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Coupled-wire constructions have been widely applied to quantum Hall systemsand symmetry-protected topological (SPT) phases. In this Letter, we use thecoupled one-dimensional nonchiral Luttinger liquids with domain-wall structuredmass terms as quantum wires to construct the crystalline higher-ordertopological superconductors (HOTSC) in two-dimensional interacting fermionicsystems 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 phasetransition between different phases of 2D HOTSC by tuning the inter-wirecouplings is investigated in a straightforward way.

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