Floquet engineering Higgs dynamics in time-periodic superconductors

TL;DR

This paper develops a Floquet theoretical framework to analyze Higgs modes in time-periodically driven superconductors, revealing how photon processes influence the steady-state order parameter and enabling more efficient analysis of these collective excitations.

Contribution

The paper introduces a Floquet Green's function approach to study Higgs modes in superconductors under periodic driving, providing new insights into their dynamics and steady-state properties.

Findings

Floquet approach simplifies the analysis of Higgs modes in driven superconductors.

Photon processes between Floquet sidebands renormalize the steady-state order parameter.

The method offers a physical explanation for the effects of periodic driving on superconducting states.

Abstract

Higgs modes emerge in superconductors as collective excitations of the order parameter amplitude when periodically driven by electromagnetic radiation. In this work, we develop a Floquet approach to study Higgs modes in superconductors under time-periodic driving, where the dynamics of the order parameter is captured by anomalous Floquet Green's functions. We show that the Floquet description is particularly powerful as it allows one to exploit the time-periodic nature of the driving, thus considerably reducing the complexity of the time-dependent problem. Interestingly, the Floquet approach is also enlightening because it naturally offers a physical explanation for the renormalized steady-state order parameter as a result of photon processes between Floquet sidebands. We demonstrate the usefulness of Floquet engineering Higgs modes in time-periodic $s$-wave superconductors.