Impact of Nonreciprocal Hopping on Localization in Non-Hermitian Quasiperiodic Systems

TL;DR

This paper analyzes how nonreciprocal hopping influences localization and phase transitions in a non-Hermitian quasiperiodic system, revealing unique skin phases and the interplay of topology and non-Hermitian effects.

Contribution

It provides analytical phase boundaries using Avila's theory and uncovers how modulated nonreciprocal hopping transforms phases into skin phases.

Findings

Identification of phase boundaries via Avila's global theory

Transformation of extended and critical phases into skin phases

Asymmetric localization behaviors in nonreciprocal systems

Abstract

We study the non-Hermitian Aubry-Andr\'e-Harper model, incorporating complex phase modulation, unmodulated and modulated nonreciprocal hopping. Using Avila's global theory, we derive analytical phase boundaries and map out the phase diagrams, revealing extended, localized, critical, and skin phases unique to non-Hermitian systems. For complex phase modulation, we determine localization lengths through Lyapunov exponents and show that topological transitions align with localization transitions. In the nonreciprocal case, we use similarity transformations to confirm phase boundaries consistent with Avila's theory and uncover asymmetric localization behaviors. Importantly, modulated nonreciprocal hopping transforms both extended and critical phases into skin phases under open boundary conditions. These results highlight the interplay between topology, localization, and non-Hermitian effects, offering new perspectives on quasiperiodic systems.