"Glide-resolved selection rules for scanning-tunneling microscopy; application to Black Phosphorus and Zirconium(III) Chloride"

Recently Queiroz et al. predicted that the Bloch bands of nonsymmorphic crystals can exhibit novel selection rules in their quasiparticle interference (QPI) pattern, characterized by a quasi-Brillouin Zone (BZ) periodicity of extinction patterns in the momentum transfer channel. Here, we focus on glide reflection symmetry-i.e. the combined operation of mirror reflection and in-plane half-integer lattice translation - to quantitatively realize `glide-resolved QPI (gQPI) selection rules' on 2D minimal tight-binding models respecting the symmetries of layer group pma2 (LG 24), considering the limits of both strong and negligible spin-orbit coupling (SOC). We numerically compute the lattice- and energy-resolved local density of states (LDOS) in the presence of a local impurity and demonstrate the existence of quasi-BZ periodicity in the momentum-space LDOS. We propose Zirconium(III) Chloride and Black Phosphorus, whose monolayers respect pma2, as material candidates for the observation of gQPI in the presence and absence of SOC, respectively. By utilizing Topological Quantum Chemistry and density functional theory to construct tight-binding models, we find numerical evidence for gQPI in these materials, which can potentially be detectable through scanning-tunneling microscopy (STM).