An investigation of the two-dimensional non-Hermitian Su-Schrieffer-Heeger Model

TL;DR

This paper explores a two-dimensional non-Hermitian SSH model with gain and loss, analyzing exceptional points, topological phases, and transport properties, revealing unique topological and electrical characteristics distinct from Hermitian systems.

Contribution

It introduces a non-Hermitian 2D SSH model with broken time-reversal symmetry, identifies exceptional points, and connects topological invariants to electrical circuit analogs.

Findings

Identification of true exceptional points via phase rigidity analysis

Vectorized Zak phase quantization in the non-Hermitian system

Derivation of topological boundary resonance conditions in topolectric circuits

Abstract

This communication presents an examination of a two-dimensional, non-Hermitian Su -Schrieffer-Heeger (SSH) model, which is differentiated from its conventional Hermitian counterpart by incorporating gain and/or loss terms, mathematically represented by imaginary on-site potentials. The time-reversal symmetry is disrupted due to these on-site potentials. Exceptional points in a non-Hermitian system feature eigenvalue coalescence and non-trivial eigenvector degeneracies. Utilization of the rank-nullity theorem and graphical analysis of the phase rigidity factor enable identification of true exceptional points. Furthermore, this investigation achieves vectorized Zak phase quantization and examines a topolectric RLC circuit to derive the corresponding topological boundary resonance condition and the quantum Hall susceptance. Although Chern number quantization is not feasible, staggered hopping amplitudes corresponding to unit-cell lattice sites lead to broken inversion symmetry with non-zero Berry curvature, resulting in finite anomalous Nernst conductivity.