Thermodynamics of a Higher-Order Topological Insulator

TL;DR

This paper studies the thermodynamic properties and phase transitions of a two-dimensional quadrupolar topological insulator, identifying different transition types and their critical behavior through numerical analysis.

Contribution

It introduces a thermodynamic approach to analyze phase transitions in higher-order topological insulators, including bulk, edge, and corner contributions.

Findings

Different phase transitions are detected in the topological phase diagram.

Transitions are characterized by critical exponents and order, consistent with Josephson hyperscaling.

A Wannier band-based grand potential describes the trivial to dipolar phase transition.

Abstract

We investigate the order of the topological quantum phase transition in a two dimensional quadrupolar topological insulator within a thermodynamic approach. Using numerical methods, we separate the bulk, edge and corner contributions to the grand potential and detect different phase transitions in the topological phase diagram. The transitions from the quadrupolar to the trivial or to the dipolar phases are well captured by the thermodynamic potential. On the other hand, we have to resort to a grand potential based on the Wannier bands to describe the transition from the trivial to the dipolar phase. The critical exponents and the order of the phase transitions are determined and discussed in the light of the Josephson hyperscaling relation.