Finite-temperature topological invariant for higher-order topological insulators

TL;DR

This paper introduces a finite-temperature topological invariant for higher-order topological insulators by generalizing ensemble geometric phase, revealing temperature-induced phase transitions in finite systems.

Contribution

It develops a finite-temperature topological invariant for HOTIs using ensemble geometric phase, extending topological characterization beyond zero temperature.

Findings

Temperature can induce a topological phase transition in finite systems.

The ensemble geometric phase remains consistent with Resta's polarization at finite temperature.

Finite-size effects influence the critical points of topological phase transitions.

Abstract

We investigate the effects of temperature on the higher-order topological insulators (HOTIs). The finite-temperature topological invariants for the HOTIs can be constructed by generalizing the Resta's polarization for the ground state to the ensemble geometric phase (EGP) for the mixed states, [C.-E. Bardyn, L. Wawer, A. Altland, M. Fleischhauer, and S. Diehl, PhysRevX.8.011035}{Phys. Rev. X 8, 011035 (2018)}]. The EGP is consistent with the Resta's polarization both at zero temperature and at finite temperatures in the thermodynamic limit. {We find that the temperature can change the critical point and thus induces a phase transition from a topologically-trivial phase to a nontrivial phase in a finite-size system, manifesting changes in the winding of the EGP.