2026/03/02 by Lavi K. Upreti · 1 voice
Physics and Astronomy · #cond-mat.mes-hall #cond-mat.other #physics.optics
9+2 pages, 9+1 figs, Appendix
arxiv published 2026/03/02 · arxiv created 2026/08/04 · arxiv updated 2026/08/04
The topological classification of a system depends on the discrete symmetries of its Hamiltonian. In Floquet photonic waveguide arrays, the abstract symmetries of the Altland--Zirnbauer (AZ) scheme -- chiral, particle-hole, and time-reversal (for photonics, z-reversal) -- arise from structural properties of the lattice, yet a systematic correspondence has not been established. Here, we illustrate this correspondence for a simpler system of one-dimensional waveguide arrays with real coupling coefficients, showing how bipartite structure and z-reflection symmetry alone determine the whole AZ class. We further demonstrate that non-bipartite networks -- lacking conventional particle-hole symmetry, chiral symmetry, and z-reversal symmetry -- can nonetheless support topologically protected boundary states at quasienergy ε = π, even in one dimension. The protecting symmetry -- shifted-particle-hole symmetry -- applies equally to higher-dimensional Floquet waveguides.