Revisiting the Floquet-Bloch theory for an exactly solvable model of one-dimensional crystals in strong laser fields

TL;DR

This paper analyzes Floquet-Bloch eigenstates in a one-dimensional crystal model under strong laser fields, deriving simplified equations, revealing anticrossings and band gaps, and demonstrating high-harmonic generation with a plateau in the spectrum.

Contribution

It provides a simplified approach to calculating Floquet-Bloch states in a solvable model, highlighting band structure modifications and high-harmonic generation under strong fields.

Findings

Anticrossings appear at Floquet band crossings.

Band gaps are observed at Brillouin zone edges and center.

High-harmonic spectrum exhibits a plateau under strong electric fields.

Abstract

We revisit the Floquet-Bloch eigenstates of a one-dimensional electron gas in the presence of the periodic Kronig-Penny potential and an oscillating electric field. Considering the appropriate boundary conditions for the wave function and its derivative, we derive the determining equations for the Floquet-Bloch eigenstates, which are represented by a single-infinite matrix rather than a double-infinite matrix needed for a generic potential. We numerically solve these equations, showing that there appear anticrossings at the crossing points of the different Floquet bands as well as the band gaps at the edges and the center of the Brillouin zone. We also calculate the high-harmonic components of the electric current carried by the Floquet-Bloch eigenstates, showing that the harmonic spectrum shows a plateau for a strong electric field.