Damping of the Collective Amplitude Mode in Superconductors with Strong Electron-Phonon Coupling

TL;DR

This paper investigates how strong electron-phonon interactions influence the damping of the Higgs amplitude mode in superconductors, revealing temperature-dependent damping behaviors and the impact of phonon dynamics on mode relaxation.

Contribution

It provides a detailed analysis of the damping mechanisms of the Higgs mode in strongly coupled superconductors using non-equilibrium simulations, highlighting temperature effects and phonon influence.

Findings

Damping depends strongly on temperature, increasing near the transition temperature.

Low-temperature damping follows a power-law, while near Tc it is exponential-like.

Phonon dynamics can soften the Higgs mode, slowing damping.

Abstract

We study the effect of strong electron-phonon interactions on the damping of the Higgs amplitude mode in superconductors by means of non-equilibrium dynamical mean-field simulations of the Holstein model. In contrast to the BCS dynamics, we find that the damping of the Higgs mode strongly depends on the temperature, becoming faster as the systen approaches the transition temperature. The damping at low temperatures is well described by a power-law, while near the transition temperature the damping shows exponential-like behavior. We explain this crossover by a temperature-dependent quasiparticle lifetime caused by the strong electron- phonon coupling, which smears the superconducting gap edge and makes the relaxation of the Higgs mode into quasiparticles more efficient at elevated temperatures. We also reveal that the phonon dynamics can soften the Higgs mode, which results in a slower damping.