2026/03/27 by Yutaro Tanaka, Shingo Kobayashi
Physics and Astronomy · #Boundary value problem #Brillouin zone #Gapless playback #Hinge #Invariant (physics) #Nonlinear Photonic Systems #Physics of Superconductivity and Magnetism #Quantum Mechanics and Non-Hermitian Physics #Topological insulator
paper · pdf · doi:10.1103/pnkp-6tzk
openalex publication_date 2026/07/06 · openalex created_date 2026/07/07 · openalex updated_date 2026/08/05
In two-dimensional systems with space-time inversion symmetry, such as C2zT, the reality condition on wave functions gives rise to real band topology characterized by the Euler class, a ℤ-valued topological invariant for a pair of real bands in the Brillouin zone. In this paper, we study three-dimensional C2zT-symmetric insulators characterized by e2, defined as the difference in the Euler classes between two C2zT-invariant planes in the three-dimensional Brillouin zone. By deriving effective surface Hamiltonians from generic low-energy continuum Hamiltonians characterized by the topological invariant e2, we reveal that multiple gapless boundary states exist at the domain walls of the surface mass, which give rise to the multiple chiral hinge modes. We also show that three-dimensional insulators characterized by e2=N support N chiral hinge modes. Notably, due to the constraint of two occupied bands in our system, these phases are distinct from stacked Chern insulators composed of N layers. Furthermore, we construct tight-binding models for e2=2 and 3 and numerically demonstrate the emergence of two and three chiral hinge modes, respectively. These results are consistent with those obtained from the surface theory.