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

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

2004-02-18

arxiv.org/abs/cond-mat/0402473v1

Eur. Phys. J. B 38, 451-456 (2004)

Physics

Condensed Matter

Superconductivity

6 pages, 4 figures

Scientific paper

10.1140/epjb/e2004-00139-4

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 $\Omega$ at small $\Omega$, while the functional derivatives which are off-diagonal in band indices diverge at $\Omega$ = 0 as 1/$\Omega$. The case of a two-band model for MgB$_{2}$ is treated numerically.

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