 You have heard about the superconductivity, the theory and other things I am not going to the details you have already seen, three lectures or so you had. You have some idea about it, the basic mechanism, some basic simple understanding of VCS theory you have by this time. I try to give you some idea of things that are happening today and maybe some of the applications that is all I can do in a very limited time like this. Mainly I will worry about high temperature superconductors, but before I do that I do not want to just start from there. I just give you some very important features which are actually important in the sense that not only for type 1 or type 2 or high temperature or normal conventional superconductors. So I am sure you have heard about this thing, generally we classify them to be type 1 or type 2 or the conventional superconductors and high TC superconductors. Basically the type 1 versus type 2 is in that category. As you have seen some of the key features of superconductivity in general is that the resistivity is very 0. So the ratio of resistance between normal and superconducting states actually is something like 10 to the power of 14. In this context there was a question, I do not know whether it was answered or not, there was a question how are you sure that your resistivity has actually become 0. Because experimentally there are limitations, what actually is done is something like this. In a superconducting circuit the current actually is found to decay in something like this. So this is the way the current actually decays and typically it takes the time that is needed r is a resistance very small value, l is the inductance of the circuit. So I think l by r. So this actually is used, this relation is actually used to find out the decay. So dk is observed and from the value of time that it takes you actually find out what is the resistance. So this is the expression which actually used. So when you tell that resistance actually becomes 0, it is not by measuring the resistance. One can actually do find out what is the time required to get the current to very very small values. This is the technique that actually is used. So this is mostly if you can see that it goes to many many years for the current to die in a good superconductor. So that is what is used and nearly getting resistance will only give you what is known as a perfect conductor. A perfect conductor is not a superconductor, you need a perfect diamagnet also. A superconductor is at the same time a perfect conductor and a perfect diamagnet and of course is given by the Meissner effect. When you have studied about persistent current which actually has lot of applications some of them I am going to come. When you have you talked about the penetration depth, there is a depth over which the fields can actually penetrate. The concept of coherence length which essentially is the dimensions over which two electrons can form the bond the so called the Cooper pair. So it is not that two electrons are very close by and they form a singlet state the spin 0 state but actually is many lattice spacings, many lattice constants that is giving the coherence length regarding the flux quantization which actually is flux that is trapped within the superconducting loop is not anything but it has to be quantized. The isotope effect you talked about it when you have seen which essentially is some justification or some support of the DCS theory then comes the difference between type 1 and type 2 superconductors. Superconductivity is a altogether different phenomenon. Some of the features I have written here there are many but I have written some of the important things. Both metals and nonmetals become superconducting so not that only metals can become superconducting in fact it is very surprising that the best not surprising because now we know the best conductors like silver or gold are never superconducting so far they have been found to be non superconducting even to the lowest temperature achieved so far. Alkali metals are good conductors but other than CCM none of them actually superconduct. It is also found that all crystalline forms all polycrystalline single crystal amorphous all these forms are known to superconduct various materials very important thing change in the crystal structure induced by pressure this is a very important thing. Pressure is somehow found to cause superconductivity in many systems in this context let me tell you that in 2015 the latest superconductor probably that is the highest TC reported superconductor is actually a hydrogen sulphide which actually subjected to very high pressures that is known I mean that is reported to have a superconducting transition of something like 203 Kelvin. I understand that is highest value ever reported where again the pressure is very high I think 30 bar or something. So the pressure is in general many materials the pressure high pressure is able to stabilize superconductivity in many many systems the latest I mentioned about it and almost all crystal structures also not that only cubic or only hexagonal will give superconductivity many of the things are known to almost all crystal structures of different materials are known to show superconductivity. So nothing crystal structure specific alloys superconduct even when the constituents are not. If I have an alloy formed between A and B and if AB is superconducting does it mean that A has to be superconducting and B has to be superconducting if A is not superconducting B is not superconducting but AB can be superconducting that is also found out. In some cases amorphous counterparts are superconducting while the crystalline phase is not very interesting again I mean the very good conductors are not becoming superconductors but very good insulators are actually becoming superconductors. So these are some of the strange things that we do not really expect but that is actually true. As you would have seen I am more worried about high TC and applications the main things to worry about from the application point of view are three critical quantities one is the critical temperature the TC the highest higher the better any application you need to have something like room temperature. So