# Glide-resolved photoemission spectroscopy: Measuring topological invariants in nonsymmorphic space groups

## TL;DR

This paper introduces a method using glide-resolved photoemission spectroscopy to measure topological invariants in nonsymmorphic space groups, revealing new classifications and experimental signatures of topological phases.

## Contribution

It extends the classification of topological insulators to include glide-symmetric Weyl metals with a new $Z_4\oplus Z$ scheme and proposes a spectroscopic technique to identify these phases.

## Key findings

- Proposes a method to measure $Z_4$ topological invariants via photoemission.
- Identifies a novel spin-momentum locking in glide-symmetric solids.
- Predicts specific materials realizing nontrivial topological phases.

## Abstract

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 $Z_4\oplus Z$ classification. We further elucidate the smoking-gun experimental signature of each class in the photoemission spectroscopy of surface states. Measuring the $Z_4$ topological invariant by photoemission relies on identifying the glide representation of the initial Bloch state before photo-excitation - we show how this is accomplished with relativistic selection rules, combined with standard spectroscopic techniques to resolve both momentum and spin. Our method relies on a novel 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 $Z_4$ classification.