The Many Universes of Quantum Materials

I sort of. Thank you very much. Well, thank you for that warm welcome, and thank you, Katherine, for the introduction. Before I get began, I'm going to do a commercial in return for the Katharine's. So she has pioneered the quantum materials colouring book, which is freely available. You can download it from the website, either Google Quantum Materials Colouring Book or use that very short web address and you have a you have a free Christmas present to give it to a young relative,

so I highly recommend it. OK, well, today what we're going to be talking about is the many universities of quantum materials. So this is the universe we actually live in or part of it. And what physicists do is they stare at the night sky or look at some of the phenomena they try and work out what's going on. So this is this is a galaxy, and scientists look at this and try and work out what's going on.

Of course, it's constrained by physical constants, so things like the gravitational constant is a fixed constant. So if you want to have some explanation of this, then you need to use those constraints. The speed of light is another fixed constants, so any physical theory has to be constrained by those rules. And of course, we don't only look out for the night sky.

We also look to the smallest parts of matter for which you have to dig up the Swiss French border and build the Large Hadron Collider. So this is here are some pictures of some of the detectors in the big ring around the border. So these very large scale experiments are used for looking at the smallest things and trying to work out what the laws of the universe are. So one of the questions we might ask and scientists have asked for a long time is what is the world made of?

And various ideas have have come up from this. So in the very early days, some of the early pre Socratic thought that everything was made of water or possibly air or fire. And then finally, we came to the view that maybe it's some combination. In other words, it's not a simple answer. Maybe it's a complex answer. It's a mixture of things. So this is this is the first pleurisy substantial list.

Somebody who thought that there was more than one thing that made up everything in the world fire, air and water. Of course, we have no idea what any of these people look like. So these are all representations. So given that the one on the right is in fact a Sicilian, I prefer to think that actually this is a better representation of what he looked like. Who knows? I think this is probably the best guess. OK, so we have different ideas of what the world is made of.

But in fact, what we now would say is probably everything is made of certain elementary particles. And what is a particle? Well, it's something which throughout the universe, it doesn't exist, but there's one place where it exists. So it's something localised. So if I want to show that graphically, I can use this kind of function, it's nowhere. And then suddenly it appears and then it's not there anymore. That's what we mean by a particle.

And of course, we know that there are certain fundamental particles. So you might think of, you know, electrons and protons and things like that. But there are also waves. There are other things in the universe as well. And the thing about a wave is rather than being localised, a wave is completely spread out. So again, we can realise that the universe must be populated by both particles and waves.

And so examples of particles are things like the electron and the proton and the neutron and the things that make those up the corks. These are what you might imagine as being localised particles and things that are waves of things like light. That's a very obviously a wave. But if in fact, of course, is probably you will know in the early 20th century, we began to doubt this separation between these two types of things.

Waves and particles, because experiments were done that show that in fact, light behaved very much like a particle. In fact, we sometimes call it a photon. And moreover, the electron, the proton, the neutron, we discovered they have wave like properties. So this separation between something localised where you know where it is and something spread out doesn't seem to be so clear.

So how do you describe it? Well, we have a new description which is basically drawn here in the centre so we can get rid of the these other pictures. So you can imagine we've got something with a little knob and we can dial this up between particle and wave and when it's when it's a wave like it looks very light wave like. But then you can dial it back again and it can become localised and a particle.

And so in fact, we now believe that all of these things are some kind of combination of a wave particle thing that, depending on how you look at it, can have both characteristics. So in fact, if you want a more modern view of what makes up the world, we would say that the world is permeated by quantum fields and particles are just excitations in those fields that regions where the field is suddenly decided to conglomerate and produce an electron.

But the universe is permeated by all these different types of quantum fields, some of them electron quantum fields, some of them electromagnetic fields, and they spread throughout the universe and where they conglomerate, they produce particles. So that's maybe a modern picture. And so a lot of our physical theories are based on these quantum fields. Now, of course, those particles I was talking about the electrons and the protons and neutrons, they make up all of this stuff.

This is the periodic table. And since in fact, this year is the 150th anniversary of Mandela's discovery of the periodic table, it's maybe just worth sort of stepping back a bit and having a look at this. So again, we see complexity. A chemist would say that the world is made up of all of these different elements.

