A signature index for third order topological insulators

TL;DR

This paper introduces a new index signature for identifying third order topological insulators in 3D and higher dimensions, generalizing previous invariants and providing a unified framework.

Contribution

It develops a novel topological index based on monomial signatures of Higgs triplet values, applicable to any dimension including second order insulators.

Findings

The index accurately characterizes third order topological phases.

The method generalizes to N-dimensional systems with open boundaries.

Known lower-dimensional results are recovered within this framework.

Abstract

In this work, we develop an index signature characterising the third order topological phases in 3D systems. This index is an alternating sum of monomial signatures of Higgs triplet values at 3D corners. We extend our method to N-dimensional systems with open boundaries, and demonstrate that the topological invariant can be efficiently generalised to any space dimension including the second order topological insulators. Known results on lower dimensional systems are recovered and an interpretation in the Higgs space parameters is given.