1304.1547 (Rudro R. Biswas)
Rudro R. Biswas
We consider Majorana fermions tunneling among an array of vortices in a 2D chiral p-wave superconductor or equivalent material. We calculate the amplitude for Majorana fermions tunneling between a pair of vortices and find that it depends on the background superconducting phase profile; it is proportional to the sine of half the difference between the phases at the two vortices. Using this result we study tight-binding models of Majorana fermions in vortices arranged in triangular or square lattices. In both cases we find that the aforementioned phase-tunneling relationship leads to the creation of superlattices where the Majorana fermions form macroscopically degenerate localizable flat bands at zero energy, in addition to other dispersive bands. This finding suggests that tunneling processes in these vortex arrays do not change the energies of a finite fraction of Majorana fermions, contrary to previous expectation. The presence of flat Majorana bands, and hence less-than-expected decoherence in these vortex arrays, bodes well for the prospects of topological quantum computation with large numbers of Majorana states.
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http://arxiv.org/abs/1304.1547
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