[Music] you [Music] you so let's take a short recap of the development of the field of superconductivity it was in nineteen hundred and eight well just write as recap so 1908 the super conductivity is seen in in writing in short for super conductivity as SC is seen in [Music] ultra-clean mercury and then on a large number of superconductors have been discovered and they have been debated upon many experiments have been done and it was around nineteen hundred and forty thirty nine forty is the first phenomenological theory of superconductivity came up which is called as the ginsburg landau theory and of course after that 1957 was the celebrated BCS Theory which was the most successful microscopic theory that explained all the phenomena all the experimental observations that are seen or that are made possible in the context of superconductivity so this is a BCS theory and as we have seen that it's a non perturbative theory it's a variational theory and it explains all the features of superconductor conventional superconductor what we mean by conventional will be made more clear later when we talk about unconventional superconductors and then of course lots of superconductors were discovered including the organic superconductors and it was only 1986 is when one has seen this development of the high-temperature superconductivity so this classes of superconductors have been seen which have TC is ranging from 40 Kelvin to about 200 Kelvin or even larger than that and these are all copper oxide based superconductors and in early 2000 they were discovery of iron based superconductors and so on so various development that took place regarding the understanding of superconductivity many of them were empirical and to say how they are let us see some of the results that were proposed and were found to be true at least in certain superconductors so some of these empirical rules cerise found that compounds with on an average average 5 to 7 electrons show larger PC and examples are the ruthenium molybdenum which has 5 electrons rather 7 electrons of 7 electrons this shorty C of 10 point 6 Kelvin whereas ruthenium which has 8 electrons rather shorty C of 0. 5 Kelvin while molybdenum which has T C which has 6 electrons short T C of 1 Kelvin so when when a compound is made of ruthenium and molybdenum which has on an average 7 electrons which shows a TC which is about an order of magnitude higher okay and then people wanted to understand the structural dependence and when these studies of the structural dependencies were done and they found that there are structures such as a 15 crystal structures just tell you what that is or which is also called as a beta tungsten structure that has a higher PC or all these structures have higher T C's let's see water a 15 or a beta tungsten looks like okay so this is typically a 15 crystal structure of a 15 crystal structure of a compound called a 3b and so these are the a atoms are actually at this or sorry a atoms are these blank ones that are not filled and the hatched ones are the B atoms so B atoms are actually at the body-centered places of this and if you form a line connecting the mid sort of mid of these sides and then you join them and then they sit the the a atoms sit at the at these symmetric positions similarly at all the sides so all the sides will have these a atoms two of them on each face and they are and the B atoms are which are shown in the thatch lines are at the a body-centered places now this has a larger T C so this is called it's also called as beta tungsten structure okay and this has a TC of about so they're two compounds which were notable at that time it was v3 si that is vanadium silicon and niobium germanium so both these have this same structure a three be a structure where a is equal to V for the v3 si and a equal to n be for the NB 3G so this has a TC of about 17 point one Kelvin and this has a TC of about n b3 GG as a TC of about twenty three point two Kelvin and so these are considered as a high T sees and in fact a large amount of research really had stopped off for pcs to be around 25 to 30 Kelvin and it has rarely in spite of all the efforts it has really gone beyond that in fact even with the discovery of the the organic superconductors the TC only rose just by a few Kelvin but it stayed pretty much around that till the discovery of the high TC superconductors so this 23. 2 was a maximum for quite a few years and it is proposed that with the electron phonon interaction this is the maximum TC that one can have as you understand that this temperature is very low this temperature is nearly 250 degrees below the freezing point and that is a freezing point of course water that we are talking about and so for industrial applications or for any sort of applications related to making of superconducting wires etc this temperature is not a suitable one if the temperatures the number that we show here are certainly not a viable to achieve however this research continued and this organic superconductors also were seen let me show you some organic superconductors so this is an organic superconductor it's called as an intercalated they are popularly known as intercalated graphite so these layers are what we know as graphene now so these are carbon atoms the black dots are the carbon atoms which are arranged in the form of a honeycomb lattice so this is a side view being shown and this is the top view being shown and then there are these two kinds of stacking x' that are usually taken when and now this graphene is actually a 2 sub lattice it has a 2 sub lattice basis with a and B so if is above a if a sub lattice carbon is above the a sub lattice carbon in the successive layers then it's called a a a stacking and if a sub lattice is above the B sub lattice and it's only in the next layer or the next to next layer again the a sub lattices are aligned these called as a a B stacking so here potassium is intercalated between these layers of graphite and you can see that this balls are the these are the potassium which is represented by K it's got a nice you know structure which is like a serpentine structure so these are the intercalated graphite and this intercalated graphite actually showed superconducting in below 1 Kelvin so this is organic superconductor so let's just write that these are organic superconductors and TC is about just about one Kelvin so it's a small transition temperature however there is another one let's show that this is called as K 360 so these huge buckyball structures or these full Aryans are occupying the the body centered positions of a cube and this has a larger TC TC is about so this called K 360 and the TC is about 18 Kelvin okay so and by various you know using various organic compounds that TC could go all the way up to 30 to 35 Kelvin I mean that's the maximum TC that one could achieve with organic superconductors these last two the one that we have shown this one the c8 k and this and this K 360 are called as the organic superconductors that is pretty much the story of this conventional super conductivity and many empirical these such laws were proposed and most of them were found to be correct within a certain restricted sense I will also see later that there is another this phenomenological or empirical plot that is presented which is called as a whim or a plot in the context of when we come to the unconventional superconductivity right now let us look at some experimental scenarios measuring the gap experiments measuring the energy gap of a superconductor so just to remind you that these superconductors have a certain TC which means that below that TC at any temperature below TC the superconductivity is robust so there's an energy gap that forms because of the formation of Cooper pairs so the Cooper pairs are bound state of two electrons of opposite spin and momentum and which gives rise to the fact that there is a certain amount of energy that is required to break that pair and that energy is supplied usually in the form of for temperature which is called as a thermal energy or it could be in the form of magnetic energy that is why a magnetic field the most important thing about a superconductor is the measurement of its energy cap so that we understand that how large is the gap because this gap is actually a measure of the transition temperature TC in fact it is found in the bcs theory that this gap is proportional to so this gap is proportional to the KT C and in fact there is a factor that is associated with it in fact the factor is that the more correct expression is that 2 T is equal to about 3.
