Unified characterization for higher-order topological phase transitions

TL;DR

This paper introduces a unified momentum-space topological framework to characterize and detect higher-order topological phase transitions, linking real-space boundary phenomena with momentum-space topological features through quench dynamics.

Contribution

It proposes a novel momentum-space topological characterization that unifies the description of both bulk and boundary gap closing transitions in HOTPTs, enabling experimental detection.

Findings

Unified framework for HOTPTs in momentum space.

Detection of topological charges crossing BISs via quench dynamics.

Differentiation between type-I and type-II HOTPTs based on charge behavior.

Abstract

Higher-order topological phase transitions (HOTPTs) are associated with closing either the bulk energy gap (type-I) or boundary energy gap (type-II) without changing symmetry, and conventionally the both transitions are captured in real space and characterized separately. Here we propose a momentum-space topological characterization of the HOTPTs, which unifies the both types of topological transitions and enables a precise detection by quench dynamics. Our unified characterization is based on a novel correspondence between the mass domain walls on real-space boundaries and the higher-order band-inversion surfaces (BIS) which are characteristic interfaces in the momentum subspace. The topological transitions occur when momentum-space topological nodes, dubbed higher-order topological charges, cross the higher-order BISs after proper projection. Particularly, the bulk (boundary) gap closes when all (part of) topological charges cross the BISs, characterizing the type-I (type-II) HOTPTs. These distinct dynamical behaviours of higher-order topological charges can be feasibly measured from quench dynamics driven with control in experiments. Our work opens an avenue to characterize and detect the two types of HOTPTs within a unified framework, and shall advance the research in both theory and experiment.