In this lecture we're going to discuss a very interesting anybody quantum effect
namely the phenomenon of super conductivity.
which is rather amazing field, because superconductors have a number of
remarkable properties, such as for instance so shown here the phenomenon of
levitation, I'm showing. A, a high-temperature superconductor,
wrapped up in a tissue to avoid heating, levitating on top of the magnet.
So, and this phenomenon is actually unique in this forum to superconductors
based on expulsion of magnetic flux or Meissner effect.
So here I'm actually showing you a movie. Of the same effect which was recorded by
my experimental colleague Johnpierre Paglione in the Joint Quantum Institute.
So and you here see a superconductor moving around on top of a magnet.
So this phenomenon of levitation is indeed, well, quite remarkable, and is
oftentimes used to to impress visitors at various science shows.
but it's just one of many exciting phenomena that appear in relation to
superconductor, and some of them we're going to discuss later today.
But let me just mention that superconductivity is an extremely rich
field, so suffices to say that it has so far resulted in about ten Nobel Prizes.
This that have been awarded for various discoveries of superconductivity and
furthermore there are definitely a lot of major mysteries that still remain in the
field. And obviously we can not discuss
everything in one lecture so I'm going to focus on the of the lecture on a key
theoretical concept that sort of underlies.
The theory so-called Bardeen Cooper Schrieffer Theory of Superconductivity.
And this is the phenomenon of Cooper pairing, which is responsible for to a,
to a large degree for the appearance of the theory .
But let me start with discussing the main property of superconductor, namely the
state of zero resistance. Which, is the reason why super conductors
is actually called super conductors. And so let me go back in time about a
hundred a little more than a hundred years ago to 1911, when this happy
looking guy, Heike Kamerlingh Onnes. was performing various low temperature
experiments to liquefy helium. And during these experiments he noticed
that the resistivity of mercury dropped exactly to zero below a certain critical
temperature of 4.2 Kelvin. So, this was very surprising.
And actually, it is very surprising, and also it should surprise you.
In particular, if you recall what we discussed in the fourth lecture, in the
last lecture last week, where we talked about the resistivity of metals.
And so I mentioned that in all real materials, there always are imperfections
that give rise to disorder, that in turn give rise to scattering and finite
resitance. So, what you would expect in a normal
metal would be that the resistance can, well, it can go down but you would want
it to saturate to a certain final value. [NOISE] If there is no localization.
If there is localization, it actually would shoot up and go to infinity, but
there is no sort of reasonable sort of a priori reason, why it would drop down to
exactly zero. Not to a small value, not to a tiny
value, to exactly as a zero and this is what Kamerlingh Onnes observed and this
was the birth of superconductivity. It was the first time people, so
superconductivity, and it was truly amazing in fact, and in particular,
because of that he was awarded. the 1913 Nobel Prize in physics.
Now another effect which already discussed in relation to this levitation,
was magnetic flux expulsion. This is probably the second very
interesting phenomenon and well. If you if you have metal let's say if you
heat up this material up to room temperature, let's say and the
penetrating with magnetic flux. Well, the flux will, more or less, just
go through the material above the critical temperature and there will be no
significant distortion of the flux. So, it's sort of amazing phenomenon that
happens once you go into the superconducting phase, is that the
magnetic field now tries to avoid the superconductor.
So an, instead of going through it. It goes around it, and so you may say
that it's expelled from the super conductor and this effect is called to
the Meissner effect. So, returning to this picture of a high
temperature super conductor levitating on top of a magnet, what's actually going on
here. Is that the magnetic field lines are sort
of, go around, primarily go around this superconductor.
And you may see that this superconductor is sort of, is sitting on this on this
flux, because it's energetically not favorable for it to go down.
It would increase the energy of this system and therefore, it's supported by
this flux. Well just a short comment here, though,
is that I'm a bit oversimplifying this picture.
so as a matter of fact there is there is indeed this Meissner effect, but apart
from the Meissner effect, there is also a little bit of a penetration of the
superconductor by a magnetic field. But this penetration happens in the form
of so-called vortices. Which are if you look at the, let's say
if you look at the cross section of the super conductor, two dimensional cross
section. And sorry let me just plot it here, so
there will be the super conductor. And most of this cross section is
magnetic field free. But there are certain regions which are
very, narrow regions, very small regions, were you do have a magnetic field, sort
of penetrating through, very thin lines and these lines are called vortices.
So if, in a superconductor these, magnetic field lines are called vortices.
And these vortices are attempt to appear in the regions where superconductivity is
suppressed due to various kinds of imperfections, a disorder that we already
discussed. And this, in turn leads to the pinning of
this magnetic field line. So, as a matter-of-fact, if you performed
this experiment with a true simple type II superconductor, which allows these
flux, flux lines. You, you not only would be able to see
that it can be levitating on top of a magnet, you can actually turn it anyway
you see fit. You can turn it at any angle and still
going to sort of retain its position. And this actually even more impressive
phenomenon is due to these flux lines and the spin.
But you know, to discuss it further would be, it'd be going too far.
So, let me just stop here and say that all and all so this magnetic field
expulsion is responsible for this phenomenon of levitation.
On a, on a different note, interestingly, the Meissner effect, this expulsion of
the magnetic flux, on the theoretical side is to some degree equivalent to the
Higgs mechanism. That occurs in elementary particle
physics. I'm sure many of you have heard about the
discovery of so-called the God particle or Higgs particle.
