Bloch band structures and linear response theory of nonlinear systems

TL;DR

This paper studies the effects of nonlinearity on Bloch band structures and linear response in a nonlinear Chern insulator model, revealing new band features and non-quantized responses due to nonlinear interactions.

Contribution

It introduces a nonlinear extension of the Qi-Wu-Zhang model, analyzing its band structures and linear response, highlighting how nonlinearity alters topological properties and response quantization.

Findings

Discovery of cone and tubed band structures in nonlinear regimes

Nonlinear effects break adiabaticity and quantization of linear response

Numerical validation of new band features and response behavior

Abstract

We investigate the Bloch bands and develop a linear response theory for nonlinear systems, where the interplay between topological parameters and nonlinearity leads to new band structures. The nonlinear system under consideration is described by the Qi-Wu-Zhang model with Kerr-type nonlinearity, which can be treated as a nonlinear version of Chern insulator. We explore the eigenenergies of the Hamiltonian and discuss its Bloch band structures as well as the condition of gap closing. A cone structure in the ground Bloch band and tubed structure in the excited Bloch band is found. We also numerically calculate the linear response of the nonlinear Chern insulator to external fields, finding that these new band structures break the condition of adiabatic evolution and make the linear response not quantized. This feature of response can be understood by examining the dynamics of the nonlinear system.