Long-range chiral pairing enables topological superconductivity in triangular lattices without spin−orbit coupling and magnetic field

This paper demonstrates a pathway to topological superconductivity in monolayer triangular lattices through long-range pairing without requiring spin−orbit coupling and magnetic field, contrasting conventional frameworks reliant on superconductivity and spin−orbit coupling and time-reversal symmetry (TRS) breaking. Berry curvature analysis reveals spontaneous TRS-breaking-induced peaks or valleys under long-range pairing, signaling nontrivial topology superconducting states. Notably, the increase in the long-range pairing strength only changes the size of the energy band-gap, without triggering a topological phase transition. This characteristic is verified by calculating Berry curvature and topological edge states. In zigzag and armchair-edge ribbons of finite width, the topological edge states are influenced by the ribbon boundary symmetry and the interaction range of long-range pairing. Under nearest-neighbor pairing, the topological edge states maintain particle−hole symmetry and match the corresponding Chern number. However, next-nearest-neighbor and third-nearest-neighbor pairings break the particle-hole symmetry of the topological edge states in armchair-edge ribbon. This work proposes a mechanism to realize topological superconductivity without relying on spin−orbit coupling and magnetic field, thereby offering a theoretical foundation for simplifying the design of topological quantum devices.