And Mandela didn't come up with a periodic table that looks exactly like this because he's had holes in and looking at the patterns of the elements he was able to predict certain elements might exist and fill in those gaps. So, for example, example germanium and gallium were elements that were not known before his time. But they fit fitted into little holes in his series.

Now, one interesting part of the history of science, if we just focus on a little bit of the the periodic table, so I've just blown a section up. And if you focus on these smaller numbers that are just above these particular elements, these were the ones that he was working on. These are the mass numbers, the the big numbers 47, 48, 49, 50. Those are the ones where you know the answer, so you can just number them in order.

But he was working with these masses. And what he realised was that in the periodic table, you went all the way from the low mass atoms like hydrogen, all the way up to the very heavy ones like uranium. And as you can see on this series, the numbers just steadily increase and they get bigger and bigger. Except those of you with sharp eyes might notice that there's a problem. So one of these tellurium? It doesn't actually work. You go one hundred and twenty one hundred and twenty seven.

One hundred and twenty six point nine. So tellurium seems to be wrong. And mentally, I've noticed this. And he came to an obvious conclusion, which was that the experiment was wrong. So he told other chemists to go and redo the measurements and measure the mass of tellurium. And they did, and it came out to be pretty much the same. So he then thought, well, maybe iodine was wrong and got people to try and we measure that and it remained an anomaly.

And in fact, this was not really properly sorted out until the work of Henry Moseley here in Oxford and Henry Moseley sadly killed shortly afterwards in the First World War. Henry mostly did experiments with X-rays to work out the energies of different atoms. What he realised was that in fact, ordering the periodic table by mass was the wrong way to do it. You had to order it by charge, and he had essentially measured the charge on the different atoms.

And so these big numbers here are the atomic charge on the atoms. And this, in fact, is the right order. This was years, of course, after Mandela had done his work, but it wasn't mass. It was charged. And that tells you something very fundamental about the universe. Electromagnetism is really important and determines the structure of chemistry.

OK, so what's the world made of particle physicist would ask the question which particles exist and they smash things together and try and work out which kind of particles are there? And they discovered the Higgs boson famously a few years ago. But that's the kind of question that they ask. One of the things that you find when you look at particles is that electricity is very important, so positive charges produce electric fields that come out. Negative charges have electric fields that go in.

But since the 19th century, in the work of Maxwell, we have realised that magnetic fields behave very differently. The magnetic field lines just go round and round in loops. In other words, they never sort of originate from a charge or they never land on a charge to use the terminology, but there were no divergences. And so what we have realised is that there are no magnetic charges or magnetic monopoles to use the jargon.

Now, in fact, there are various reasons why we might like magnetic monopoles to exist. And so therefore, over the last 100 years, physicists have intensively looked for magnetic monopoles and there have been detailed searches using very sophisticated, time consuming experiments. And so far, they have all failed to find any of these magnetic monopoles. So what we certainly know is that they don't exist in any abundance and possibly they don't exist at all.

Now, that's an important thing to take away for what I'm going to say later. There's a big but in all of this, we are stuck when we do physics experiments with the fixed rules of the universe. In other words, we're stuck with a fixed set of particles, the ones that we've discovered so far. Maybe there are a few others yet to discover, but they probably don't live very long. And there's a fixed set of parameters, the fundamental constants that sit at the back of our physics textbooks.

Things like the speed of light. And they're set at fixed values. And that constrains the way the universe is, that's a very good thing because it means that life can exist in various other properties can exist. But one of the questions we might like to ask is what if the rules were different?

What if we set up the universe a different way? Now, people speculate about this, and they wonder about the multiverse, for which there is no experimental evidence, so I'm not going to talk about that at all today. I'm going to talk about things for which there are experimentally evidence. Essentially, is there a way to explore ways in which the universe could be set up with a different set of rules, which might then produce different sets of particles and different constraints?

