A Brief Overview

Abstract

The phenomenon of superconductivity is still one of the most exciting topics in solid state physics. In the history of superconductivity it was always a challenge for both experimentalists and theorists to reveal the nature of superconductivity. After the discovery of the first superconductor by Kamerlingh-Onnes in 1911 [1] it took almost half a century until a pairing theory was developed which was able to account for many properties of superconductors known at that time. This famous pairing theory, formulated in 1957 by Bardeen, Cooper and Schrie.er (BCS) [2] points out that even a weak attraction between fermions will lead to simultaneous formation and condensation of so-called Cooper pairs. The Cooper pairs are bound electron pairs of opposite spin and momentum proposed in 1956 by Cooper [3]. In classical superconductors, first considered by the BCS theory, the electron pairs have a total spin S = 0 (singlet pairing) and total orbital momentum L = 0. In analogy to quantum mechanics, the pairing is described by an isotropic wave function, and denoted as s-wave pairing. The weak attractive interaction arises from the virtual exchange of phonons and the screened Coulomb repulsion between electrons. A macroscopic quantum state is formed by the bosonic condensate which breaks the gauge invariance by setting a macroscopic phase relationship. S -wave pairing mediated by the electron-phonon interaction is the key ingredient of conventional superconductors like most element and alloy superconductors. In contrast, superconductivity is denoted unconventional, if below the transition temperature T_c additional symmetries are broken besides the gauge symmetry, or if the pairing mechanism is mediated by non-phononic interactions. A generalized BCS theory [4, 5] can account for unconventional superconductivity, a fact that emphasizes the brilliance, universality and significance of the concepts of the BCS pairing theory.