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

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 $\mathrm{Cu}_x\mathrm{Bi}_2\mathrm{Se}_3$ and $\mathrm{Sn}_{1-x}\mathrm{In}_x\mathrm{Te}$.