Strongly correlated crystalline higher-order topological phases in two-dimensional systems: A coupled-wire study

Coupled-wire constructions have been widely applied to quantum Hall systems and symmetry-protected topological (SPT) phases. In this Letter, we use the coupled one-dimensional nonchiral Luttinger liquids with domain-wall structured mass terms as quantum wires to construct the crystalline higher-order topological superconductors (HOTSC) in two-dimensional interacting fermionic systems by two representative examples: $D_4$-symmetric class-D HOTSC and $C_4$-symmetric class-BD\1 HOTSC, with Majorana corner modes on the edge. Furthermore, based on the coupled-wire constructions, the quantum phase transition between different phases of 2D HOTSC by tuning the inter-wire couplings is investigated in a straightforward way.