# Nonlinear electromagnetic response and Higgs mode excitation in BCS superconductors with impurities

## TL;DR

This paper demonstrates that impurities in BCS superconductors enable effective excitation of the Higgs mode by electromagnetic radiation, explaining recent experimental observations of third-harmonic signals.

## Contribution

It introduces a quasiclassical formalism to describe nonlinear electromagnetic response and Higgs mode excitation in disordered BCS superconductors, including analytical solutions matching impurity diagram summations.

## Key findings

- Impurities facilitate Higgs mode excitation by electromagnetic radiation.
- Analytical solutions match impurity diagram summations.
- Resonant third-harmonic signals are explained by Higgs mode excitation.

## Abstract

We reveal that due to the presence of disorder oscillations of the order parameter amplitude called the Higgs mode can be effectively excited by the external electromagnetic radiation in usual BCS superconductors. This mechanism works for superconductors with both isotropic s-wave and anisotropic, such as d-wave, pairings. The non-linear response in the presence of impurities is captured by the quasiclassical formalism. We demonstrate that analytical solutions of the Eilenberger equation with impurity collision integral and external field drive coincide with the exact summation of ladder impurity diagrams. Using the developed formalism we show that resonant third-harmonic signal observed in recent experiments is naturally explained by the excitation of Higgs mode mediated by impurity scattering.