Topological phases of commensurate or incommensurate non-Hermitian Su-Schrieffer-Heeger lattices

TL;DR

This paper explores the topological properties of a non-Hermitian Su-Schrieffer-Heeger lattice with modulating potentials, revealing anti-PT transitions, novel edge states, and their dynamics in both commensurate and incommensurate cases.

Contribution

It introduces new topological invariants for non-Hermitian systems and analyzes the effects of incommensurability on edge states and phase transitions.

Findings

Anti-PT transition at exceptional points of edge states.

Edge states can appear in trivial Berry phase regimes when potential exceeds critical value.

Distinct dynamics observed for different initial states and lattice commensurability.

Abstract

We theoretically investigate topological features of a one-dimensional Su-Schrieffer-Heeger lattice with modulating non-Hermitian on-site potentials containing four sublattices per unit cell. The lattice can be either commensurate or incommensurate. In the former case, the entire lattice can be mapped by supercells completely. While in the latter case, there are two extra lattice points, thereby making the last cell incomplete. We find that an anti-PT transition occurs at exceptional points of edge states at certain parameters, which does not coincide with the conventional topological phase transition characterized by the Berry phase, provided the imaginary on-site potential is large enough. Interestingly, when the potential exceeds a critical value, edge states appear even in the regime with a trivial Berry phase. To characterize these novel edge states we present topological invariants associated with the system's parity. Finally, we analyze the dynamics for initial states with different spatial distributions, which exhibit distinct dynamics for the commensurate and incommensurate cases, depending on the imaginary part of edge state energy.