And it turns out that there are a way to change the rules, and that is through quantum materials. Unsurprisingly, given this is the Quantum Materials Symposium. The thing about a quantum material, it's a crystal. It may not necessarily be a crystal, but that's all I'm going to be talking about today. It's a crystal like this with atoms moving over a very large distance or fixed in a lattice, which is over an enormous distance on the scale of an atom.

That may be something that you can actually hold in your hand. And each one essentially behaves like a new universe with its own set of rules, its own set of fields and its own set of particles. So what we have in every single different crystal that we work with is a different universe to play with. And that's where the excitement is now. Many of these quantum materials have rather complicated chemical formulae.

And if you didn't like chemistry at school, you'll see these chemical formulae and think, No, this is not what I want to really be thinking about. I've come to a physics lecture. I don't want to see these things. But the great thing is about these crystals, they have to be made of atoms, and all we have is the periodic table. So we have to have various different combinations of atoms.

But the great thing about the periodic table is there are lots of atoms in it, so there are lots of combinations. So there are lots of things that we can do that these are actually rather simple compounds here or some other ones that actually I've worked on recently. And one of them, as you can see, the the chemical formula just goes on forever and ever. So some of these things are chemically quite complicated.

But as physicists, why we're interested interested is because they can sometimes show incredibly simple, beautiful properties, which don't really depend on the complexity of the chemistry that lies behind them. OK. How do you make quantum materials? Well, what you really need? This is an example of a quantum material. This is a crystal of copper near bait, and to make it, you need a very specialised piece of apparatus.

This is a mirror furnace and we have one upstairs here in the cloud inventory. But you don't just need the material. You need somebody very clever who has spent their career optimising this, and we have Dr. Prabhakaran here who does this. Now, that's not the only way you can do it. This is how physicists make quantum materials. We tend to like crystals. But in fact, if you want to make some completely new material, what you really need is clever chemists.

And here's to that. I work with who are based here in Oxford. But there are many, many others, and it's a very, very large community of people who have to make innovative choices in terms of designing new materials and the clever thing that these two people do in different ways is trying to find systems that are made out of equilibrium. So rather than just finding the ground state, they find clever ways of tricking nature into producing very unusual materials.

OK, so we have these quantum materials. Each one is a new universe. Each one is set up with these new rules, new fields and new particles, and that's what I'm going to be telling you about today. So let me, first of all, start with a really, really simple example. So this is almost trivial. But if you take something like diamond, diamond is essentially carbon arranged in a particular lattice, then it has a rather unusual property, which is that light.

We can actually change the speed of light in diamonds. Now this is something you will know and has been known for centuries that materials have a thing called a refractive index and that changes the speed of light. It's quite a dramatic change in diamond. Two point four times slower is a big effect.

Why does it occur? It occurs because when you fire light into diamonds, all of the atoms of carbon are surrounded by charge, and the light interacts with that charge in such a complicated way, it gets absorbed and irradiated. And that complexity can be just summarised in a simple number two point four, the refractive index. And that's what gives diamond.

It's rather shiny properties because you get a lot of total internal reflection when you have a lot of high refractive index interfaces with air, which has a low refractive index. So that's one simple example we can change the speed of light. It's almost trivial. Slightly less trivial is this. This is calcite, a different material. And the interesting thing about this is that it has a speed of light, which is different along different directions.

So I took this photograph earlier today. If you just move the crystal down over where I'd written quantum materials. You get a double image. And this is because light with different polarisations goes through the calcite crystal with a different speed of light. And so you get a double image of so-called by refrigerant effect. So another very, very simple case these these two are almost trivial and you're probably relatively familiar with those.

So let's maybe go to something more complicated. Let's look to see if we can make new particles. So this, again, is a simple example that some of you may have heard of and a semiconductor, you have what's known as a valence band, which is largely full of electrons. Then you have a band gap and then you have a conduction band, which is largely empty. This is the kind of structure that you have in something like silicon inside silicon chips.

Now, the valence band is pretty much full of electrons. The conduction band is almost empty. But what can happen if you're not at zero temperature is that some of the electrons in the violence band can move up into the conduction band and they can wander around. And what they leave in the valence band are holes. Now the holes themselves can move around and they behave like independent particles. Now, you might say. And physics students often do, but hold on a whole doesn't really exist.

