Floquet-Theoretical Formulation and Analysis of High-Harmonic Generation in Solids

TL;DR

This paper develops a Floquet-theoretical approach to analyze high-harmonic generation in solids, revealing the emergence of multiple plateau structures in the harmonic spectrum influenced by system parameters.

Contribution

It introduces a Floquet eigenstate-based formula for calculating high-harmonic components and analytically explains the origin of multiple plateaus in the spectrum.

Findings

Two distinct plateau structures are identified in the HHC spectrum.

Plateau widths are proportional to field amplitude and inversely proportional to laser frequency and its square.

Multi-step plateaus occur under strong field and potential conditions.

Abstract

By using the Floquet eigenstates, we derive a formula to calculate the high-harmonic components of the electric current (HHC) in the setup where a monochromatic laser field is turned on at some time. On the basis of this formulation, we study the HHC spectrum of electrons on a one-dimensional chain with the staggered potential to study the effect of multiple sites in the unit cell such as the systems with charge density wave (CDW) order. With the help of the solution for the Floquet eigenstates, we analytically show that two plateaus of different origins emerge in the HHC spectrum. The widths of these plateaus are both proportional to the field amplitude, but inversely proportional to the laser frequency and its square, respectively. We also show numerically that multi-step plateaus appear when both the field amplitude and the staggered potential are strong.