080. Good evening, everybody, and welcome to this evening. I'm Andrew Boothroyd. I'm a professor of physics here. And I'm going to tell you a little bit about some rather unremarkable looking materials. But when you reach when you cool them down to low temperatures, possess some very remarkable properties, including complete loss of electrical resistance and the ability to levitate indefinitely.
And I'm talking, of course, about superconductors. And what I hope to do this evening is to say a little bit about what electrical resistance is, and I'll give you a little bit of history of superconductivity, which of which Oxford. This department has played a vital role. Outside. It's a bit about what superconductors do in magnetic fields. Which is important for applications.
And I'll talk about quantum coherence, which is something you've heard about elsewhere and exciting about the applications of superconductivity. So that's the recipe. And let me start off by talking a little bit about electrical resistance. So what is electrical resistance? Well, we know that electrical current is carried by electrons which flow through a metal.
And if you were paying attention in your GCSE physics, you will know that the flow of current is controlled by Ohm's Law, which tells you that the current is proportional to the voltage and the constant of proportional functionality is its resistance.
And our understanding of resistance, at least at some level, is that you imagine that the electrons are just passing through the metal and every time they encounter some object they they scatter, they scatter randomly and they form this kind of pinball path through the material.
So I like to think of that a bit. This is a bit like if you're at a party and you're trying to get from one end of the party to the bar and there's all these people dancing away and you've got to keep pumping into people and working your way round people. This is a bit like what electric electrons do in solids in metals. All right. Now, resistance is something which changes with temperature.
And this graph on the right here shows the resistance of copper metal that's used in many wires and conductors as a function of temperature. And you can see that the resistance just drops smoothly as you reduce the temperature. This is in units of this in absolute units of Kelvin. So in these units, room temperature is actually somewhere near to this end of the graph and this is the absolute zero of temperature.
And people were actually very interested in the early part of the 20th century and what actually really happens as you approach the lowest possible temperatures down here. And I noticed that. So actually what I'm plotting here is not resistance, but resistivity, which is a measure of the intrinsic resistance of material and independent of the shape of the sample that you make.
So it's always the same for raw materials. The resistivity is just a measure of the intrinsic resistance, and notice you probably can't read it, but this is in units of ten to the minus nine, I think. So this is just part of that number in your mind for later, ten to the minus nine oh metres is the size of resistance in copper.
So people are very interested in what happened as you cool metals down to low temperatures and some people said oh well what happens is that the the atom stopped vibrating because everything's very cold. And so that will let the resistance let the metal have a low resistance because the electrons can just travel without colliding so much. And other people said, oh, but at very low temperatures, the electrons won't have any energy.
So in fact what will happen is they will stop moving and the resistance will just rise up at low temperatures. So there is just no understanding. And at that time, the person who was pioneering refrigeration technology was this man here, Hideki, coming on as in Leiden. This is a picture of his laboratory. It looks a little bit like what our laboratories look like today, full of wires and pipes and tubes and things like that.
But this was his refrigeration apparatus to cool down to very low temperatures. And his achievement actually was to be able to cool down to the temperature at which helium liquefies. And for that, he was awarded the Nobel Prize in 1913. So it's a very impressive achievement. Now, one of the first things he did with his liquid fire was to measure the resistance of mercury as a function of temperature. And these are his original measurements that he made. So you can see these the points.
And as he cool down and if you don't but you can see the scale but this is 4.4, 4.3, 4.2. These are units of Kelvin as he cooled down his mercury sample and his liquid fire. Eventually, all of a sudden, he found this a sudden drop from this value to essentially something which was close to zero on his scale. And then from at lower temperatures, he could not measure the resistance. And you can see here is written by hand, ten to the minus five ohms.
That was the lowest you could measure the resistance of mercury with his apparatus. So it was like an upper limit. And actually when he first saw this, he thought there must be some problem with the apparatus because actually 4.2, which is this. Access temperature here. This is exactly the temperature which helium liquefies. So he assumed that this was just a spurious effect due to the liquid liquefying of helium. But however, he repeated this measurement and got the same result.
And then he tried with different metals and found that they also had this very sharp drop ten code, a bit lower temperature led occurred in a bit higher temperature. So this seemed to be a common property of the metals that he was measuring. It wasn't just an artefact of the apparatus, so in fact it was just really bad luck in a way that his his first measurement produced a material that had this sharp drop at exactly the same temperature as the liquefying point of helium.
