Engineering Majorana Bound States with Periodic Structures

Majorana bound states within semiconductor-superconductor heterostructures are a promising platform for future topological quantum computation. Here we theoretically explore the effects of periodic potentials and periodic structures on the emergence and properties of topological superconductivity and Majorana bound states within 1D and quasi-1D systems. Three key findings suggest that periodic structures may possess some advantages over homogeneous systems in supporting topological superconductivity. The three findings to be discussed are (1) an increased region of parameter space in which the topological phase and Majorana bound states are realized, (2) an increasing topological gap as one moves to higher energy mini-bands, and (3) an increased robustness against disorder compared to homogeneous systems. We also explore several physical systems in which the periodic potential/structure can be engineered and discuss their outlook.