A NEW METHOD FOR CALCULATING THE FUNCTIONAL DERIVATIVE δTc/δα2F(Ω): APPLICATION TO MgB2

Abstract

We present a new method for calculating the functional derivative of the superconducting transition temperature Tc with respect to the electron–phonon coupling function α2F(Ω). The method relies on a highly efficient procedure for finding the largest eigenvalue and the corresponding eigenvector of a Hermitian matrix. The convergence problems that arise in the calculation of δTc/δα2F(Ω) for systems with low Tc and a large maximum phonon frequency Ωmax using the method based on the pair-breaking parameter are eliminated. We apply the new method of calculating δTc/δα2F(Ω) to MgB2, to the prototype strong coupling superconductor Pb and to weak coupling (BCS) superconductor Al.