And he didn't know what was causing this, but he coined the term superconductivity. Obviously, the resistance is very low. That means that conduction is very high. And so in this in the case of Mercury, he said that the transition temperature to this, whatever is happening here was at 4.2 Kelvin. Oh. So this is a picture of an ice hockey coach coming on, isn't his wife Maria. This is one of the house parties and he's got some of his physicist friends here.
And you can see that in those days, what they used to do at parties is they used to talk about physics of the blackboard here with they've been discussing physics. And I don't know, can anybody recognise any famous people on this on this picture artist? Yes, of course. We have Einstein here. So. So honest was he moved in, you know, in high circles in physics. He's very well known, champ. Right.
So on this realised of measured that the resistance of mercury and other metals went to very, very low values, but nobody really knew how low it was. And there were many experiments where people tried to measure how low the resistance really was after the metal went through this sharp superconducting transition. And one of the most celebrated experiments that was done was it was done in the sixties by Finland mills. And what they did was they made a ring out of a superconducting material.
They cooled it down to very low temperature. So that became superconducting. So it had a very low resistance. Then they passed the magnet through this ring and this will induce a current in the ring. Just just like the way a dynamo works, you pass a magnet through, you get a current flowing in it. So after the current had been induced, the current has associated with it a magnetic field. And what file of mills did was they measured this magnetic field strength as a function of time.
And in fact, they continued the experiment for several months and continued measuring this magnetic field strength as it decayed over time and in fact, decayed extremely slowly. So, so slowly, in fact, that they couldn't really detect a reduction in the current over a timescale of several months. And the conclusion from the work was, in fact, that the current in this loop would persist for 100,000 years if they let it continue going for that long, which of course, not very practical.
So from that from that value, they they could calculate that the resistance of their loop here was the resistivity I should say was not greater than ten to the -23 oh metres. Remember I said before that the resistivity of copper is ten to the minus nine oh metres around room temperature. So this is 14 orders of magnitude lower resistance than the resistance of copper.
And we now believe in fact that the in the superconducting state there really is zero resistance so that this current here is the nearest thing we have on earth to perpetual motion. Very good. So the next development which occurred in this field was by these chaps myself. An auction felt this is Meisner. He was a professor in. Leipzig and this is his PhD student at the time Oxford Felt. And what they did was they did an experiment where they cooled a metal in a magnetic field.
And if it's just an ordinary metal like copper, then as you cool it down, nothing very, very much happens. The magnetic field is not disturbed by the copper sample at all, and it's all very uneventful. But if you cool the superconductor down in the magnetic field at high temperatures, it's still just behaving like a metal.
But at low temperatures when it goes superconducting, remarkably what happens is that the superconducting material just expels, excludes the flux and expels it actively from the interior of the metal. So literally the flux is pushed out of the metal like this. It's as if the superconductor develops an opposite pointing magnetic field. It just cancels out within the volume of the superconductor.
This is very remarkable and unexpected and it's a behaviour that cannot be described by classical physics at the time. So it's a quantum mechanical phenomenon. And the story goes that when this when this happened, oxygen fell within the laboratory, making the measurements, rushed into my office and said, Hey, Meisner, I have just discovered that the superconductor is excluding the flux. And Meissner said, Wunderbar, you've just discovered the Meissner effect.
So I like to call it the Meissner Ox and wealth effect. But in the textbooks it's usually called the Meissner effect, which I think is a bit uncharitable. And at this point, though, there was no there was no theories of superconductivity that described superconductors in any adequate way. And many people had tried. And this this is one man who tried, Felix Bloch. He was a PhD student and then a postdoc working with Heisenberg.
And he tried for a whole year, did nothing else, but tried to develop a theory of superconductivity. In the early sort of 1930s. He was working late 1920s and he he made one good theorem of superconductivity, which is correct and and is still known today. But he actually made a second sort of technique tongue in cheek theorem of superconductivity, which became known as Bloch Second Theorem of Superconductivity.
And he made this as a way of as a statement to describe his conclusions from this one year's futile attempts to make a theory. What he said was, The only theorem about superconductors that can be proved is that any theory of superconductivity is refutable. So essentially nothing works. So this this was his. This is frustrated, Mr. Bloch. All right. This is a bit about Oxford now, so you can pay attention here. This these are two brothers called the London Brothers.
This is Fritz and this is Heinz. And these they were German Jewish physicists in the early 1930s who were who had to escape Germany to escape the persecution of the Nazis. And like many Jewish scientists of that time, they moved around. They moved to other parts of the world. Quite a few came to the U.K. quite a few came to Oxford, brought by Linda Lindemann, who is a director of the kind in the poetry at the time.
