UBC Theses and Dissertations
Majorana bands in topological superconductors Liu, Tianyu
Majorana fermions can exist in condensed matter systems as quasi-particle excitations called Majorana bands. The details of Majorana bands will be the central concern of this thesis. In the thesis, Majorana bands are studied analytically and numerically in two square lattice systems with vortices. The p+ip superconductor, containing two vortices in each magnetic unit cell, exhibits slightly dispersing Majorana bands in the middle of the superconducting gap. With the same vortex geometry, the Fu-Kane model shows similar Majorana bands, which, however, can become completely flat when chemical potential is tuned to coincide with the Dirac point. By comparison to a tight binding model of vortex lattice, it is clear that the dispersion is mainly contributed by first and second nearest neighbor hoppings of Majorana fermions bound in vortices. The hoppings, which are extracted from numerical diagonalization, are not quite identical to the existing analytical prediction. Therefore, we built two simple equations that show the phenomenologically correct trends of the hoppings.
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