Superconductivity

Abstract

The history of the discovery of superconductivity and the salient features of superconductors, such as zero resistance, the Meissner effect, the specific heat discontinuity, etc. are discussed. Type-I and type-II superconductors are introduced along with their magnetic phase diagrams. Hence, we discuss the microscopic theory of superconductivity due to Bardeen, Cooper, and Schrieffer, the so called BCS theory which relies on the instability of a filled Fermi sea toward the formation of Cooper pairs, and the resultant Hamiltonian is solved via variational calculations on a paired many body state. We present an elaborate description of the BCS ground state, along with computing its key properties, such as, specific heat, expulsion of the electromagnetic field, the isotope effect, etc. A brief introduction to the phenomenological theory, namely, the Ginzburg-Landau theory, is presented thereafter. Furthermore, a finite momentum pairing state is discussed along with its possible experimental realization in heavy fermion and organic superconductors. Next, an account of the experimental methods for determining the spectral gap in superconductors is discussed. To compare and contrast with the findings of the BCS theory, two classes of unconventional superconductors, namely, the high-Tc cuprates and the iron-based pnictides and chalcogenides are discussed. The applications of superconductivity, such as the Josephson effect, and the properties of superconductor-based junctions, namely, the SQUIDs, are presented. Finally, a brief account of the Fermi liquid theory, which lies at the heart of microscopic superconductivity, is included in the appendix with an aim to point out the bottlenecks in explaining the unconventional normal state in cuprates and iron-based superconductors.