Third harmonic generation from collective modes in disordered superconductors

TL;DR

This paper investigates how disorder affects third-harmonic generation in superconductors by analyzing collective modes and quasiparticle responses using a non-perturbative, time-dependent approach, revealing dominant charge and phase fluctuation contributions at strong disorder.

Contribution

It introduces a comprehensive non-perturbative method to include all collective modes and disorder effects in modeling third-harmonic generation in superconductors.

Findings

Paramagnetic effects dominate quasiparticle response at small disorder.

Charge and phase fluctuations significantly contribute at strong disorder.

Disorder alters the polarization dependence of the non-linear response.

Abstract

Recent experiments with strong THz fields in both conventional and unconventional superconductors have clearly evidenced a marked third-harmonic generation below the superconducting temperature $T_c$. Its interpretation challenged substantial theoretical work aimed at establishing the relative efficiency of quasiparticle excitations and collective modes in triggering such a resonant response. Here we compute the non-linear current by implementing a time-dependent Bogoljubov de-Gennes approach, with the twofold aim to account non-perturbatively for the effect of local disorder, and to include the contribution of all collective modes, i.e. superconducting amplitude (Higgs) and phase fluctuations, and charge fluctuations. We show that, in agreement with previous work, already at small disorder the quasiparticle response is dominated by paramagnetic effects. We further demonstrate that paramagnetic processes mediate also the response of all collective modes, with a substantial contribution of charge/phase fluctuations. These processes, which have been overlooked so far, turn out to dominate the third-order current at strong disorder. In addition, we show that disorder strongly influences the polarization dependence of the non-linear response, with a marked difference between the clean and the disordered case. Our results are particularly relevant for recent experiments in cuprates, whose band structure is in a first approximation reproduced by our lattice model.