5 KT C so you can see that the Delta and KT see are of the same order in fact this a number 3. 5 actually ranges from 3 to 4. 5 for most superconductors so the question is that how do we determine the gap so that we know what the TC of that particular superconductor is and a variety of things our measurement techniques are there one of them is the absorption of electromagnetic radiation I'm writing in short for electromagnetic cm radiation so the first question comes that what is the radiation frequency that we should use in order to measure the gap for that we should have an idea of what is the magnitude of the gap this is of course we don't know a priori was the magnitude of the gap because that's what we are trying to find out but at least we should have an idea so that we know what the frequency of the radiation is and this gap Delta is of the order of a 1 to 2 milli electron volt now how do we say it's a 1 milli electron volt and your one electron volt just for your knowledge it's 11,000 nearly 12 thousand Kelvin it's 11 thousand 600 Kelvin so if it's a 1 MeV then of course it's about 10 to 12 Kelvin so that's that transition temperature that we were talking about so this gap must be of the order of a few million volt may be of the order of 1 milli electron volt so if we want to use an electromagnetic radiation the frequency should be this is that or let's just write it so it's by basically H nu has to match Delta in order to break the Cooper pair so this is by Delta over H and this is equal to about if you use 1 milli electron volt it comes to around 2.
4 into 10 to the power 11 Hertz so it's basically in that regime sorry we write Hertz like this okay so basically it's in this regime of 10 to the power 11 to 10 to the power 12 Hertz which are more than a gigahertz and around 1900 and 20s and 30s this kind of electra frequencies or other magnetic radiation with this kind of frequencies were not available it was only available probably in the early fifties 1950s where such things are are possible or rather they are achieved and now of course we have even micrometer range electromagnetic radiation that are possible so let's see what how the experiments are done so in the experiment a cavity is made in the superconducting specimen whose gap we want to measure then the e/m radiation is guided into the cavity and allowed to undergo several reflection finally the radiation is captured after it has under undergone multiple reflection and and hence absorption so what we actually see is the absorption intensity so this is that absorption intensity of this of this radiation and what happens is that this absorption intensity of the radiation is actually plotted as a function of the frequency but before that what is plotted is actually I s so assuming that the specimen is in the superconducting regime and - I n so this means that the super conductivity is destroyed while the experiment is carried on keeping at the same temperature but using a magnetic field so we know that magnetic field destroys super conductivity give in reacts to a normal state so that normal state intensity is also captured and divided by basically that's the normalization by the normalized intensity so basically you try to understand that there is a kind of superconducting specimen and there's a small cavity being dug into it the radiation electromagnetic radiation of that 10 to the power 11 - 10 to the power 12 Hertz frequencies guided into it it undergoes a lot of reflection and finally it's been captured by a detector the absorption intensity it's done for two cases one is when the sample is superconducting and when the sample is normal and the normal state is achieved by keeping the same experimental setup however I and at the same temperature but however using a magnetic field the superconductivity is destroyed giving rise to a normal state and these are the intensities the absorption intensities of this the normalized of absorption intensities of this superconducting at a normal state and this is plotted as a function of nu and so this is say nu in in units of you know maybe 10 into 10 to the power 11 Hertz and so on and then what is seen is that that the the plot is so this is around 5 and this is around maybe 10 and this is 0 and so on so this is that intensity let's say it is in arbitrary units okay so what happens is that below a certain frequency which is below 5 into 10 to the power 11 Hertz one actually gets the superconducting state has a larger absorption and suddenly what happens is that this goes to zero in the vicinity so there's an absorption edge and in the vicinity of that 5 into 10 to the power 11 Hertz it goes to zero probably a little more sharp but this is what we show here I mean this could be a little sharp depending on the on the material and so basically what it see means is that beyond these 5 into 10 to the power 11 Hertz this frequency there is no difference between the superconducting state absorption and the normal state absorption now the question is that why does it happen and of course if you go to larger frequencies the difference between them remains as 0 and so this abrupt drop of this absorption spectrum results from the quantum this theory of or rather the quantum energy of the radiation is breaking or it's becoming equal to the binding energy of the pair or the energy gap that we talked about and then the pairs are the Cooper pairs are dissociated to summarize this plot beyond a certain frequency which is a here that 5 into 10 to the power 11 Hertz frequency the absorption in superconducting state and normal state vanishes which means that there is no distinction between the superconducting state and the normal state which means that it's basically the superconductivity is gone so that tells you that there is this frequency which is equal to the gap and by the gap can be estimated for this kind of from this kind of experiments it is a notable to mention that similar absorption ages are also seen in semiconductors however the gap in semiconductors is typically three orders of magnitude more or ten thousand or a thousand times more than that of the superconducting gap and in silicon it's about 1. 4 electron-volt in germanium it's about 0.
