Gapless Superconductivity

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Abstract
The remarkable feature that a superconductor can display “gapless behavior” has been discovered by Abrikosov and Gor’kov ( 1 ) in their study of the effect of magnetic impurities on superconductivity. It was known experimentally that magnetic impurities decrease strongly the transition temperature of superconductors ( 2 ). Abrikosov and Gor’kov not only succeeded in explaining this rapid decrease of the transition temperature but also predicted that the electronic properties of superconductors are drastically modified. In particular, they pointed out the existence of a gapless region in a certain range of concentration of impurities (e.g., at T = 0°K, 91% of the critical concentration at which the superconductivity is completely destroyed). For example, in the gapless region the specific heat behaves linearly in temperature at low temperatures. Furthermore, the above conclusion shows clearly that superconductivity is characterized by the existence of pair correlations rather than by the existence of a finite threshold energy in the excitation spectrum of quasi-particles. It has become gradually clear that this gapless situation is a rather common feature in superconductivity in the presence of strong perturbations. More precisely speaking, if the transition to the normal state in the presence of the perturbation is of the second order, as the perturbation is increased the superconductor first goes into a gapless state before it becomes normal. We will list here several typical examples. Superconducting small specimen in the presence of a magnetic field ( 3,4 ). A superconductor in the presence of a spin exchange field ( 5,6 ). Superconducting alloys containing magnetic impurities ( 1,7 ).

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