  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 2-d 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 bulk topological phase
diagrams, and we study the conditions for weak topology which predicts 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.
