Majorana modes in striped two-dimensional inhomogeneous topological superconductors

Majorana zero modes have attracted significant attention for their potential use in topological quantum computing and for realizing exotic quantum phases. These zero-energy quasiparticle excitations localize at the vortex cores of two-dimensional topological superconductors or at the ends of one-dimensional topological superconductors. Here, we describe an alternative platform: a two-dimensional topological superconductor with inhomogeneous superconductivity, i.e., in the Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) phase. In certain regimes, Majorana modes localize at the ends of topologically nontrivial one-dimensional stripes induced by the spatial variations of the order parameter phase.



Under certain conditions, these Majorana modes combine to form a single highly nonlocal state that spans spatially separated locations, possessing precisely zero energy in finite-sized systems. Additionally, this state exhibits an emergent quantum-mechanical supersymmetry. We then provide detailed descriptions of how to manipulate and combine these Majorana modes through braiding and fusion protocols. We also demonstrate the versatility of our proposal by suggesting potential experimental setups for realizing Yang-Lee anyons and the Sachdev-Ye-Kitaev model using these topologically nontrivial stripes.