Multiple amplitude modes in strongly-coupled phonon-mediated superconductors

TL;DR

This paper investigates collective amplitude modes in strongly-coupled phonon-mediated superconductors, revealing a Higgs mode matching the superconducting gap and a novel phonon-involved mode, with implications for time-resolved spectroscopy.

Contribution

It uncovers a new collective mode involving phonons and the order parameter, and demonstrates their signatures in photoemission spectra beyond traditional quasiparticle excitations.

Findings

Higgs mode frequency matches the superconducting gap.

Discovery of a phonon-involved collective mode with higher frequency.

Resonance peaks in photoemission spectra distinguish these modes from quasiparticles.

Abstract

We study collective amplitude modes of the superconducting order parameter in strongly-coupled electron-phonon systems described by the Holstein model using the nonequilibrium dynamical mean-field theory with the self-consistent Migdal approximation as an impurity solver. The frequency of the Higgs amplitude mode is found to coincide with the superconducting gap even in the strongly-coupled (beyond BCS) regime. Besides the Higgs mode, we unravel another collective mode involving the dynamics of both the phonons and the superconducting order parameter. The frequency of this mode, higher than twice the renormalized phonon frequency in the superconducting phase, is shown to reflect a strong electron-mediated phonon-phonon interaction. Both types of collective excitations contribute to time-resolved photoemission spectra after a strong laser pump as vertex corrections to produce resonance peaks, which allows one to distinguish them from quasiparticle excitations.