Emergent multi-loop nested point gap in a non-Hermitian quasiperiodic lattice

TL;DR

This paper introduces a non-Hermitian quasiperiodic lattice model with a geometric series modulation, revealing complex multi-loop point gaps and mobility edges that merge into a single structure in the infinite limit, with analytical confirmation.

Contribution

It presents a novel geometric series modulated non-Hermitian quasiperiodic lattice model and analytically characterizes the merging of mobility edges and point gaps in the infinite summation limit.

Findings

Multiple mobility edges and high winding number point gaps are induced.

In the infinite limit, mobility edges merge into one and point gaps form a ring with winding number one.

Analytical expression for mobility edges confirms the merging behavior.

Abstract

We propose a geometric series modulated non-Hermitian quasiperiodic lattice model, and explore its localization and topological properties. The results show that with the ever-increasing summation terms of the geometric series, multiple mobility edges and non-Hermitian point gaps with high winding number can be induced in the system. The point gap spectrum of the system has a multi-loop nested structure in the complex plane, resulting in a high winding number. In addition, we analyze the limit case of summation of infinite terms. The results show that the mobility edges merge together as only one mobility edge when summation terms are pushed to the limit. Meanwhile, the corresponding point gaps are merged into a ring with winding number equal to one. Through Avila's global theory, we give an analytical expression for mobility edges in the limit of infinite summation, reconfirming that mobility edges and point gaps do merge and will result in a winding number that is indeed equal to one.