolution because we can use conventional imaging to see objects in real space.
Superconducting tape does have reasonably good resolution, and we can also tell that it's a high gap, high tech superconducting chip.
We know that because we made it by picking up a piece of material, but also we can measure the spectrum and that tells us the gap in the tip.
So finally you put all this together. Nick Miller Kelvin Hijab, Nanometre Resolution Low Junction Resistance Scan.
Josephson Tunnelling Microscope. I won't tell you about the engineering.
Here is the critical current. Here's the Josephson critical current.
Measured on such a tip on a high tech compound. So now we want to image not the single electrons but the cooper pairs.
Where are the Cooper pairs? So this is a topographic image with such a tip, and this is a scanned Josephson image.
Actually, it's the first scan Josephson image with atomic resolution, and it already contains a tremendous amount of information.
But there's some scepticism that actually we were visualising the condensate, the Cooper pairs, the density of Cooper pairs.
There is no precedent and you know, there are always sceptics.
So we were motivated to do one more thing, which is the following.
It's known it has been known for many decades that if you put zinc atoms on the Cooper site in Cuprates.
A hole appears in the superconducting order parameter.
The superfluid diminishes to zero for a small radius about two nanometres surrounding each zinc atom.
So, you know, obvious for obvious reasons.
This is called a Swiss cheese model of zinc doping of the Cuprates, and it's known from the US arm that this happens.
So we wanted to use this to validate the contrast in our imaging.
So we had zinc atoms substituted in one of these crystals.
I mean, new crystals made with zinc atoms substituted.
And we can find where each zinc atom is with rather high spatial resolution,
a fraction of a nanometre from the normal tunnelling spectrum, nothing to do with the superconductivity.
And then simultaneously, we can look at the Josephson image everywhere.
There's a zinc atom, the Josephson current dimensions close to zero.
You can see that for yourself. Every place where there is income and justice, power diminishes to a very low value.
So this allowed us to quantify the contrast of San Jose sin and pretty good the city that is around 90%.
We're sure that the things we're seeing here are real spatial variations in the superconducting condensate.
Okay, last but not least, what you should do with this is now the obvious thing.
Take the for you and transform and before you transform shows for peaks there at.
Zero comma a quarter or quarter a sorry, a quarter comma zero.
That means there are four units out. Periodic modulation in the density of Cooper pairs along the two axes in this compound.
This is great.
This really gives us a new handle on the situation, and it also constrains them a variety of theoretical approaches you can take to the cuprates.
Because now we know a great deal about the pseudo gap physics. We know two broken symmetries.
We know how they impact the superconductivity in the density wave.
And so at the empirical level, these are have been rapid advances also.
And this is cool. So suppose you hate the cuprates.
I know that that's not possible, but suppose it's true. There are many other problems theoretical predictions,
proposals for the properties of condensates which have never been validated because there was no way of visualising or condensate.
Well, now, with this technique, we can think about pursuing those new.
Or maybe you guys can think about pursuing those new avenues. All right.
No good. Conclusions and the future.
So one conclusion I can tell you immediately is that these two guys are very happy so that I know them both very well.
Of course, the basic pieces of their theory are right.
Even their phase diagram, which is in another, which is in another frame from this paper,
appears to be right when you don't feel correlated insulator enough to make it metallic.
First it breaks rotational symmetry inside the unit itself, and if the susceptibility is there,
then it breaks translational symmetry in the same degree of freedom the way a molecular liquid crystal would.
So that part of their theory is right. And now the difficulty is that we don't have a quantitative theory for understanding the
relationship between the electronic liquid crystal phase and the high tech superconductivity.
I mean, we have a number of theories. We just don't know which one is right.
But this is the key practical question now, if you have this stuff.
Okay. Is it beneficial to the high tech?
Do you need more of it or do you need less of it? Is the new magic beneficial?
You would guess the new magic is beneficial because there are two families of high tech superconductors that have pneumatic electronic states.
But that's just a logical guess rather than a theory. So the frontier, now it's back.
The ball is back in the court of theorists to understand if doped correlated insulators contain electronic liquid crystals.
What is the the Zen style theory which explains the interplay between the two auditoriums?
If we could find that, then we understand these materials. Also, this technique is very powerful.
You can do all kinds of other things that I haven't had time to talk about.
You can see nanoscale domains and electronic disorder.
This is the scattering interference. You can see individual impurity atoms.
You can see heavy fermions. This is an this is the pseudo gapped fluid whose properties we don't understand.
You can see electronic liquid crystals. You can see where every doping is in the material and what the doping atoms due to the electronic structure.
You don't have to guess. You can just make a movie and find out, etc.
Thanks very much.