Weak ${\mathbb{Z}}_2$ Supertopology

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 $\ddot{I}€$-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.

12 pages, 10 figures, 3 tables