Following the Higgs mode across the BCS-BEC crossover in two dimensions

TL;DR

This study investigates the Higgs mode in a 2D fermionic superfluid across the BCS-BEC crossover, revealing how its spectral features depend on the chemical potential and are unaffected by Coulomb interactions.

Contribution

It provides a detailed analysis of the Higgs mode's dispersion and visibility in spectroscopic measurements throughout the BCS-BEC crossover in two dimensions.

Findings

Higgs mode exhibits a well-defined spectral peak for positive chemical potential.

The Higgs pole remains hidden without a peak when the chemical potential is negative.

Long-range Coulomb interactions do not alter the Higgs mode in charged superconductors.

Abstract

Although substantial effort has been dedicated to analyzing the Higgs (amplitude) mode in superconducting systems, there are relatively few studies of the Higgs peak's dispersion and width, quantities which are observable in spectroscopic measurements. These properties can be obtained from the location of the pole of the longitudinal (Higgs) susceptibility in the lower half-plane of complex frequency. We analyze the behavior of the Higgs mode in a 2D neutral fermionic superfluid at $T=0$ throughout the crossover from Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensation (BEC) behavior. This occurs when the dressed chemical potential $\mu$ changes sign from positive to negative. For $\mu >0$, we find a pole in the Higgs susceptibility in the lower half-plane of frequency and demonstrate that it leads to a well-defined peak in spectroscopic probes. For $\mu<0$, the pole still exists, but is "hidden," not giving rise to a peak in spectroscopic probes. Extending this analysis to a charged superconductor, we find that the Higgs mode is unaffected by the long-range Coulomb interaction.