The Quadrupole Moment of Higher-Order Topological Insulator at Finite temperature

TL;DR

This paper explores the finite temperature behavior of higher-order topological insulators, revealing temperature-induced phase transitions, reentrant topological phases, and disorder-driven topological changes, expanding understanding of topological phases beyond zero temperature.

Contribution

It introduces a generalized real-space quadrupole moment framework for finite temperature analysis and uncovers novel temperature and disorder effects on higher-order topological insulators.

Findings

Finite temperature quantizes quadrupole moments to 0 or 1/2.

Temperature can induce topological phase transitions.

Disorder can drive trivial systems into topological phases.

Abstract

We study the higher-order topological insulators at finite temperature based on a generalized real-space quadrupole moment, which extends the ground state expectations to ensemble averages. Our study reveals that chiral symmetry alone dictates that the quadrupole moment must be quantized to two values of $0$ and $1/2$, even at finite temperature. It is found that finite temperature can induce a topological phase transition from non-trivial to trivial. Furthermore, we found that the anisotropic intra-cell hopping can lead to a reentrant topological phase transition, in which the system becomes topological again with rising temperature. This reentrant behavior is in stark contrast to the results at zero temperature. We also investigate the effects of the quasi-disorder hopping on the topology. It is found that the initially trivial system can be driven into a topological phase with strong enough disorder strength, which closely resembles the topological Anderson transition. Our work provides an example for studying the finite temperature topology of higher-order topological insulators.