Whole is just an absence. So how can a hole really exist? If the hole moved one place to the right, it's really because an electron moves one place to the left. So why are you going for this complicated description of talking about holes? But the reason because physicists like it is we always focus on the simple thing where there's very few of them. And that's the way human brains work. So we focus on the holes. And there's a there's a sort of similar analogy with this.

If later on after this lecture, you need some refreshments. Then as you stare into your your beer, you will probably notice absences of beer floating up to the surface. Now, of course, we call these bubbles. Yes, they've got carbon dioxide in them, but they're basically regions where there's no beer. So really, what you should be saying is the beer is falling down, but in fact, you focus on the on the bubbles going up. And the reason you focus on the bubbles is because there's few of them.

If there's lots and lots of bubbles, if your beer glass is absolutely full of bubbles and no beer, it's time to get another beer. OK. That's one way in which you can make new particles just by removing old particles. But here's a rather subtle way. So if you take something that's definitely a wave and oscillating mass on a spring, the kind of thing that we torture first, geophysicists, physics students here working out. So the spring goes, the mass goes up and down and the spring compresses.

Now one thing you can ask is what happens if I take energy out of this system? So here is a mass on a spring with less energy in it. And here now is one with even less energy in it. So as you can see, the frequency stays the same, but the amplitude goes down. Now what happens if I keep on taking energy out? Well, eventually the mass will be stationary.

I didn't draw that because I thought you could imagine it. When it's completely stationary, though, there's a problem because Heisenberg's uncertainty principle say says that if you know that it's stationary, you know that it isn't moving. You don't know where it is. And the consequence of that is you can't take all of the energy out. There has to be a little bit left. So eventually, the mass on the spring has to be vibrating very, very slightly.

Not so much that you can see with a real big one kilogram mass on a spring. But if it's an atom vibrating on a bond, then this so-called zero point energy is a very real thing. And another consequence of that, it turns out, is that when you add the energy back in, you can only add it in lumps. And those lumps are cancer, so it's a little bit like a vending machine that will only allow you to enter your your money in multiples of 20p or something,

it won't accept 10 days. So there's a basic unit that you have to add energy. And what that essentially means is waves make particles because of this fact that you can only add energy in lumps. It means that there is a natural quantum nature to the way you add energy. So any wave like system has associated with it particles of energy. And this is a rather fundamental feature. Of course, it's rather simple for mass on a spring.

But when we deal with the quantum material, what we typically have is a huge number of atoms in our crystal. I'm just showing you a plane here with a rather interesting normal mode, but you have lots and lots of different ways in which the crystal can vibrate, and each one of those will correspond to a particular particle. These are known as photons, and they behave very much like real particles in the system.

Now, it turns out we can do the same with magnetism, so here is a whole lot of spins which are all aligned. These are magnetic moments. Each one is a magnetic atom. And what I've done is I've set up a wave motion in them and this is a self-sustaining wave motion. And because essentially it's behaving like a wave. There are particles associated with it. We call those magnums. Here's another example of.

And now in two dimensions of a whole lot of magnetic moments or processing in a rather complicated dance, that's one of the normal modes. Here's another one. Slightly different. So if I go back to the previous one, you can probably see lines of these magnetic moments or vibrating together. If I move to the next one, you can see the lines now go in a different direction. So there are lots of these different normal modes that you can play with.

And if you stare at that long enough, you will soon be hypnotised. So I should probably move on from this. But each one of these normal modes are associated with particles. Now, how can we really detect that those particles are there? Well, one of the ways we can do it is we can go to somewhere that will scatter things off those particles. And this is very close to us here.

This is the Rutherford Appleton laboratory, about 15 miles south of Oxford, so we can hear use very high energy photons, X-rays. We can use neutrons. We could also use muons. For those of you that are local, that's the A34 going down there. Actually, this is an old photograph, so you can see the power station, which no longer exists. So I've rubbed it out. But what happens in these types of measurements, particularly the neutrons and the X-rays, is we do something which is very much like this.

It's essentially snooker. So a neutron or an X-ray is fired into the sample and it will bounce off one of these particles one of these magnums, or phonons. And so we can see these particle like excitations, we really know that they're there. There are various people in the department, my colleagues here, Andrew, Radu, Paolo and Roger, who do these kinds of measurements using these techniques to study these types of materials.

