BCS superconductivity in metallic nanograins: Finite-size corrections, low-energy excitations, and robustness of shell effects

Antonio M. García-García, Juan Diego Urbina, Emil A. Yuzbashyan, Klaus Richter, and Boris L. Altshuler
Phys. Rev. B 83, 014510 – Published 20 January 2011

Abstract

We combine the BCS self-consistency condition, a semiclassical expansion for the spectral density and interaction matrix elements to describe analytically how the superconducting gap depends on the size and shape of a two- and three-dimensional superconducting grain. 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 find shell effects; i.e., for certain values of the electron number N a small change in N leads to large changes in the energy gap. With regard to possible experimental tests we provide a detailed analysis of the dependence of the gap on the coherence length and the robustness of shell effects under small geometrical deformations.

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  • Received 15 November 2009

DOI:https://doi.org/10.1103/PhysRevB.83.014510

© 2011 American Physical Society

Authors & Affiliations

Antonio M. García-García

  • CFIF, IST, Universidade Técnica de Lisboa, Av. Rovisco Pais, P-1049-001 Lisbon, Portugal

Juan Diego Urbina

  • Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany

Emil A. Yuzbashyan

  • Center for Materials Theory, Rutgers University, Piscataway, New Jersey 08854, USA

Klaus Richter1 and Boris L. Altshuler2

  • 1Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany
  • 2Physics Department, Columbia University, 538 West 120th Street, New York, New York 10027, USA

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Issue

Vol. 83, Iss. 1 — 1 January 2011

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