Topological aspects of periodically driven non-Hermitian Su-Schrieffer-Heeger model

TL;DR

This paper investigates a non-Hermitian, periodically driven Su-Schrieffer-Heeger model, revealing topological phases, zero modes, and phase transitions controlled by external driving, with implications for understanding non-Hermitian topological systems.

Contribution

It introduces a non-Hermitian driven model where bi-orthonormal geometric phase acts as a topological index, identifying new phases and phase transitions.

Findings

Identification of trivial, non-trivial insulator, and Möbius metallic phases.

Topological phase transitions driven by external field amplitude.

Observation of non-robust zero modes in metallic phase.

Abstract

A non-Hermitian generalization of the Su-Schrieffer-Heeger model driven by a periodic external potential is investigated, and its topological features are explored. We find that the bi-orthonormal geometric phase acts as a topological index, well capturing the presence/absence of the zero modes. The model is observed to display trivial and non-trivial insulator phases and a topologically non-trivial M${\"o}$bius metallic phase. The driving field amplitude is shown to be a control parameter causing topological phase transitions in this model. While the system displays zero modes in the metallic phase apart from the non-trivial insulator phase, the metallic zero modes are not robust, as the ones found in the insulating phase. We further find that zero modes' energy converges slowly to zero as a function of the number of dimers in the M${\"o}$bius metallic phase compared to the non-trivial insulating phase.