Bulk-edge correspondence for the nonlinear eigenvalues problem of the Haldane model

Author:

Shujie Cheng, Yonghua Jiang, Gao Xianlong

Keyword:

Condensed Matter, Disordered Systems and Neural Networks, Disordered Systems and Neural Networks (cond-mat.dis-nn)

journal:

date:

2023-11-23 00:00:00

Abstract

Recently, there is an interest in studying the bulk-edge correspondence for nonlinear eigenvalues problems in a two-dimensional topological system with spin-orbit coupling. By introducing auxiliary eigenvalues, the nonlinear bulk-edge correspondence was established. In this paper, taking the Haldane model as an example, we address that such a correspondence will appear in two dimensional topological system without spin-orbit coupling. The resulting edge states are characterized by the Chern number of the auxiliary energy band. A full phase diagram containing topological nontrivial phase, topological trivial phase, and metallic phase is obtained. Our work generalizes the study of the bulk-edge correspondence for nonlinear eigenvalue problems in two-dimensional system.

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