Weak $\mathbb{Z}_2$ Supertopology

TL;DR

This paper classifies symmetry-enforced $ ext{Z}_2$ supertopologies in centrosymmetric materials, revealing how crystal symmetries induce topological features like Dirac nodal lines and quantum spin Hall states under different spin-orbit coupling regimes.

Contribution

It provides a comprehensive catalogue of space groups enforcing $ ext{Z}_2$ supertopologies and discusses potential material realizations and experimental signatures.

Findings

Dirac nodal lines protected by $ ext{π}$-Berry phase in weak SOC

Weak $ ext{Z}_2$ topologies in 2D subplanes with strong SOC

Identification of centrosymmetric space groups enforcing these topologies

Abstract

Crystal symmetries can enforce all bands of a material to be topological, a property that is commonly referred to as ``supertopology". Here, we determine the symmetry-enforced $\mathbb{Z}_2$ supertopologies of non-magnetic centrosymmetric materials with weak and strong spin-orbit coupling (SOC). For weak (i.e., negligible) SOC, crystal symmetries can enforce Dirac nodal lines protected by a $\pi$-Berry phase, while for strong SOC, crystal symmetries can give rise to nontrival weak $\mathbb{Z}_2$ topologies in 2D subplanes of the 3D Brillouin zone. We catalogue all centrosymmetric space groups whose symmetries enforce these $\mathbb{Z}_2$ supertopologies. Suitable material realizations are identified and experimental signatures of the supertopologies, such as quantum spin Hall states, are being discussed.