Superconductivity was discovered by H. Kamerlingh Onnes on April 8, 1911, who was studying the resistance of solid Mercury (Hg) at cryogenic temperatures. Liquid helium was recently discovered at that time. At T = 4.2K, the resistance of Hg disappeared abruptly. This marked a transition to a new phase that was never seen before. The state is resistanceless, strongly diamagnetic, and denotes a new state of matter. K. Onnes sent two reports to KNAW (the local journal of the Netherlands), where he preferred calling the zero-resistance state ‘superconductivity’’.

There was another discovery that went unnoticed in the same experiment, which was the transition of superfluid Helium (He) at 2.2K, the so-called λ transition, below which He becomes a superfluid. However, we shall skip that discussion for now. A couple of years later, superconductivity was found in lead (Pb) at 7K. Much later, in 1941, Niobium Nitride was found to superconduct below 16 K. The burning question in those days was: what would the conductivity or resistivity of metals be at a very low temperature?

The reason behind such a question is Lord Kelvin’s suggestion that for metals, initially the resistivity decreases with falling temperature and finally climbs to infinity at zero Kelvin because electrons’ mobility becomes zero at 0 K, yielding zero conductivity and hence infinite resistivity. Kamerlingh Onnes and his assistant Jacob Clay studied the resistance of gold (Au) and platinum (Pt) down to T = 14K. There was a linear decrease in resistance until 14 K; however, lower temperatures cannot be accessed owing to the unavailability of liquid He, which eventually happened in 1908.

In fact, the experiment with Au and Pt was repeated after 1908. For Pt, the resistivity became constant after 4.2K, while Au is found to superconduct at very low temperatures. Thus, Lord Kelvin’s notion about infinite resistivity at very low temperatures was incorrect. Onnes had found that at 3 K (below the transition), the normalised resistance is about 10⁻⁷. Above 4.2 K, the resistivity starts appearing again. The transition is too sharp and falls abruptly to zero within a temperature window of 10⁻⁴ K.

All superconductors are normal metals above the transition temperature. If we ask in the periodic table where most of the superconductors are located, the answer throws some surprises. The good metals are rarely superconducting

Perfect conductors, superconductors, and magnets

All superconductors are normal metals above the transition temperature. If we ask in the periodic table where most of the superconductors are located, the answer throws some surprises. The good metals are rarely superconducting. The examples are Ag, Au, Cu, Cs, etc., which have transition temperatures of the order of ∼ 0.1K, while the bad metals, such as niobium alloys, copper oxides, and 1 MgB2, have relatively larger transition temperatures. Thus, bad metals are, in general, good superconductors. An important quantity in this regard is the mean free path of the electrons. The mean free path is of the order of a few A⁰ for metals (above T_c), while for good metals (or the bad superconductors), it is usually a few hundred of A⁰. Whereas for the bad metals (good superconductors), it is still small as the electrons are strongly coupled to phonons. The orbital overlap is large in a superconductor. In good metals, the orbital overlap is small, and often they become good magnets. In the periodic table, transition elements such as the 3D series elements, namely Al, Bi, Cd, Ga, etc., become good superconductors, while Cr, Mn, and Fe are bad superconductors and in fact form good magnets. For all of them, that is, whether they are superconductors or magnets, there is a large density of states at the Fermi level. So, a lot of electronic states are necessary for the electrons in these systems to be able to condense into a superconducting state (or even a magnetic state). The nature of the electronic wave function determines whether they develop superconducting order or magnetic order. For example, electronic wavefunctions have a large spatial extent for superconductors, while they are short-range for magnets.

Meissner effect

The near-complete expulsion of the magnetic field from a superconducting specimen is called the Meissner effect. In the presence of a magnetic field, the current loops at the periphery will be generated so as to block the entry of the external field inside the specimen. If a magnetic field is allowed within a superconductor, then, by Ampere’s law, there will be normal current within the sample. However, there is no normal current inside the specimen. Thus, there can’t be any magnetic field. For this reason, superconductors are known as perfect diamagnets with very large diamagnetic susceptibility. Even the best-known diamagnets (which are non-superconductors) have magnetic susceptibilities of the order of 10−5. Thus, the diamagnetic property can be considered a distinct property of superconductors compared to zero electrical resistance.

