A model Hamiltonian for MgB2 which takes into account its unusual phononic features

TL;DR

This paper develops a model Hamiltonian for MgB2 that incorporates its unique phononic features, including anharmonicity and complex electron-phonon interactions, successfully matching experimental observations.

Contribution

It introduces a novel Hamiltonian model that accounts for MgB2's anharmonic phonons and quadratic electron-phonon coupling, advancing understanding of its superconducting properties.

Findings

Model reproduces experimental phonon frequencies and linewidths.

Explains the single critical temperature for two superconducting gaps.

Links phonon-induced inter-band coupling to temperature-dependent superconductivity.

Abstract

Taking as a starting point the results of LDA calculations, which show that in MgB2 the phonons have a strong quartic anharmonicity and that the bond-stretching electron-phonon interaction (EPI) has both a linear and a large quadratic component, we propose a model Hamiltonian which succesfully matches a number of experimental evidences. We relate the single critical temperature for both superconducting gaps to a phonon-induced inter-band coupling whose amplitude increases with temperature. We also obtain phonon frequencies and linewidths depending on the band filling, as well as band energies and hybridization amplitudes depending on the phonon number.