Topological Anderson insulator and reentrant topological transitions in a mosaic trimer lattice

TL;DR

This paper investigates how quasiperiodic disorder influences topological phases in a one-dimensional mosaic trimer lattice, revealing disorder-induced topological Anderson insulators and reentrant topological transitions at different fillings.

Contribution

It provides a detailed analysis of the effects of quasiperiodic disorder on topological phases, including the emergence of topological Anderson insulators and reentrant transitions, in a mosaic trimer lattice.

Findings

Quasiperiodic disorder enhances topological phase at 2/3 filling, leading to a topological Anderson insulator.

Disorder suppresses the topological phase at 1/3 filling and induces reentrant topological transitions.

Topological phase diagrams are verified by many-body ground state fidelity susceptibility calculations.

Abstract

We study the topological properties of a one-dimensional quasiperiodic-potential-modulated mosaic trimer lattice. To begin with, we first investigate the topological properties of the model in the clean limit free of quasiperiodic disorder based on analytical derivation and numerical calculations of the Zak phase $Z$ and the polarization $P$. Two nontrivial topological phases corresponding to the $1/3$ filling and $2/3$ filling, respectively, are revealed. Then we incorporate the mosaic modulation and investigate the influence of quasiperiodic disorder on the two existing topological phases. Interestingly, it turns out that quasiperiodic disorder gives rise to multiple distinct effects for different fillings. At $2/3$ filling, the topological phase is significantly enhanced by the quasiperiodic disorder and topological Anderson insulator emerges. Based on the calculations of polarization and energy gap, we explicitly present corresponding topological phase diagram in the $\lambda-J$ plane. While for the $1/3$ filling case, % the topological phase is dramatically suppressed by the same quasiperiodic disorder. the quasiperiodic disorder dramatically compresses the topological phase, and strikingly, further induces the emergence of reentrant topological phase transitions instead. Furthermore, we verify the topological phase diagrams by computing the many-body ground state fidelity susceptibility for both the $1/3$ filling and $2/3$ filling cases. Our work exemplifies the diverse roles of quasiperiodic disorder in the modulation of topological properties, and will further inspire more research on the competitive and cooperative interplay between topological properties and quasiperiodic disorder.