A recent work [Potter and Lee, Phys. Rev. Lett. 105, 227003 (2010)] demonstrated, for an ideal spinless $p+\mathit{ip}$ superconductor, that Majorana end states can be realized outside the strict one-dimensional limit, so long as (1) the sample width does not greatly exceed the superconducting coherence length and (2) an odd number of transverse subbands are occupied. Here we extend this analysis to the case of an effective $p+\mathit{ip}$ superconductor engineered from a Rashba spin-orbit-coupled surface with induced magnetization and superconductivity, and find a number of additional features. Specifically, we find that finite-size quantization allows Majorana end states even when the chemical potential is outside of the induced Zeeman gap where the bulk material would not be topological. This is relevant to proposals utilizing semiconducting quantum wires; however, we also find that the bulk energy gap is substantially reduced if the induced magnetization is too large. We next consider a slightly different geometry, and show that Majorana end states can be created at the ends of ferromagnetic domains. Finally, we consider the case of meandering edges and find, surprisingly, that the existence of well-defined transverse subbands is not necessary for the formation of robust Majorana end states.

• Received 29 November 2010

DOI:https://doi.org/10.1103/PhysRevB.83.094525