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

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