Article ID Journal Published Year Pages File Type
1591360 Solid State Communications 2015 4 Pages PDF
Abstract

•Analytical solution of the BCS Hamiltonian at the first-order perturbation theory.•Determination of the number of single electrons, ground-state and excited pairs.•Superconductivity as a Bose–Einstein condensate of Cooper pairs for weak coupling.

In this paper, we find analytically the first order solutions of the Bardeen, Cooper and Schrieffer (BCS) Hamiltonian with degenerated single-electron energy levels. The results are compared to the Richardson exact solutions calculated numerically, showing good agreement in the weak interaction limit. Using this first-order solution, we further calculate the number of pairs at the ground state as a function of temperature. In particular, the Bose–Einstein condensation (BEC) temperature is found when the population of ground-state pairs starts growing. This study provides a BEC analysis of the superconductivity for weak coupling regime, which traditionally belongs to the BCS side of the BCS–BEC crossover picture.

Related Topics
Physical Sciences and Engineering Materials Science Materials Science (General)
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