So I'm also involved as well with the muons, as you heard earlier. Other types of new particles. Now this is my one equation in this talk. This is a public lecture, so this is kinetic energy equals a half the squared. I'm looking at a couple of people here right now know this very good. So if you have the energy as a half mass times, the velocity squared and you plot it as the graph, you have a parabola. That's a very simple thing that people learn for their GCSE physics.

And if you look inside a quantum material, what's the equivalent? Well, it looks a little bit like this. So this is for Strontium Erudite, which was discussed in our symposium earlier today. So I'm putting energy against essentially velocity its momentum, but it's essentially the same thing. And so what you see is something that looks rather complicated, so it looks a little bit like this. Lots and lots of these energy bands. So what can we say that's going on? Why is it so complicated?

Well, it's partly so complicated because we're dealing with electrons moving through a complicated periodic system with lots of atoms that. The electronic states are all made out of the electronic states around atoms and atoms have lots of energy levels, so that means lots of lines of spaghetti. But the interesting thing that you might notice is at the bottom of some of these bands, they look approximately parabolic.

And that means we can say that they behave a little bit like an electron in a vacuum, except the curvature is different, and looking at this equation, you can see that means the mass must be different. So the interesting thing about many of these materials is the electron takes on a different mass. So one of our fundamental constants in the universe, we're able to adjust in these different materials because we can have the mass being anything we like.

In fact, it can even sometimes be negative because we can be we can have something that looks like an empty parabola. So the design changes. So this is a very interesting thing, and it also turns out because of interactions between electrons and other electrons. We sometimes end up having strange enhancements of the mass. And this is something very interesting for physicists to understand. It's a little bit like the effect that you might have is if you go to a cocktail party

and there are lots of people standing around and you want to get to the end of the room. And the problem is, there's lots of people in your way. So it takes you a long time to get from one end of the room to the other. It's like your mass is enhanced, and this kind of effect also occurs in these quantum materials. So one of the people who studies that here in Oxford is Amalia Kildare, who does very elegant experiments to explore these kinds of band structure.

OK, so lots of new particles in these materials, some of them are rather complicated, so I'll just will quite quickly through some of the more exotic things that have been seen. So in graphene, the wonder wonder material made out of carbon sheets. In fact, you can make graphene if you have a pencil. What comes off your pencil is lumps of graphene, sometimes graphene stacks.

And it turns out that when you do the similar kind of analysis for the electrons in graphene, you end up having electrons that behave not like quadratic x, but a linear behaviour. And this looks very much like a particle, like a photon, except the speed of light is different. So the electrons in graphene behave very much like light, but with a speed 300 times slower. So that's a very interesting phenomenon.

Another type of particle that is studied in some of these materials, tantalum arsenide is one that shows this a so-called vhile fermions. Herman Vail was a physicist who worked in the first half of the 20th century, and he worked on various problems of what are known as massless chiral fermions. This was an exotic particle theory that at some point looked like might describe neutrinos, so particle physicist became very interested in it.

In the last 10 years or so, quantum materials physicists have become really interested in these these types of particles because it's clear that they show up in certain compounds and, in other cases, Majorana fermions. These have been found in various different materials. These are very strange fermions, which are their own antiparticle and again have been posited as something that might be important in neutrinos.

But again, it's not clear that that's the case. The interesting thing about Maiorana is that these Majorana fermions, they were proposed by this physicist atory Maiorana in 1937, a brilliant Italian physicist. He then went missing in 1938 and nobody knows what happened to him. So there are two mysteries about Maiorana. First of all, what happened to him? And secondly, what's really going on with his fermions? So we're really at the moment able to work on the second problem.

And my colleague Julian Chen here in Oxford works a lot on determining the properties of these systems. Not only are the new particles, but there are also new properties. And one of those properties actually discovered more than 100 years ago in superconductivity.

So here is a superconductor levitating above the magnet. Now, in fact, there's a big Oxford connexion with superconductivity because of Fritz London Fritz London was one of the German emigre scientists who came over in the 1930s fleeing Nazi Germany and Oxford gave him a home for a period.

