Topological phases of coupled Su-Schrieffer-Heeger wires

The phase diagrams of an arbitrary number $N_{\text{w}}$ of diagonally and perpendicularly coupled Su-Schrieffer-Heeger wires are identified. The diagonally coupled wires exhibit rich topological phase diagrams with insulating phases characterized by winding numbers $0\leq w \leq N_{\text{w}}$ and topological critical lines constrained by mirror reflection symmetry. They also exhibit completely flat bands at specific values of the model parameters, indicated by lines in the phase diagrams. An even number of perpendicularly coupled wires exhibits either gapless or topologically trivial phases. An odd number of perpendicularly coupled wires additionally exhibits nontrivial topological phases with winding number $w=1$. Due to mirror reflection symmetry, their gapless regions can be topologically nontrivial. They also reveal confined coherent correlations in the odd-indexed wires at strong inter-wire coupling away from the gapless regions.