TC room temperature is what is desired but it is not there at the point then the critical magnetic field the magnetic field it can actually survive you can apply and survive the superconducting. Similarly, the critical current density which is very important the current density it can tolerate the maximum value so the problem here. So this is basically a history of superconductors you how do you tell that something is high TC or something is low TC it is very difficult above 10 Kelvin they are actually classified as high TC superconductors they are really high TC superconductors if they are actually in the vicinity of something like liquid nitrogen temperature something like 77 Kelvin because then you do not have to you can use liquid nitrogen and do anything above that if it is 50 Kelvin it is you cannot use liquid nitrogen you have to use something else mostly helium liquid helium because liquid helium I mean boiling point is 4.2 Kelvin whereas liquid nitrogen is 77 Kelvin. So anything above 77 is ok actually everything anything above room temperature is what is looked for but anything above 77 is considered great and anything above 10 K is considered ok and they are listed as high TC superconductors there are many as various classes some of the I think I mentioned during my this one. So what are the main things was what is known as a heavy fermion superconductor I mean ok the starting point was this N B T I alloy which actually is used in many of the superconducting magnets in reality I will come to some pictures later on there is what is known as a N B 3 SN is at alloy again which is a very important in many applications these are alloys they are known from 1950s onwards. Then there are certain heavy fermion I mentioned about a heavy fermion yesterday that is they some of them are known to be superconducting these are all surprises at that time so that is why it is written here there were organic superconductors many of them were known in the 80s the cuprate superconductors came in 86 L A M N O 3 those kind of uterium varium copper oxide actually started a big boom in that direction thousands of papers came lot of patents came lot of things were happening at that time that is because of this cuprate superconductors uterium varium copper oxide started with when the fuller in came fuller in and modifications of fuller in many of them were found to be superconducting that was in the 85s I mean that range very interesting happened in 90s that was when again the magnetic some water magnetic components like boron carbides many of the things which contain rare earth and boron and carbon they were accidentally found to be superconducting recently in 2001 M G B 2 that is magnesium diborite is found to be superconducting lot of work is going on in fact M B G B 2 is supposed to be a good superconductor and from the applied point of view also lot of people are working on it so iron based superconductors came in 2006 iron is something which is supposed to be an enemy of superconductor because iron is a good ferromagnet so you do not expect for superconductivity from Fe at all or Fe based systems at all in that context this was a real surprise many of the Fe based systems are actually superconducting and lot of work is going on at the moment this I came around 2006 as I mentioned 2015 we have a new candidate high pressure candidate which actually gives you a TCF something like 2200 Kelvin which is of course high pressure means you cannot use for applications these are the things which you have already seen so the since I am talking about high TC this is essentially type 2 what you have is main difference is this one so you have a superconducting region before it actually becomes a normal region you have what is not as a mixed region where you have some magnetism and some superconductivity coexisting I will come to the picture soon or if I actually talk about the internal field and external field how the internal field varies as a function of external field as long as in the type 1 superconductor as long as external field is below the critical value the BC value I talked about the internal field is 0 there is no internal field this is a miscellaneous effect and then suddenly it becomes normal and it gets a full field whereas in the case of type 2 it is not like that up to a lower critical field it is true there is miscellaneous effect and then it slowly starts tolerating the magnetic field and it goes something like abrupt gem that you see is not here that is a type 2 or a so called high TC superconductors this is a list of so various things including the TC value here that is shown just tell you this shows you how the development happened over the period of time this I talked about LASR CO4 it is a very important compound then Euterium-Virium-Coporax I talked about some of the things which I have taken from literature just to give you an idea about some of the organic compounds also shown here some metals some metallic systems all are shown here fuller in is here fuller in modified fuller in is here so all these things are shown here essentially it happened over the last 20 30 years how the TC has been gradually increasing towards room temperature this another picture which again shows how the development happened you can see both oxide material that is insulators and the metallic systems how the TC's are distributed as I mentioned again liquid nitrogen is taken as a reference because anything below liquid nitrogen is not so good anything above liquid nitrogen is definitely very great achievement so these are some of the main differences between type 1 and type 2 as I already showed you certain laws of magnetization whereas here it is a gradual loss the Meissner effect is not very discontinuous in this case there is a mixed state in this case mixed state means the normal and superconducting states and this is actually a soft superconductor generally these are all hard superconductors examples lead and tin are the standard examples of type 1 superconductors mercury of course and here as I mentioned nvsn nv3ti all nv3sn all these alloys mostly they belong to type 2 superconductors which are actually commercially exploited as I am going to show this is actually