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Topological phases and type-II edge state in two-leg-coupled Su–Schrieffer–Heeger chains

Topological quantum states have attracted great attention both theoretically and experimentally. Here, we show that the momentum-space lattice allows us to couple two Su–Schrieffer–Heeger (SSH) chains with opposite dimerizations and staggered interleg hoppings. The coupled SSH chain is a four-band model which has sublattice symmetry similar to the SSH4. Interestingly, the topological edge states occupy two sublattices at the same time, which can be regarded as a one-dimension analogue of the type-II corner state. The analytical expressions of the edge states are also obtained by solving the eigenequations. Finally, we provide a possible experimental scheme to detect the topological winding number and corresponding edge states.