Non-relativistic dynamics of the amplitude (Higgs) mode in superconductors

TL;DR

This paper investigates the behavior of the Higgs mode in superconductors, especially under strong coupling or disorder, revealing it never forms a distinct mode due to mixing with phase fluctuations, impacting optical absorption interpretations.

Contribution

It demonstrates that in disordered or strongly coupled superconductors, the Higgs amplitude mode does not manifest as a separate resonance, due to persistent mixing with phase fluctuations.

Findings

Higgs mode resonance occurs at 2Δ₀, coinciding with quasiparticle excitation threshold.

Strong disorder or coupling prevents the Higgs mode from becoming a distinct real mode.

Amplitude fluctuations always mix with phase fluctuations, affecting optical absorption analysis.

Abstract

Despite the formal analogy with the Higgs particle, the amplitude fluctuations of the order parameter in weakly-coupled superconductors do not identify a real mode with a Lorentz-invariant dynamics. Indeed, its resonance occurs at $2\Delta_0$, which coincides with the threshold $2E_{gap}$ for quasiparticle excitations, that spoil any relativistic dynamics. Here we investigate the fate of the Higgs mode in the unconventional case where $2E_{gap}$ becomes larger than $2\Delta_0$, as due to strong coupling or strong disorder. We show that also in this situation the amplitude fluctuations never identify a real mode at $2\Delta_0$, since such "bosonic" limit is always reached via a strong mixing with the phase fluctuations, which dominate the low-energy part of the spectrum. Our results have direct implications for the interpretation of the sub-gap optical absorption in disordered superconductors.