Topological delocalization transitions and mobility edges in the nonreciprocal Maryland model

TL;DR

This paper introduces a non-Hermitian extension of the Maryland model, revealing real-to-complex spectrum transitions, mobility edges, and topological phase changes in a new class of non-Hermitian quasicrystals.

Contribution

It provides explicit phase diagrams, mobility edges, and topological characterization for a non-Hermitian Maryland model with no extended phases at finite nonreciprocity.

Findings

Real-to-complex spectrum transition at finite asymmetry

Existence of mobility edges separating localized and delocalized states

No extended phases at finite nonreciprocity in the thermodynamic limit

Abstract

Non-Hermitian effects could trigger spectrum, localization and topological phase transitions in quasiperiodic lattices. We propose a non-Hermitian extension of the Maryland model, which forms a paradigm in the study of localization and quantum chaos by introducing asymmetry to its hopping amplitudes. The resulting nonreciprocal Maryland model is found to possess a real-to-complex spectrum transition at a finite amount of hopping asymmetry, through which it changes from a localized phase to a mobility edge phase. Explicit expressions of the complex energy dispersions, phase boundaries and mobility edges are found. A topological winding number is further introduced to characterize the transition between different phases. Our work introduces a unique type of non-Hermitian quasicrystal, which admits exactly obtainable phase diagrams, mobility edges, and holding no extended phases at finite nonreciprocity in the thermodynamic limit.