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Majorana bound states on a periodic superconducting vortex lattice Pathak, Vedangi

Abstract

Majorana quasi-particles can exist as zero-energy excitations bound to vortices present on the surface of a topological insulator that is proximity-coupled to a type-II superconductor. Such a system finds its natural realisation on the surface of the iron-based superconductor FeTe₀.₅₅Se₀.₄₅ which has been identified as a potential topological superconductor and is expected to host Majorana quasi-particles as zero-energy excitations on vortices. This thesis aims to explain the occurrence of Majorana vortex bound states present on such materials by constructing a model for a vortex lattice on periodic manifolds. A two-dimensional square lattice model is developed to capture the low energy physics of the surface states of a topological insulator proximity-coupled to an s-wave superconductor. Using the Franz-Tesanovic singular gauge transformation, multiple vortices can be incorporated in the system by circumventing the problem of branch cuts. To construct finite vortex lattice on periodic manifolds (torus in two dimensions), we need to account for the fluxes through the non-contractible loops of the torus, leading to certain correction terms appearing in the singular gauge transformation. This thesis provides the details of the construction of vortex lattice on a periodic manifold on the surface of topological insulator proximity-coupled to a superconductor and investigates the Majorana zero modes present on the vortices. The theory developed for periodic vortex lattice on the topological insulator-superconductor heterostructure is successful in replicating the experimental observations of Majorana vortex bound states on the surface of the iron-based superconductor FeTe₀.₅₅Se₀.₄₅.

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