what is known as a mixed state which actually is called the flux spin the state you can see the you have normal regions where actually the otherwise superconducting region this normal magnetic field regions are penetrating and you have normal and conducting regions coming together separated like the domain separated by domain walls. So what you are seeing here is I will give a very elementary picture of this what you are seeing here is there is a wall there is a surface which is actually separating the normal region and the superconducting region these surfaces are the one which actually is very important how do you know that that is very important very very simple empirical understanding that has been obtained is this one your two main length scales are a superconductor one is a penetration depth other thing is a coherence length one can actually get an empirical relation conducting the two and try to see whether something is going to be in type 1 or type 2 remember whenever a surface energy is positive that means it will not be possible to have it and then you will not be able to have two regions. So that means you will have only one region type 1 so what is found is when your penetration depth is actually smaller and the coherence length and the coherence length is more what is found the calculations have shown that the surface energy is going to be positive which means that the surface cannot be supported which means that it has to be only one type only s type or n type so that essentially gives you a type 1 superconductor. On the other hand if the penetration depth actually is more than the coherence length it is an empirical relationship but actually works in many cases if it is this way then the surface energy is found to be negative which means that the surface energy can be energetically favorable which means that you can have a normal region and superconducting region giving rise to the so called type 2 superconductor it is a very empirical thing but it actually is very useful. I will come to the application some of the applications we think that superconductivity has today there is no application that is not true superconductivity has large number of applications as listed here from the energy point of view it is a very important consideration today because energy is a global demand clean energy and other things are being talked about lot of things more than that the magnets have become an important thing as far as superconductivity application is concerned. In medical case of course this MRI is something which is a routine test today MRI works with a very high magnetic field which cannot be obtained with the electromagnets that somebody asked earlier also electromagnets can give you typically 1, 1.5 tesla magnetic field these can even in many labs we have fields of the order of 9 tesla which actually can be produced only with the help of a magnetic superconducting magnet where the persistent current is giving rise to this magnetic field. So MRI machines we need MRI is essentially an NMR magnet NMR instrument NMR magnets or MRI magnets are heavily dependent on this superconducting magnets there are other applications which are not very straightforward but they are very important one very important thing that is not written here is actually superconductors generally cannot support type 1 basically type 1 superconductors generally cannot support any property that depends on the gradients thermal conductivity is one thing thermal conductivity is temperature gradient it depend on temperature gradient gradient. So thermal conductivity is actually very poor in the case of superconductors in general. So because of this one we can use as a switch you have one region hot region cold region you want to have connection between the two sometimes you want them to be connected sometimes you do not want them to be connected what you can do is that you can put a superconductor in between as long as this is in the superconducting state the temperature is low then this acts as a off switch off position because it cannot this is having a very low thermal conductivity when you increase the temperature locally it becomes normal it gives you a normal conductivity. So this is between on and off there are n number of such applications possible because of the special properties of superconductors one I am just giving you anything related to gradient cannot be supported electrical resistivity is again the same issue because it cannot support voltage differences voltage gradients cannot be supported. So it cannot have any resistance change so resistance between two points it cannot have so it actually becomes 0. So there are such applications where one can actually see this kind of things. So when if there is a current then the current has to move in such a manner that there is no potential difference between the two any differences it cannot tolerate any gradients it cannot tolerate. So when there is a current and if there is a resistance there is an IR drop this IR drop between two points is not allowed because you cannot have you cannot have differences within the so called condensate the picture another picture is a condensate picture I am sure it does in it. So this is not possible so only way is you have to have current but there is no drop means your resistance has to be 0. So similarly the thermal conductivity has to be 0 thermal power has to be 0 all these things are determined by differences in some properties all these things have to be 0 very elementary way of looking at it. So this is something which is very important instrument which some of you will be having in the search labs if you are having magnetism activity this is a skewed magnetometer. I am showing you this because here superconductivity has two important applications not just one here you are using a superconducting magnet made up from type 1 superconductor which actually giving rise to the magnetic field of the order of 9 Tesla or 12 Tesla depending on the money you pay that is one number one use very important any 5 field is superconducting magnet other thing is this is used to detect very small magnetic moments associated with materials or very small magnetic fields it produce your sample