Effective Theory of Superconductivity in Strongly-Coupled Amorphous Materials

TL;DR

This paper develops an effective theory for phonon-mediated superconductivity in strongly-coupled amorphous materials, linking vibrational disorder to superconducting properties and explaining experimental observations.

Contribution

It introduces a novel analytical framework that accounts for vibrational disorder effects on superconductivity, especially the role of transverse excitations and the boson peak.

Findings

Transverse vibrational excitations significantly influence the Eliashberg function.

Disorder-induced vibrational scattering affects the electron-phonon coupling and $T_c$.

Material design principles for enhancing $T_c$ in amorphous superconductors are proposed.

Abstract

A theory of phonon-mediated superconductivity in strong-coupling amorphous materials is developed based on an effective description of structural disorder and its effect on the vibrational spectrum. The theory accounts for the diffusive-like transport of vibrational excitations due to disorder-induced scattering within the Eliashberg theory of strong-coupling superconductivity. The theory provides a good analytical description of the Eliashberg function $\alpha^{2}F(\omega)$ in comparison with experiments, and allows one to disentangle the effects of transverse and longitudinal excitations on the Eliashberg function. In particular, it shows that the transverse excitations play a crucial role in driving an increase or excess in the Eliashberg function at low energy, which is related to the boson peak phenomenon in vibrational spectra of glasses. This low-energy excess, on one hand drives an enhancement of the electron-phonon coupling but at the same time reduces the characteristic energy scale $\omega_{log}$ in the Allen-Dynes formula. As a consequence, the non-monotonicity of $T_{c}$ as a function of alloying (disorder) in $\text{Pb}$-based systems can be rationalized. The case of $\text{Al}$-based systems, where disorder increases $T_{c}$ from the start, is also analyzed. General material-design principles for enhancing $T_{c}$ in amorphous superconductors are presented.