Investigation of the Two-Dimensional Non-Hermitian Su–Schrieffer–Heeger Model

Abstract

This article presents an examination of a two-dimensional, non-Hermitian Su–Schrieffer–Heeger model, which differs 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 enables identification of true exceptional points. Furthermore, this investigation achieves vectorized Zak phase quantization and examines a topolectric resistors–inductors–capacitors 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.