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.