Spatially-resolved dynamics of the amplitude Schmid-Higgs mode in disordered superconductors

• Published in: arXiv.org 2024-09
• Main Authors: Nosov, P A, Andriyakhina, E S, Burmistrov, I S
• Format: Article
• Language: English
• Subjects: Amplitudes; Coherence length; Damping; Mean free path; Oscillations; Particle decay; Riemann surfaces; Superconductors
• ISSN: 2331-8422

We investigate the spatially-resolved dynamics of the collective amplitude Schmid-Higgs (SH) mode in disordered Bardeen-Cooper-Schrieffer (BCS) superconductors and fermionic superfluids. We identify cases where the long-time SH response is determined by a pole in the averaged SH susceptibility, located on the unphysical sheet of its Riemann surface. Using analytic continuation across the two-particle branch cut, we obtain the zero-temperature dispersion relation and damping rate of the SH mode linked to this pole. When the coherence length significantly exceeds the mean free path, the pole is ``hidden'' behind the two-particle continuum edge at \(2\Delta\), leading to SH oscillations at late times decaying as \(1/t^2\) with frequency \(2\Delta\). Nevertheless, the pole induces a peak in the retarded SH susceptibility at a frequency above \(2\Delta\) and causes sub-diffusive oscillations with a dynamical exponent \(z=4\) at both late times and long distances. Conversely, long-distance oscillations at a fixed frequency \(\omega\) occur only for \(\omega\) exceeding \(2\Delta\), with a spatial period diverging at the threshold as \(1/(\omega - 2\Delta)^{1/4}\), up to logarithmic factors. When the coherence length is comparable to the mean free path, the pole can reemerge into the continuum, resulting in additional late-time oscillations at fixed wave vectors with frequencies above \(2\Delta\).