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

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 $\Omega$ 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.

6 pages, 4 figures

References in corpus (2)

• Electronic Structure, Electron-Phonon Coupling, and Multiband Effects in MgB2
• Reply to "Comment on `First-principles calculation of the superconducting transition in MgB2 within the anisotropic Eliashberg formalism'"

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• The higher superconducting transition temperature T${}_c$ and the functional derivative of T${}_c$ with ${\alpha }^{2}F(\omega )$ for electron-phonon superconductors