And the London Brothers. So they were so Heintz was a Ph.D. student here, and Fritz was a post-doc here in the department. And while they were here for a relatively short time, they worked in an upstairs room in Headington. On a theory of that, they tried to explain this. This phenomenon called the mice knocks and felt the fact they tried to understand this and they worked on it very hard and eventually they got the theory that worked.
Basically, the theory is a sort of a quantum mechanical equivalent of Ohm's Law that applies to superconductors in the magnetic field. And they realised from their theory that for it to correctly describe this flux exclusion effect, what must happen is that all the electrons in the superconductor must be in exactly the same state of motion. This is a consequence. This is the only consequence that can lead to this phenomenon here.
So this was this was a real breakthrough, although at the time it wasn't particularly recognised as a breakthrough, it was being particularly important and as is the way the money ran out. And so both of them had to be let go by the department. And hindsight, she went to Bristol University, had a successful career in Bristol for it, went to Paris and then went to North Carolina, Duke University in North Carolina.
And the story goes that Fritz, because of his German passport, he wasn't allowed to travel on the the ship that he planned to travel on. He had to delay by by one sailing. And and so he went on the next sailing. And then it turned out that the previous sailing was torpedoed by the Germans with great loss of life. So he was actually a very lucky man. Sometimes you have to be lucky in physics. So I'm still charting the historical development of superconductivity.
And really, really important breakthrough was made by these three gentlemen, Bardeen, Cooper and Schrieffer in the late 1950s. Cooper, in fact, realised that electrons in a metal in metals, in fact attract one another, which sounds a bit counterintuitive because they're both because electrons are negatively charged, but actually they exist in a a background, a positive charge, which so essentially the whole metal is neutral.
And it turns out that Cooper showed Cooper was able to show that any small interaction between the electrons would cause the electrons to want to pair up to form a repaired state, which would have a lower energy and if the electrons remained unpaired and just randomly moving around. So these are called Cooper pairs now. And I like to think of it this rather like this.
The lattice in which the electrons move. It's a little bit like a mattress, and if two people sleep on a mattress close together, then what happens is the mattress deforms and attracts the people together. On the other hand, if the two people lie on the mattress too far apart and the defamation of the mattress does not tend to attract the people. So this is a bit like this is a bit like what causes the attraction between electrons in the superconductor? There is a defamation of the lattice.
Which is actually a dynamic defamation, which causes an effect of attraction between the electrons that makes them want to pair up like this. And if you want to sort of more real space picture of what's going on, here's the crystal lattice with the positive ions. The electrons are moving through this lattice. Here's one particular electron because it's negatively charged, it attracts the atoms towards it like this.
Then it moves on and then another atom, seeing a positively charged region will actually be attracted to that region. And so, in effect, these two electrons of kind of talk to each other. And in a set in effect, what happens is as the electron moves through the metal, it leaves behind a wake of positive charge, which is like a transient charging of the metal.
And then another electron will also leave a wake like that. And so you can see that as the electrons are attracted towards the positive charge, you can see that there's a sort of a net tendency for that wants to be bound together like that. So this is a sort of hand-waving picture for why you get these so-called Cooper Pairs superconductors. And in essence, the BCS theory is founded upon the notion that electrons pair up in this way.
And the second thing that they do is they form what's called the macroscopic quantum coherence state. So I want to just try to explain in very simple terms what a macroscopic quantum coherence state is. And for this, we have to appreciate that all particles, according to quantum mechanics, behave in some circumstances, like as if they have waves, like as if they were waves. And we all know what waves are.
If you have a collection of waves like this, which have got no particular relationship to one another and you sort of add them all together, what you end up with is kind of bunches of waves which are rather which oscillate for a bit, and then they decay away. So you have little sort of packets of waves, but with no particular regularity to the whole. So this is a bit like the picture we would have for waves on water. If you look at the surface of water, you can sort of see waves.
But after a little time, they eventually decay away and become rather jumbled up again. And there's no kind of regular behaviour in the surface like this. Another another example is the light that comes from ordinary lamps like this actually consists of packets, wave packets, which are very, very short in duration, but have no special relationship to one another. So it looks a bit like this. So this is a situation that you this is how we normally encounter waves in real life.
