Topological phases of coupled Su-Schrieffer-Heeger wires

The phase diagrams of arbitrary number $N_{\text{w}}$ of diagonally and perpendicularly coupled Su-Schrieffer-Heeger wires have been identified. The diagonally coupled wires have rich topological phase diagrams exhibiting insulating phases with winding numbers $0\leq w \leq N_{\text{w}}$ and topological critical lines restricted by the reflection mirror symmetry. Even number of perpendicularly coupled wires exhibit either gapless or trivial topological phases. Odd number of perpendicularly coupled wires additionally exhibit nontrivial topological phases with winding number $w=1$. Due to the mirror reflection symmetry, their gapless regions can be topologically nontrivial. Odd number of perpendicularly coupled wires reveal coherent confined correlations in the odd indexed wires with strong wire-wire coupling away from the gapless regions.