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.