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Topological edge states are protected states that form between two insulators with different topological properties. The dimensionality of the interface, as well as the type of insulators that form it, endow the topological edge state further properties. I will focus on situations where one of the materials is a superconductor --a quasiparticle insulator. In the case where the edge is zero dimensional, the topological states are Majorana zero-modes localized in the core of a vortex or bound to the end of a nanowire. They are anyons with non-Abelian braiding statistics, but when they are immobile, one cannot demonstrate this by exchanging them in real space and therefore indirect methods are usually needed. I will talk about how to use the chiral motion along the boundary of the superconductor to braid a mobile vortex, either with another mobile vortex in the edge channel or with an immobile vortex in the bulk. When two vortices are fused, they transfer charge into a metal contact. We calculate the time dependent current profile for the fusion process, which consists of ±e/2 charge pulses that flip sign if the world lines of the vortices are braided prior to the fusion. This is an electrical signature of the non-Abelian exchange of Majorana zero-modes. Next, I will discuss how one can deconfine the Majorana zero-modes localized in the vortex cores by applying a spatially oscillating pair potential. In the deconfined phase at zero chemical potential the Majorana fermions form a dispersionless Landau level, protected by chiral symmetry against broadening due to vortex scattering. The Majorana Landau level also has a signature that distinguishes it from a regular Landau level: the coherent superposition of electrons and holes in the Majorana Landau causes a local density of states oscillation with a wave vector set by the Cooper pair momentum as well as the inverse coherence length. This striped density of states pattern also provides a means to measure the chirality of the Majorana fermions. I will conclude by discussing the quantal dynamics in the deconfined phase.

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Inanc Adagideli, Sabanci University
0.03 ETP building
Contact: Erwann Boquillon