But there's another type of situation that can arise, which is where you have what's called a coherent wave. And this occurs if all if you start with a whole bundle of waves, all of which have the same wavelength, and where the maxima and the minima of the waves are all lined up like this, then if you add these together, they reinforce one another, constructive interference, and give you one big wave with a large amplitude and which will extend over a large distance.
So this is this is a coherent wave. And this is the kind of this is this is a coherent wave is the kind of wave that you get in laser light. So this pointer here consists of a long stream of photons, of light waves, which is coherent over very, very long distances and times. Now in a superconductor, we have electron waves.
And when the superconductor is just acting as a normal metal or is just a normal metal, then then we get the situation where we have just short waves in this liquid incoherent mixture like this. Whereas when the superconductor becomes superconducting, when it loses its resistance, then what happens is the electron waves all kind of organise themselves so that the phases and the wavelengths are all matched to match together and form what's known as is this coherent,
microscopically coherent state like this. So like the laser light. And it's the reason why they do this is subtle. The reason why it's favourable, favourable for them to to lock all their phases together like that is rather subtle. But I think by analogy the same is my kind of party analogy where normal resistance is a bit like trying to get to the bar in a party with lots of people that are in the way.
The other thing that you could do is you could all agree in the party, in the room, that everybody is going to step sideways together and keep on doing that. And if you do that and you can see that you can get from one end of the room to the other without bumping into anybody, that requires a degree of kind of cooperation organisation. And that's that's essentially what the electrons can do when they go into a superconducting phase.
So I want to talk a little bit about magnetic levitation, which is the other property that superconductors have. And for this, I want to to demonstrate a little bit this property. This is a piece of one piece of black ceramic, which is actually a superconducting material when we cool it down. So I want to I want to just demonstrate that stuff to get the needle.
So I'm going to cool the superconductor down with a little bit of liquid nitrogen, a soup spoon, and I've got another one here, which is the same, but it's wrapped up in like a foam that's just to insulate it a bit. I'm going to cool that one down as well. It just takes a little bit of time to just take all the heat out of the superconductor when you can you can tell once it's cooled down because it stops sort of bubbling vigorously. So that one's nearly there. This one is not. Okay.
So with this one, what I want to do is I've got a little steel plate here which contains which has got some strong magnets which are just laid on the surface like this, and they create a magnetic field. And what I want to do is to just show you what happens when we when we put the superconductor on the magnet. So. But. Look. And you see that that's floating. And then after a rather a few seconds, it loses all of its superconductivity because it warms up above the transition temperature.
So I tried that again. Oops. So this rather unstable, as you can see. You can see it. It's floating. And then it just warms up. And then it goes it goes normal like that. So this is an example where the superconductor is actually behaving a bit like a magnet and it's just repelling. It's as if the superconductor has a magnetic pole and it's just repelling the magnetic poles here.
Light poles repel. It's just it's just floating about. So this one here is a bit easier to play with because of the insulation. It lasts a bit longer. So what I've got here is a number of these magnets laid on a track like this, and I've just cooled it down with a little bit of space between the track and the superconductor itself. And you can see that now the superconductor is actually trapped onto the magnets.
So the magnets and the there's a row of three magnets north, south and north like that. And that the superconductor actually trapped on that magnet because the magnetic field has stopped it from moving. And it's actually quite it's quite well tracked. For example, you can turn it sideways like this. You should even be able to turn it upside down. But it just warmed up too far and. Let's just try that again. So that's unusual, right? Do you think that's unusual? Why is it doing this?
Because it's behaving as if it's behaving almost as if it's both repelling the magnet. And also when it's underneath, it is attracting the magnet. So so no conventional magnet can can do that. So what's going on here? Well. What's happening is that when the when the superconductor is a normal metal just behaving like an ordinary metal, the magnetic field lines just go all the way through the metal as if nothing happens and it would drop.
And that's what happened the first time because it wasn't sufficiently cold, it just dropped. But if we place the superconductor on top of the magnetic, the magnet, as shown here, you see the magnetic field lines sort of distort and they get squashed like this. And this provides an upward force which holds the superconductor up. And it's doing this because the magnetic field cannot get inside the superconductor.
These waves are supposed to represent those coherent electron waves. These these lines here, there's no magnetic field inside the superconductor. Now, you can see that actually some of these magnetic field lines actually go above the superconductor. That's because I as I cooled it on here, some of the magnetic field lines would actually go over the top of a superconductor like that.
