Effective Floquet Hamiltonian in the low-frequency regime

TL;DR

This paper introduces a theory for deriving effective Floquet Hamiltonians in the low-frequency, weak drive regime, enabling accurate predictions of quasienergy spectra and Floquet states in driven solid-state systems.

Contribution

It develops an analytic method for low-frequency Floquet Hamiltonians, analogous to band theory, emphasizing self-consistency for high accuracy in multi-band systems.

Findings

Accurately predicts quasienergy spectrum in low-frequency regime

Provides analytic expression for effective Floquet Hamiltonian

Highlights importance of self-consistency in the theory

Abstract

We develop a theory to derive effective Floquet Hamiltonians in the weak drive and low-frequency regime. We construct the theory in analogy with band theory for electrons in a spatially-periodic and weak potential, such as occurs in some crystalline materials. As a prototypical example, we apply this theory to graphene driven by circularly polarized light of low intensity. We find an analytic expression for the effective Floquet Hamiltonian in the low-frequency regime which accurately predicts the quasienergy spectrum and the Floquet states. Furthermore, we identify self-consistency as the crucial feature effective Hamiltonians in this regime need to satisfy to achieve a high accuracy. The method is useful in providing a realistic description of off-resonant drives for multi-band solid state systems where light-induced topological band structure changes are sought.