Majorana Fermions in Vortex Lattices
Majorana fermion bound states are at the front and center of approaches to realizing topological quantum computation. In this talk, I will first introduce the peculiar quantum characteristics of Majorana bound states. Then, I will argue that the amplitude for Majorana fermions to tunnel between a pair of vortices necessarily depends on the background superconducting phase profile; it is proportional to the sine of half the difference between the phases at the two vortices.
I shall then use this result to explore tight-binding models of Majorana fermions in vortices arranged in triangular or square lattices. In both cases the aforementioned phase-tunneling relationship leads to macroscopically degenerate localizable flat bands at zero energy, in addition to other dispersive bands. The presence of flat Majorana bands, and thus less than previously expected decoherence, in these vortex arrays, bodes well for the prospects of doing topological quantum computation with large numbers of Majorana states.
"Majorana Fermions in Vortex Lattices", Rudro R. Biswas, PRL 111, 136401 (2013)