While he was here in Oxford, he came up with a crucial theory about superconductivity, realising that electrical current can be conducted by a super conductor forever and ever with no resistance in exactly the same way that electrons go around an atom forever and ever. And the reason is because they are in a quantum coherent state, unlike electrons travelling along the usual copper wire, which scatter and quickly lose their coherence.

The electrons in a superconductor have that kind of aethereal beauty that you get with electrons going round and round an atom with no battery needed. And so that was a crucial insight to the theory of superconductivity, which both later this is the structure of a high temperature superconductor.

One of the one of the compounds that was discovered in the 1980s, another quantum material which shows superconductivity at very high temperature, just quickly mention about the history of superconductivity. This is a graph of the transcendent transition temperature below which superconductivity can be observed against year of discovery. So superconductivity was discovered in Mercury, and it was then found in lead also found in aluminium.

So your aluminium saucepan will be superconducting if you get it below one degree above absolute zero. So something you can try at home. Niobium is another very good material. But the real breakthroughs took place after the Second World War, when various alloys of niobium pushed the transition temperature. Still, a long way from room temperature, we're up here. But these materials are incredibly useful.

And so these led to the development of MRI scanners, which all contain superconducting wire and that coils and also the coils inside. So one of the big companies that took advantage of this, this sort of period was Oxford Instruments, founded by Martin Wood, now Sir Martin Wood, and you're all here in the Sir Martin Wood lecture theatre. So we're actually in a lecture theatre which comes off the profits of this discovery.

And the real breakthrough took place in the late 1980s with the discovery of discovery of the high temperature superconductors, and you can see the transition temperature. It's now getting almost halfway to room temperature, so there's the high temperature superconductor again.

More recently, the iron based superconductors were discovered and something that a number of us have been studying quite intensively here in Oxford very recently to new discoveries of pushed the transition temperature very close to room temperature. The only problem with these two materials is that they are only superconducting under extraordinarily high pressure, almost half the pressure at the centre of the Earth. So these are not going to be very practical materials.

But what it does show is that there's nothing unfeasible about having superconductivity at room temperature. We just haven't done it yet. So there's a lot of understanding, a lot of hard work that has to be done to understand these, these superconductors, and this is something for which there is a lot of work going on worldwide. Superconductivity is all to do with the pairing of electrons, electrons essentially doing this complicated dance to get into this coherent state.

But superconductivity isn't the only type of dance that electrons can do. And that's actually something that we're starting to do in quantum materials is to understand the subtle choreography of electrons. So if you think of this analogy of dance as the dance, this could all be information. This is what we call ferromagnetic order, whether the the magnetic moments all are aligned. We can also have stripe order. This is the fractional quantum hall liquid.

And here we have a so-called spin liquid or a string liquid. So you can see this is a rather recent article trying to use trying to find the right analogies to describe these rather complicated ways in which electrons do a rather subtle dance. Now, I just want to finish with one example, which is rather a deep example, but I think exemplifies a lot of these ideas about new universes.

Let me take you back to a very familiar piece of physics. So if you have ball magnets that you may have played around with as a child, you probably know that north and south attract and south and south repel and north and north repel. So that's a basic property of magnets. So another thing you might know about magnets is that and this is an experiment that was done, I think, first about 700 years ago. If you take a magnet and you cut it.

You make two new magnets, almost like one of these snakes, if you cut it and you form a new head or a new tail in mythology, this was how William Gilbert described it in sixteen hundred. But this certainly happens. You make a new South Pole in the new North Pole. So one problem is we don't seem to be able to separate the North and South Pole. And that's another way of saying what I said right at the beginning of the lecture.

We can't make magnetic monopoles in our universe. What about in a quantum materials universe? Is there a way of doing it? Well, there's a little experiment. You can kind of do a little thought experiment that might show you how this works if you take a periodic line of magnets, and let's just pick the one in the middle and let's rotate it.