So when you turn the superconductor up upside down, what will happen is that these magnetic field lines will still be going around the end of the superconductor, but the superconductor cannot drop because these lines cannot pass into the superconductor. They're forced to stay underneath. And this can provide enough force if you do it properly to hold the superconductor in place. So this is why it can behave both as a like as attractive and as a repulsive magnet.
And you can imagine that this this phenomenon could have applications in real life because you could you could make a trek, a train track out of these magnets, and you could put blocks of superconductors on the underside of the train and levitated. And because there's no friction or sound, for that matter, the only resistance is the air resistance. This would be a very efficient way to travel along very fast and with little energy.
And in fact, these so-called mark-ups have been in existence for a long time, but the technologies up till now has been based on non superconducting magnets. So it requires a lot of energy then to to make them work. But there are demonstration maglev which are made precisely on this principle. There's one in China and now maybe this will be one of the technologies in the future. I have to finish shortly, but I just want to say something about how this field is moving.
Of course, for this technology to be practical, we don't want to have to keep on cooling things down with liquid nitrogen. We want things to work at room temperature. And the evolution of superconducting materials as a function of time has had a rather erratic and unpredictable history. So this was the first superconductor discovered by honours in 1908, and this had a transmission temperature of 4.2 Kelvin, if you remember.
And then he discovered lead, which is seven Kelvin. And then other people discovered niobium and so on and so forth. And gradually people discovered metals or alloys with higher and higher superconducting transition temperatures. A big breakthrough was made in 1986 when Bad Notes and Müller discovered this material, which I've been showing you today, which is a ceramic based on copper and oxygen with various other elements.
And this actually shot the superconducting transition temperature up to well above 100 Kelvin. In fact, the highest is about 150 Kelvin. But you have to pressurise it to get to that kind of temperature. And there's also been another family discovered in the last ten years based on iron, which is which has reached quite high temperatures around about 50 or 60 Kelvin. And even actually three years ago, this this field is moving on.
And even three years ago, a group in Germany discovered and you won't believe this discovered a superconductor based on hydrogen sulphide. Yeah. Stink bomb where if you pressure pressurised it to unimaginably high pressures. These are geological pressures 150 gigapascals. That's a hundred and that's that's like a million more than a million atmospheric pressures. I think then what they found was they got a superconducting material which which worked at just below 200 Kelvin.
So that's that's the highest that's a world record for the highest temperature that we have at the moment. And on this graph, there's actually two important temperatures. One of them is the temperature of liquid nitrogen, which is this stuff here, and that is at 77, Kelvin. So you can see that anything that works up at higher temperatures than that can be demonstrated on, you know, in a laboratory like this. And this is quite cheap. This this costs about the same as milk.
So this is actually reasonably inexpensive, this technology. And the other relevant temperature is this one here, which is the lowest recorded temperature on Earth at the Vostok Antarctic base, -89 Celsius. And that hydrogen sulphide is slightly above that. So, in fact, one can argue that this actually is a room temperature superconductor. If you go to Vostok on a cold day, one of the big applications of superconductors apart from transportation is and carrying current is in magnets.
And the advantage over ordinary magnets that have resistance, of course, is that you can put much higher current in them because they don't dissipate energy and so you can generate much higher magnetic fields. And they also cost a lot less to run because there's no there's very little energy lost in the power that's that's used to generate the currents. And I'm sure you're well aware that MRI magnets are, in fact, these days are entirely made of superconductors.
If you're ever unfortunate enough to have to go into one of these things, this is a big superconducting magnet carrying about a thousand amps. And so you roll into here. And yeah, it's interesting because a thousand amps is a big current and if that was to fail and you were inside it. But fortunately, because it remains because it remained superconducting, you just don't notice any current there at all.
These are magnets in the sun, particle accelerator, superconducting magnets all the way around a 27 kilometre diameter ring and these carry of about 12,000 amps. So huge, huge currents, but no power dissipation. So they don't heat up at all. So these are two of the applications of superconducting magnets. And just to finish. Those of us who work in superconductors and there's quite a big group here in the department that do we all have the vision of a future which looks something like this?
We have we have we have superconducting wires that carry power that's generated by some sort of renewable source with superconducting generators, superconducting storage devices that holds the current until you need it. Superconducting motors know basically everything is made of superconductors, even possibly quantum computers made of squid technology. So there's a huge number of potential applications.
And the only limitation at the moment is in the fact that the materials have to be cooled down to low temperatures, which which just has practical and cost considerations. But if if somebody can find a room temperature, superconductivity, then this this vision will become a reality. So wish us luck. Thank you.