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

U.P. Tyagi, P. Goswami Physics Department, D.B. College (University of Delhi), Kalkaji, New Delhi 110019, India

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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.

DOI:10.12693/APhysPolA.148.40 topics: Su-Schrieffer-Heeger (SSH) model, imaginary on-site potential, vectorized Zak phase, topolectric resistors-inductors-capacitors (RLC) circuit