Now, if we rotate it, it will not like this, this will cost energy because what we've done is we put two south poles together and we put two north poles together. So this will cost a lot of energy. So this isn't a very good thing to do. But having done that, there's another interesting thing that can happen if I take the next Margaret and I rotate that round. That won't cost me any extra energy, because all I've done is move the pain from one place to the other.

But what I have now done is I've got a double south and a double north, and I've separated them. And of course, I could now rotate this magnet magnets and move this along. So this whole business of being able to just move the pain from one place to another means that what I've done is I've made two exhortations that can separate to use the jargon they fractionalised. We've taken a single flip. We've sold it in half and move the two parts away from each other.

So just another kind of picture of the same thing. Here's a line of ball magnets. Then I've just rotated one, and then I've separated the two by a whole series of spin flips. And you can see what I've now done is I've made something that looks like a monopole here and a monopole there. Well, this is clearly just a little game in one dimension, but it turns out in quantum materials you can find a material. It's called dysprosium tie tonight. That does essentially the same thing.

This looks rather complicated, but these magnetic moments have what's known as the two in two out rule. So two of the spins points in two of them point out, If I take a spin and I flip it. What I do is I do just as before. I make a defect here and a defect here that cost me some energy. But then with no further energy, I can just move the defects apart. And so what I've done is I've made things that behave very much like magnetic monopoles, and I've separated the north and the south poles.

Interestingly, this can be done in this material dysprosium tie tonight, and here's how it looks. So this is one of Dr. Background's crystals of Dysprosium Titan eight. You can hold it between your thumb and forefinger, and it does contain magnetic monopoles. There a special type of magnetic monopoles, they're not breaking any fundamental laws, but they are proper emergent monopoles that have one overall squared force between them.

And so now there's a lot of work to study these magnetic monopoles. Very recently with my my colleague Seamus Davis, who's just moved from Cornell. We've been thinking a lot about how to do this, and this is the sound of magnetic monopoles. So this is measurements of dysprosium tie tonight in his crystal. And this is with the sample in the squid. And this is with it out so you can tell the difference.

It turns out the noise of the fluctuating monopoles are such that the fluctuations are in the kilohertz regime, which means you can hear them. So although we normally plot graphs for this particular case, we thought it was rather fun to actually listen to the data. So you've just heard the sound of magnetic monopoles. OK, I've talked a lot about these monopoles holes in semiconductors, magnums, phonons, vile fermions, magnetic monopoles. So one question you might ask is, are these real?

After all, isn't the fundamental thing the things that you measure in particle physics, those are the things in our real universe. These are things that are just existing in crystals. They're somehow not as fundamental. Well, in fact, even the real particles in our universe are just excitations in a quantum field, and that's our current best theory.

And when we do the descriptions of these crystals, we're using exactly the same kind of mathematics, quantum field theory and these monopoles and these various other things are just excitations in the quantum field. So I think from a philosophical point of view, it's just as valid. I'm not claiming that the particle physics is a wasting their time. No, that's a very important avenue of research.

But what I'm really trying to make the case for is that in quantum materials, we have a richness that is really extraordinary. It's limited only by the combinatorial nature of chemistry. And what's more, some of the things that we work on also turn out to be useful. But if I'm honest, that's not what really draws us into it. It's not just trying to find a room temperature superconductor. It's the fascination of understanding these many universes. The one very final example.

I should say that not only do these different crystals, each one gives us a new universe, but when we have a crystal, we can also tune it. So this is a particular material that is tuned by both magnetic field and pressure and temperature to make all these different phases that I'm not going to talk about. The superconductivity spin density waves, metallic behaviour, field induced and spin density waves and enormous amounts of complexity.

And we have lots of control parameters, temperature, magnetic field. We can press the sample to change the interactions between the atoms. We can use chemical doping. We can use strain by and isotopically tuning the materials in one of the talks we heard today in our symposium. We heard how you can use coherent light to tune materials. So all of these things are available to us. So, yes, we have the many universes of quantum materials.

But I should finish with a conclusion. And so my conclusion is from William Blake. Yes, he wrote Jerusalem and some of the some of the words in that a lot of nonsense. But I think this is rather profound. So to see a world in a grain of sand and a heaven in a wild flower, hold infinity in the palm of your hand and in eternity in an hour. Thank you very much.