produce that means it is used to find out very very low magnetic very weak magnetic properties of very weakly magnetic substances this use this is using the principle of skewed magnetometer the flux quantization Josephson junction you have studied. So this is basically usually the DC Josephson effect is used in the super what is known as a quantum interference property which actually is really used in this case is a commercial instrument where we use again the superconducting quantum interference property which actually comes from the Josephson effect. So here you are using the persistent current for producing the magnetic field and the Josephson effect to sense the magnetic field that your small sample is producing. So that way this is a very unique example where you have using two different very important properties of superconducting do not worry whether it is type 1 or type 2 but it is actually an important application of superconducting. Another very important thing is actually the production of magnetic field itself this is a way you connect us switch usual case what we have is like electromagnet the power must always be there to get the magnetic field as a answer to somebody earlier but in this case because of the persistent current once it is energized you can remove this and the system will produce a magnetic field which will decay as I mentioned after several several years. So this is something a part which is actually there in the earlier superconducting magnetometer. So this has this thing this is as far as a magnetic part is concerned of course then the other part the detection part using the quantum interference is another issue. This is of course all of you have heard about in the mag left if you ask me is it a reality or not yes and no because people have successfully demonstrated it is possible at least in Japan you would have heard about it something like 300 kilometer per hour I think very high speed trains have been successfully run where you have a superconducting part there and it produces a diamagnetic effect on some of the some points on the rails which is able to levitate it because of the perfect diamagnetism and it is able to levitate which means that your friction is considerably reduced and hence that gives you a very good free movement which actually is saving lot of power. So in that context again today it is a very very important aspect the last thing I will show is a magnetic shielding you can not only that it can produce magnetic field because of this flux exclusion it can do if you are really looking for some place some part some instrument to be completely shielded at least theoretically one can think in this line you can completely screen the particular region away from the magnetic field there are various ways of doing it magnetically also because if you if I want to cover some electronic equipment free from magnetic field earth including the earth magnetic field what we generally do is we cover it with a high permeability material. So high permeability means all the magnetic lines of force coming from wherever it is it will actually go through that because high permeability will absorb everything it will take everything it will go through that nothing will go inside that is one way of shielding it but this super conductivity principle can also be used to shield a region completely from the external magnetic fields. So these are some of the applications again this list can really go a long way like in the case of magnetism just to give you a flavor in connection with the some of the important properties only I have shown you and this is something which is going on even today as I mentioned 2015 you have a new material whether it is going to be produced in an industrial scale or not that is a different issue but there are materials coming up lot of new unexpected in fact all the materials that have been found to be good they were all from unexpected categories. So like that this will still go on and I am sure that depend on superconducting materials and magnetic materials is huge today and it is only growing with this I finish all my lectures I can take some questions you are not able to ask the questions or you do not want to ask at this point of time but you still want to have some problems please write to me I will be answering in the remaining days does not matter when I will be able to do I can always do that over the email. 1136 PSG college go ahead. Good morning. I have a question to be clarified in band ferromagnetism yeah ignoring the orbital contribution yeah with the help of overlapping alone it is possible to determine the non integer value just as it is stated how it is possible to estimate the exact value of non integer I would like to know answer for this. How to know the exact value of how do we measure the non integer value with the help of band overlapping alone yeah I get so what I have actually I have written one example there since because of lack of time I could not explain nothing but it is there in the slide if you see what we can do is that we generally do what is known as a rigid band model. So what you can do is you can actually find out various techniques are available today if you want to do that you can find out depending on the number of electrons that are actually transferred from the 3d band to the conduction band you can find out and from subtracting that because that contribution magnetic contribution from the 4s electrons will be quite small compared to the contribution from the 3d. So if you do the calculation one can see that when you add the 3d contribution and the 4s contribution it will never happen to be an integer. So you have to essentially find out how much is a charged transfer that is happening which actually is determined by the degree of overlap between the 3d and 4s. So in standard cases assuming a rigid band model you can actually get some idea about how much is the transfer between the 3d and 4s we know how much is in the case of nickel how much is in the case of cobalt that is known. If you want to do experimentally of course one can do but it will do is other way we do an experiment to find out how much is the I am getting and then do a back calculation and see