# Disorder Effects on the Origin of High-Order Harmonic Generation in Solids

## TL;DR

This paper investigates how disorder in solid lattices affects high-order harmonic generation, revealing the interplay between coherent and incoherent scattering and emphasizing the importance of crystal periodicity.

## Contribution

It introduces a perturbative analysis of disorder effects on HHG in solids using Floquet-Keldysh Green functions, highlighting the role of lattice periodicity.

## Key findings

- Coherent harmonic components decrease with disorder
- Incoherent components increase as disorder grows
- Total harmonic signal approaches a nonzero value despite disorder

## Abstract

We consider noninteracting electrons coupled to laser fields, and study perturbatively the effects of the lattice potential involving disorder on the harmonic components of the electric current, which are sources of high-order harmonic generation (HHG). By using the Floquet-Keldysh Green functions, we show that each harmonic component consists of the coherent and the incoherent parts, which arise respectively from the coherent and the incoherent scatterings by the local ion potentials. As the disorder increases, the coherent part decreases, the incoherent one increases, and the total harmonic component of the current first decreases rapidly and then approaches a nonzero value. Our results highlight the importance of the periodicity of crystals, which builds up the Bloch states extending over the solid. This is markedly different from the traditional HHG in atomic gases, where the positions of individual atoms are irrelevant.