Theory of Superconductivity Mediated by Topological Phonons

TL;DR

This paper presents a theoretical framework for superconductivity mediated by topological phonons in topological phononic insulators, revealing a resonance condition that enhances the critical temperature significantly.

Contribution

It introduces a self-consistent two-band gap equation for topological phonon-mediated superconductivity and identifies a resonance condition that maximizes the critical temperature.

Findings

Superconducting critical temperature exhibits non-monotonic behavior with phononic frequency.

Resonance occurs when electrons and phonons share the same energy, boosting electron-phonon interaction.

Maximum $T_c$ enhancement occurs in the degenerate phononic flat-band limit.

Abstract

Topological phononic insulators are the counterpart of three-dimensional quantum spin Hall insulators in phononic systems and, as such, their topological surfaces are characterized by Dirac cone-shaped gapless edge states arising as a consequence of a bulk-boundary correspondence. We propose a theoretical framework for the possible superconducting phase in these materials, where the attractive interaction between electrons is mediated by topological phonons in nontrivial boundary modes. Within the BCS limit, we develop a self-consistent two-band gap equation, whose solutions show that the superconducting critical temperature has a non-monotonic behaviour with respect to the phononic frequency in the Kramers-like point. This remarkable behaviour is produced by a resonance, that occurs when electrons and phonons on the topological surfaces have the same energy: this effectively increases the electron-phonon interaction and hence the Cooper pair binding energy, thus establishing an optimal condition for the superconducting phase. With this mechanism, the $T_{c}$ can be increased by well over a factor two, and the maximum enhancement occurs in the degenerate phononic flat-band limit.