Curvature effect induces topological phase transitions in two dimensional topological superconductor

Recently, topological superconductors have emerged as a pivotal frontier in condensed matter physics, owing to the exotic properties of Majorana quasiparticles residing on edges, surfaces, and vortex cores. In this work, we investigate a two-dimensional s+p wave noncentrosymmetric superconductor (NCS) with Rashba spin-orbit coupling (SOC) on a cylindrical manifold. By employing a thin-layer quantization approach, we derive the effective Bogoliubov-de Gennes (BdG) Hamiltonian to elucidate the interplay between surface curvature and topological phase transitions. Our analytical and numerical results demonstrate that the curvature-induced geometric potential (da Costa potential) and the spatial reconfiguration of spin-momentum locking effectively modulate the superconducting gap. From a band theory perspective, we confirm that curvature serves as a critical tuning parameter, capable of driving topological phase transitions by inducing band inversion.

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