Double-twisted surface spectrum from hybridized Majorana Kramers pairs and wallpaper fermions

Abstract: We theoretically investigate the superconducting surface states of wallpaper fermions, which are surface quasiparticles of topological nonsymmorphic crystalline insulators protected by a wallpaper group $p4g$ symmetry, based on a tight-binding model for the space group $P4/mbm$ (No. 127). A symmetry-based analysis shows that four types of on-site pair potentials are allowed. Using the symmetries of the wallpaper group $p4g$ and the one-dimensional topological invariants, we clarify that for the $\mathrm{A_{1u}}$ representation, wallpaper fermions and two Majorana Kramers pairs coexist, and hybridization between them give rise to a double-twisted surface state and produces four peaks in the surface density of states. We further find that the mirror Chern number vanishes, indicating that our system realizes mirror-helicity-free surface states. This distinguishes superconducting wallpaper fermions from the other superconducting topological (crystalline) insulators, such as $\mathrm{Cu}<em>x\mathrm{Bi}_2\mathrm{Se}_3$ and $\mathrm{Sn}</em>{1-x}\mathrm{In}_x\mathrm{Te}$.