okay I can tell that this much is a fraction that is actually residing in the 3d 4s band instead of the 3d band. So it is other way that is actually done but definitely if I do a proper calculation I can actually find out how many will reside in the 4s band. Thank you sir. Good morning sir. Good morning. Sir in slide number 3 it is mentioned that the metals and nonmetals can be superconducting at low temperature. Yeah. How a nonmetal can be superconducting at low temperature sir. Yeah so this I would have seen in the other lectures, Professor Gorsh's lectures. Superconductivity has nothing to do with the conductivity or the such properties. It essentially at least as per the BCS theory which we believe in many times is the electron phonon coupling. Electron phonon coupling is found to be very strong in many of these oxides and that is what actually binds the two electrons and if you are able to get a cooper pair, a stable cooper pair you are supposed to get superconductivity. So if the conductivity has nothing to do with that. So that is why the best conductor is not superconductor. Silver or gold is never a superconductor. So what is more important is not that conduction electrons are the conductivity, the conduction electron concentration. What is more important is the electron phonon at least in this picture what is the electron phonon coupling that you are able to get so that the usual screen and the coulomb repulsion of the two electrons can be overcome so that you can create a cooper pair. In this picture I am not telling that this is really the correct which BCS is not always true but going by the BCS model one can actually tell this is the mechanism. So depending on the system you will not be you will be able to tell whether your electron phonon coupling is strong or not. If it is strong naturally you will get superconductivity depending on the strength you will get a low TC or high TC. So nothing to really really related to the coupling. Of course the conductivity but of course the band structure plays a big role that is very important. Hello sir again what is the difficulty of using high digit superconductor model? Difficulty? Yes sir. Yeah so difficulty in the sense that first of all for any application you should get them in the proper shape mostly in the case of in the form of a wire in the form of a thin film and other things. I know that people have been working on the wires of MGB2 at least I know that work. So and you should be able to produce the in the bulk scale at a reasonable cost. So that is an issue whether you are able to get them large quantities in the proper shapes and in a low cost then definitely that will be used. Good morning sir. Yeah please. Very basic question. Yeah. Actually school students are studying that they do not keep the magnets near the heat source but our earth is exhibiting the magneticism even though it has a tremendous amount of heat in its core how is this possible sir? So okay so only thing I can tell is that so earth I mean first of all somebody was asking I do not think we have a clear understanding of the reason for the earth's magnetic moment strictly speaking. I do not think we have a clear picture of why the earth has a magnetic moment. All I can say is I mean what we have earth is a dipole a single dipole earth can be treated as a giant dipole whereas the magnets that we are talking about they are actually ferromagnets they have the properties of ferromagnets and when we try to and this is something which is magnetized there is a difference between a magnetic dipole and a magnet this is a magnet which actually has been created by us. So as I told you any magnet that is produced by applying a magnetic field that is magnetized is subjected to its own de-magnetizing factor so it is the natural tendency itself is to lose the magnetization. So in addition to the natural tendency if you are applying heat energy and things like that naturally it will come down whereas in the case of earth it is a it can be considered as a single dipole. It is a single dipole and that dipole the dipole moment whatever it has is determined by whatever charge the distribution or the current distribution it has got we do not know exactly the details but whatever it has got. So even if there is a change for example if due to some extra reason if there is a change that may be adjusted in such a manner that the field is changing but I do not know whether people are actually measuring the field changes of magnetic earth magnetic field everyday basis I do not know. So the comparison is not very fair what you are telling a magnet is made by us and it is actually operating against all negative conditions all hostile conditions including its own de-magnetizing field whereas earth is just one dipole. So there is no comparison that way and I am not telling that the earth magnetic dipole moment is not changing it may be changing but the effect is so small at least in our scale the effect is much smaller. So I do not know whether it is changing whether the change can be measured how it can be accurately measured I do not know but for certain geomagnetism people and other people I am sure they will be even finding out how these variation happens across the I mean when the seasons change and other things I am sure they will do even including the wind related issue and other things. But in this case I think it is quite different here you are talking about a collection of very strongly coupled dipoles whereas earth is at the most a single dipole. So that way it is not fair to compare that. Thank you sir and one more question sir. Yeah. So the material gets magnetized when we are applying the magnetic field. Yeah. Similarly in the case of multiferous material we are applying the electric field it gets magnetized. Yeah. How sir the dipoles are how I done it. Okay that is again little more details are needed send me a question. Multiferous thing is that you can apply the magnetic field as well as electric field you can actually get the cross properties it is not very simple to talk in two lines. Just send me a this thing that is much more complicated than magnetism because you have two effects coming there. Just send me the email. Okay sir.