Flat Majorana bands in two-dimensional lattices with inhomogeneous magnetic fields: Topology and stability

In this paper, we show that for a range of configurations of inhomogeneous magnetic fields, it is possible to create flat bands of Majorana states localized on the edges of two-dimensional lattices. Majorana bound states have been predicted to exist in both one-dimensional and two-dimensional systems with Rashba spin-orbit coupling, magnetic fields, and placed in proximity to a superconductor. For the proposed systems, we present the topological phase diagrams, and we study the conditions for weak topology which predict the formation of bands of Majorana states. The Majorana bands are demonstrated to be relatively stable with respect to a variety of different perturbations on both square and hexagonal lattices.