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Gapless surface states in a three-dimensional Chalker-Coddington type network model

We present the emergence of gapless surface states in a three-dimensional Chalker-Coddington type network model with spatial periodicity. The model consists of a ring network placed on every face of the cubic unit cells in the simple cubic lattice. The scattering among ring-propagating modes in the adjacent rings is described by the S-matrices, which control possible symmetries of the system. The model maps to a Floquet-Bloch system, and the quasienergy spectrum can exhibit a gapped bulk band structure and gapless surface states. Symmetry properties of the system and robustness of the gapless surface states are explored in comparison to topological crystalline insulator. We also discuss other crystal structures, a gauge symmetry, and a possible optical realization of the network model.