The near-complete expulsion of the magnetic field from a superconducting specimen is called the Meissner effect

A typical experiment demonstrating the Meissner effect can be thought of as follows: Take a superconducting sample (T < Tc), sprinkle iron filings around the sample, and switch on the magnetic field. The iron filings are going to line up in concentric circles around the specimen. This implies the expulsion of the flux lines outside the sample, which makes the filings line up.

Distinction between perfect conductors and superconductors

The distinction between a perfect conductor and a superconductor is brought about by magnetic field-cooled (FC) and zero-field-cooled (ZFc) cases, as shown below in Fig. 1.

In the absence of an external magnetic field, temperature is lowered for both the metal and the superconductor in their metallic states from T > Tc to T < Tc (see left panel for both in Fig. 1). Hence, a magnetic field is applied, which eventually gets expelled owing to the Meissner effect. The field has finally been withdrawn. However, if cooling is done in the presence of an external field, after the field is withdrawn, the flux lines get trapped for a perfect conductor; however, the superconductor is left with no memory of an applied field, a situation similar to what happens in the zero-field cooling case. So, superconductors have no memory, while perfect conductors have memory.

Microscopic considerations: BCS theory

The first microscopic theory of superconductivity was proposed by Berdeen, Cooper, and Schrieffer (BCS) in 1957, which earned them a Nobel Prize in 1972. The underlying assumption was that an attractive interaction between the electrons is possible, which is mediated via phonons. Thus, electrons form bound pairs under certain conditions, such as (i) two electrons in the vicinity of the filled Fermi Sea within an energy range ¯hωD (set by the phonons or lattice). (ii) The presence of phonons or the underlying lattice is confirmed by the isotope effect experiment, which confirms that the transition temperature is proportional to the mass of ions. Since the Debye frequency depends on the ionic mass, it implies that the lattice must be involved. 3 A small calculation yields that an attractive interaction is possible in a narrow range of energy. This attractive interaction causes the system to be unstable, and a long-range order develops via symmetry breaking. In a book by one of the discoverers, namely, Schrieffer, he described an analogy between a dancing floor comprising couples, dancing one with any other couple, and being completely oblivious to any other couple present in the room. The couples, while dancing, drift from one end of the room to another but do not collide with each other. This implies less dissipation in the transport of a superconductor. The BCS theory explained most of the features of the superconductors known at that time, such as (i) the discontinuity of the specific heat at the transition temperature, Tc. (ii) Involvement of the lattice via the isotope effect. (iii) Estimation of Tc and the energy gap. The value of Tc and the gap are confirmed by tunnelling experiments across metal-superconductor (M-S) or metal-insulator-superconductor (MIS) types of junctions. Giaever was awarded the Nobel Prize in 1973 for his work on these experiments. (iv) The Meissner effect can be explained within a linear response regime. (v) Temperature dependence of the energy gap, confirming gradual vanishing, which confirms a second-order phase transition. Most of the features of conventional superconductors can be explained using BCS theory. Another salient feature of the theory is that it is non-perturbative. There is no small parameter in the problem. The calculations were done with a variational theory where the energy is minimised with respect to some free parameters of the variational wavefunction, known as the BCS wavefunction.

Unconventional Superconductors: High-T_c Cuprates

This is a class of superconductors where the two-dimensional copper oxide planes play the main role, and superconductivity occurs in these planes. Doping these planes with mobile carriers makes the system unstable towards superconducting correlations. At zero doping, the system is an antiferromagnetic insulator (see Fig. 2). With about 15% to 20% doping with foreign elements, such as strontium (Sr), etc. (for example, in La2−xSrxCuO4), the system turns superconductivity. There are two things that are surprising in this regard. (i) The proximity of the insulating state to the superconducting state; (ii) For the system initially in the superconducting state, as the temperature is raised, instead of going into a metallic state, it shows several unfamiliar features that are very unlike the known Fermi liquid characteristics. It is called a strange metal.

In fact, there are some signatures of pre-formed pairs in the ‘so-called’ metallic state, known as the pseudo gap phase. Since the starting point from which one should build a theory is missing, a complete understanding of the mechanism leading to the phenomenon cannot be understood. It remained a theoretical riddle.