Functional derivatives of Tc for a two-band superconductor: application to MgB2

B. Mitrović

doi:10.1140/epjb/e2004-00139-4

EPJ

Functional derivatives of T_c for a two-band superconductor: application to MgB₂

B. Mitrović^a

Physics Department, Brock University, St. Catharines, Ontario, Canada L2S 3A1

Received: 18 February 2004
Published online: 28 May 2004

Abstract

We address the question of how phonons of various frequencies contribute to the superconducting transition temperature T_c of a multi-band superconductor by considering the functional derivatives of T_c with respect to various intraband and interband electron-phonon coupling functions. A general scheme for computing such functional derivatives is developed. The proofs are given that the functional derivatives which are diagonal in band indices are linear in phonon energy Ω at small Ω, while the functional derivatives which are off-diagonal in band indices diverge at Ω = 0 as 1/Ω. The case of a two-band model for MgB₂ is treated numerically.

PACS: 74.20.-z – Theories and models of superconducting state / 74.70.Ad – Metals; alloys and binary compounds (including A15, MgB2, etc.) / 74.62.-c – Transition temperature variations