  We study one dimensional (1D) and quasi-1D periodic structures as possible
platforms for the emergence of Majorana bound states with enhanced robustness
against disorder and system inhomogeneity. First, using a simple 1D model, we
analytically derive the effective parameters characterizing the minibands
generated by the periodic potential. We show that, for strong enough periodic
potentials, the higher energy minibands hosting Majorana bound states have
significant advantages compared to their counterparts in uniform systems,
including increased topological gaps, enhanced robustness against disorder, and
enlarged parameter space regions consistent with the presence of topological
superconductivity. We identify the problem of engineering a strong enough
periodic potential as a key roadblock to realizing efficient periodic 1D
structures. To address this challenge, we propose an efficient implementation
of the periodic potential based on quasi-1D channels realized in 2D
semiconductor heterostructures proximity coupled to superconductor strips of
periodically modulated width. Our numerical study of the modulated channel
device shows excellent agreement with the simple 1D model, reveals a
topological phase diagram that is quite insensitive to the details of the
confining potential associated with screening by the superconductor, and
demonstrates that engineering patterned 2D structures represents a powerful and
versatile approach to realizing robust Majorana bound states.
