Negative superfluid density and spatial instabilities in driven superconductors

TL;DR

This paper investigates the instability of homogeneous solutions in driven superconductors, revealing negative superfluid density and spontaneous spatial inhomogeneities due to Floquet band overlaps, indicating a breakdown of uniform superconductivity.

Contribution

It demonstrates that time-dependent superconductors can exhibit negative superfluid density and spatial instabilities, highlighting the limitations of homogeneous solutions under dynamic conditions.

Findings

Negative superfluid density occurs when Floquet-Bogoliubov bands overlap.

Homogeneous solutions become unstable and break into spatially inhomogeneous states.

Spontaneous topological excitations emerge during instability.

Abstract

We consider excitation of Higgs modes via the modulation of the BCS coupling within the Migdal-Eliashberg-Keldysh theory of time-dependent superconductivity. Despite the presence of phonons, which break integrability, we observe Higgs amplitude oscillations reminiscent of the integrable case. The dynamics of quasiparticles follows from the effective Bogolyubov-de Gennes equations, which represent a Floquet problem for the Bogoliubov quasiparticles. We find that when the Floquet-Bogoliubov bands overlap, the homogeneous solution formally leads to a negative superfluid density, which is no longer proportional to the amplitude of the order parameter. This result indicates an instability, which we explore using spatially-resolved BdG equations. Spontaneous appearance of spatial inhomogeneities in the order parameter is observed and they first occur when the superfluid density becomes unphysical. We conclude that the homogeneous solution to time-dependent superconductivity is generally unstable and breaks up into a complicated spatial landscape via an avalanche of topological excitations.