Glide-resolved photoemission spectroscopy: Measuring topological invariants in nonsymmorphic space groups
The two classes of 3D, time-reversal-invariant insulators are known to subdivide into four classes in the presence of glide symmetry. Here, we extend this classification of insulators to include glide-symmetric Weyl metals and find a finer $\mathbb{Z}_4 ⊕\mathbb {Z}$ classification. We further elucidate the smoking-gun experimental signature of each class in the photoemission spectroscopy of surface states. Measuring the $\mathbb{Z}_4$ topological invariant by photoemission relies on identifying the glide representation of the initial Bloch state before photoexcitation—we show how this is accomplished with relativistic selection rules, combined with standard spectroscopic techniques to resolve both momentum and spin. In this work, our method relies on a spin-momentum locking that is characteristic of all glide-symmetric solids (inclusive of insulators and metals in trivial and topological categories). As an orthogonal application, given a glide-symmetric solid with an ideally symmetric surface, we may utilize this spin-momentum locking to generate a source of fully spin-polarized photoelectrons, which have diverse applications in solid-state spectroscopy. Our ab initio calculations predict Ba 2 Pb, stressed Na 3 Bi, and KHgSb to realize all three, nontrivial insulating phases in the $\mathbb{Z}_4$ classification.