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. Based on ab-initio calculations, we predict materials that realize all three, nontrivial insulating phases. We further elucidate the smoking-gun experimental signature of each class in the photoemission spectroscopy of surface states. Measuring the Z_4 invariant relies on identifying the glide representation of the initial Bloch state before photo-excitation -- this is accomplished with relativistic dipole selection rules, combined with standard spectroscopic techniques to resolve both momentum and spin. As an orthogonal by-product of our method, we propose how to generate a source of 100% spin-polarized photoelectrons, which have diverse applications in solid-state spectroscopy.