Last year, but actually the mathematical theory of this Higgs mechanism, in a
different context of condensed metrics. Physics was put together before Higgs by
Phil Anderson. As speaking, I would call it
Anderson-Higgs mechanism. I'm not going to go into [NOISE] details
of why this expulsion of magnet flux is equal in to Higgs.
But, you may have heard that Higgs really is important to elementary particle
physics because it gives rise, because it gives rise to masses for some elementary
particles. Here you may see that the Higgs mechanism
in this form gives rise to mass of the magnetic field.
So, it becomes energetically unfavorable for the magnetic field to be inside the
superconductor. And well this energy, this energy
apparently for it to be there, is sort of proportional to the so called,
superconductivity order parameter that appears below the critical temperature.
So, I already advertised the fact that superconductors host an amazing variety
of various new phenomena. And the discoveries of this phenomena
have in turn led to these ten Nobel prizes.
And I list here these major discoveries, sort of hallmark discoveries in the
field. And the first one, I've already talked
about, this is Kamerlingh Onnes discovery of the effect itself back in 1911.
Then John Bardeen, Leon Cooper, and Bob Schrieffer, got a 1972 Nobel Prize for
developing a microscopic theory of super connectivity in the 50s.
Brian Josephson and Ivar Giaever, got the 1973 Nobel prize for discovering
tunneling phenomena is a very interesting tunneling event in superconductors.
In particular quantum, right here, Josephson if he acts simple, Josephson if
you act other than you are talking about it, but's very interesting.
So, this guys made a major breakthrough in the field, I'm going to mention it in
the next slide, by discovering so-called, the family of high temperature copper
superconductors And finally just ten years ago Alexei A
Abriskosov and Vitaly L Ginzburg, along with Tony Leggett, got a Nobel prize
In particular, these two gentlemen have a put together a theory of vortices
topological excitations, that appear in these quantum fluids.
And I'm also including here a future Nobel prize, which almost guaranteed to
be awarded sometime in the future for a theory, of this high numbers of
superconductors, that I just mentioned. We don't really know yet the nature of
these guys/g. We know they exist and know a lot of
their properties, very unusual properties, but what's really going on
there, we don't know. So, maybe it's going to be you.
Who knows? But you should hurry because I think the
new experiments are getting us closer and closer to the to understanding the, sort
of uncovering the mystery of this high-temperature coppers.
In any case I want, what I want to emphasize here on this slide, is a very
large time gap between the discovery and the corresponding prize for, of the
different superconductor in the microscopic theory of superconductivity.
Which was put together about 40-50 years later, it's not for a lack of trying.
People have tried very hard, and couldn't succeed so it turned out to be very
difficult to explain the basic nature of superconductors.
Even though it took a while for the theories to provide an explanation of
superconductivity. The experimental work on this in fact
never really stopped since 1911 since the discovery by Kamerlingh Onnes.
And, the motivation for these experiments is really easy to understand.
So, as I mentioned of course a super conductor is are special in that, they
have exactly zero resistance. So they have no losses whatsoever.
And they are able to conduct electricity with no heating.
So, if we were able to have a superconductor at room temperature, such
a room temperature superconducting wires, would have been able to transport
electricity over large distances with, with no losses.
And this of course would have been great, especially now in the view of this
looming energy crisis. Of course now we transport electricity
from where we produce it, to where we use it, using well normal wires, metallic
wires. And those involve wide resistance and
heating. And so this heat, which is loss, so this
goes nowhere. So to have a room temperature
superconductor would be great. Unfortunately, we don't really know
whether such a material may exist, or whether it is possible at all.
There has been a lot of progress, growing materials, which have a much higher
transition temperatures. Then the first 4.2 kelvin superconductors
back here. So, this is the discovery of
superconductors, and this plot here is really a diagram, so here is the year
from the early 1900s. Up to almost now, and the points are the
correspond to compounds, with the various transition temperatures.
And so it, you see that for the first let's say 70 or so years the progress has
been really slow. But then in the, in the 80s, there is a
huge jump up to here, and this class of materials are what I already mentioned.
The high temperature superconductors, so-called Copper Superconductors
conductors, which are getting, which is, is somehow dangerously enclosed, close to
room temperature but we are not, they are not yet.
So, they're close, but you know, we still have about 100 kelvin to go.
Now and also very recently, there was a discovery of a new class of a material
so-called iron based superconductors, and it does also look promising.
but so far, although this phrase to increase the transition temperatures is,
in superconductors hasn't really involved much theories,.
It's mostly about experimental magic of growing materials and trying out
different compounds. To emphasize this fact let me actually,
in the last slide in this segment, let's actually mention a guy who was really,
really good at finding new super conductors.
He was an experimentalist working at Bell Labs.
His name was Bernd Matthias. and he was a legend in in this business.
And he, back in the 50s and 60s, he came up with a set of rules to help others
discover new super conductors and here I just list those rules.
I don't expect you to understand their significance of actually, they're not, to
be taken too, too seriously, because, in these high-temperature superconductors
most of these rules are actually violated.
But let me go over them, so he said that high symmetry is good, cubic symmetry is
best, wants you stay away from oxygen. Stay away from magnetism, stay away from
insulator, by the way, this is all we find in high-t superconductors.
And impose the most important rule due to Matthias was to stay away from theories.
And this was really bad we know because it was deserved, because again for many
years there was no theory of super conducting.
But fortunately the situation has changed in, in the 1950s, when Leon Cooper and
then John Bardeen and Bob Schrieffer, came up with the, a very, clear
explanation of the effect. And in the remaining three segments we're
going to go over, this explanation but in the next video I'm going to mostly talk
about the preliminary materials we need to know to get there.