The ends of one-dimensional $p+ip$ superconductors have long been predicted to possess localized Majorana fermion modes [A. Kitaev, arXiv:cond-mat/0010440]. We show that Majorana end states are robust beyond the strict 1D single-channel limit, so long as the sample width is not much larger than the superconducting coherence length, and they exist when an odd number of transverse quantization channels are occupied. Consequently, the system undergoes a sequence of topological phase transitions driven by changing the chemical potential. These observations make it feasible to implement quasi-1D $p+ip$ superconductors in metallic thin-film microstructures, which offer 3–4 orders of magnitude larger energy scales than semiconductor-based schemes. Some promising candidate materials are described.

• Received 26 July 2010

DOI:https://doi.org/10.1103/PhysRevLett.105.227003