Direct dynamical characterization of higher-order topological insulators with nested band inversion surfaces

TL;DR

This paper introduces a universal, dynamics-based method to characterize higher-order topological insulators by linking quantum quench dynamics with nested band inversion surfaces, enabling experimental detection of topological invariants.

Contribution

It proposes a novel approach connecting quench dynamics with nested BISs to identify all topological orders without relying on symmetry considerations.

Findings

Dynamically detects all topological orders via nested BISs

Connects quantum quenches with Clifford algebra operators

Experimental measurement of topological invariants is feasible

Abstract

Higher-order topological insulators (HOTIs) are systems with topologically protected in-gap boundary states localized at their $(d-n)$-dimensional boundaries, with $d$ the system dimension and $n$ the order of the topology. This work proposes a rather universal dynamics-based characterization of one large class of $Z$-type HOTIs without specifically relying on any symmetry considerations. The key element of our innovative approach is to connect quantum quench dynamics with nested configurations of the so-called band inversion surfaces (BISs) of momentum-space Hamiltonians as a sum of operators from the Clifford algebra (a condition that can be relaxed), thereby making it possible to dynamically detect each and every order of topology on an equal footing. Given that experiments on synthetic topological matter can directly measure the winding of certain pseudospin texture to determine topological features of BISs, the topological invariants defined through nested BISs are all within reach of ongoing experiments. Further, the necessity of having nested BISs in defining higher-order topology offers a unique perspective to investigate and engineer higher-order topological phase transitions.