Bardeen-Cooper-Schrieffer theory of finite-size superconducting metallic grains.
We study finite-size effects in superconducting metallic grains and determine the BCS order parameter and the low energy excitation spectrum in terms of the size and shape of the grain. Our approach combines the BCS self-consistency condition, a semiclassical expansion for the spectral density and interaction matrix elements, and corrections to the BCS mean field. In chaotic grains mesoscopic fluctuations of the matrix elements lead to a smooth dependence of the order parameter on the excitation energy. In the integrable case we observe shell effects when, e.g., a small change in the electron number leads to large changes in the energy gap.
García-García
Antonio M
AM
Physics Department, Princeton University, Princeton, New Jersey 08544, USA.
Urbina
Juan Diego
JD
Yuzbashyan
Emil A
EA
Richter
Klaus
K
Altshuler
Boris L
BL