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 Z2 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 π-Berry phase, while for strong SOC, crystal symmetries can give rise to nontrival weak Z2 topologies in 2D subplanes of the 3D Brillouin zone. We catalogue all centrosymmetric space groups whose symmetries enforce these Z2 supertopologies. Suitable material realizations are identified and experimental signatures of the supertopologies, such as quantum spin Hall states, are being discussed.
@article{arxiv.2408.00042,
title = {Weak $\mathbb{Z}_2$ Supertopology},
author = {Kirill Parshukov and Moritz M. Hirschmann and Andreas P. Schnyder},
journal= {arXiv preprint arXiv:2408.00042},
year = {2025}
}