Research

Kaito Yoda and Ai Yamakage, "Double-twisted surface spectrum from hybridized Majorana Kramers pairs and wallpaper fermions", arXiv:2603.11637.
[Abstruct]
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 A1u 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 and CuxBi2Se3 and Sn1–xInxTe.

Kaito Yoda and Ai Yamakage, "Superconducting gap structures in wallpaper fermion systems", J. Low Temp. Phys. 222, 44 (2026). [arXiv:2509.25823]
[Abstruct]
We theoretically investigate the superconducting gap structures in wallpaper fermions, which are surface states of topological nonsymmorphic crystalline insulators, based on a two-dimensional effective model. A symmetry analysis identifies six types of momentum-independent pair potentials. One hosts a point node, two host line nodes, and the remaining three are fully gapped. By classifying the Bogoliubov–de Gennes Hamiltonian in the zero-dimensional symmetry class, we show that the point and line nodes are protected by ℤ2 topological invariants. In addition, for the twofold-rotation-odd pair potential, nodes appear on the glide-invariant line and are protected by crystalline symmetries, as clarified by the Mackey–Bradley theorem.