Long‐Range Interactions in Topological Superconducting Systems: A Mini Review

ABSTRACT The role of long‐range interactions in topological quantum systems is reviewed with emphasis on the long‐range ‐wave superconductor and its variants. Basic concepts of the lattice model with couplings decaying by power law of distance are introduced to frame the underlying theoretical formalism. This review centers on properties of the long‐range phase that finds no counterpart in the short‐range limit. The breakdown of conformal symmetry in critical regimes and the appearance of massive edge modes differing from conventional Majorana zero modes are discussed. Relevant features including the fractional topological invariant, violations of the area law, and anomalous transport characteristics are also described. Theoretical studies of realistic condensed‐matter realizations such as helical Shiba chains, hybrid nanowires, and other platforms are covered to assess their feasibility under various experimental constraints. Finally, experimental efforts are surveyed where implementations in solid‐state devices and other systems that can simulate effective long‐range topological Hamiltonians are both highlighted.