Exact complex mobility edges and flagellate spectra for non-Hermitian quasicrystals with exponential hoppings

TL;DR

This paper analytically determines complex mobility edges in non-Hermitian quasiperiodic lattices with exponential hoppings, revealing loop structures in the complex energy plane and flagellate-like spectra that separate localized and extended states.

Contribution

It introduces an exact analytical method for complex mobility edges in non-Hermitian quasiperiodic models, utilizing Avila's global theory and revealing universal loop structures.

Findings

Complex mobility edges form loop structures in the energy plane.

Flagellate-like spectra emerge, separating localized and extended states.

Unified formula describes mobility edges across different hopping parameters.

Abstract

We propose a class of general non-Hermitian quasiperiodic lattice models with exponential hoppings and analytically determine the genuine complex mobility edges by solving its dual counterpart exactly utilizing Avila's global theory. Our analytical formula unveils that the complex mobility edges usually form a loop structure in the complex energy plane. By shifting the eigenenergy a constant $t$, the complex mobility edges of the family of models with different hopping parameter $t$ can be described by a unified formula, formally independent of $t$. By scanning the hopping parameter, we demonstrate the existence of a type of intriguing flagellate-like spectra in complex energy plane, in which the localized states and extended states are well separated by the complex mobility edges. Our result provides a firm ground for understanding the complex mobility edges in non-Hermitian quasiperiodic lattices.