Majorana fermions are special types of quasiparticles that are proposed to occur in a proposed new state of matter known as a topological superconductor (TS). These quasiparticles are made out of electrons and holes in a particular way that makes them their own antiparticle, and they appear at certain surfaces, edges or defects of these superconductors where their existence is guaranteed due to a topological protection. They have generated great excitement in the last years because their unambiguous detection would be a smoking-gun proof of the existence of a new phase of matter, and moreover, because thanks to their non-Abelian statistics they could be used to implement fault-tolerant quantum computation. The prospects of detecting and manipulating them are now seen with increasing optimism, and indeed some very recent experiments report evidence that suggests we may already have them at our fingertips.
This theoretical project will critically assess three promising proposals of TS where experiments are already available, making new predictions that will help to discern when Majorana fermions can be reliably identified. First, chains of magnetic atoms in the surface of a regular superconductor will be considered. This simple system should realize Majorana fermions at the chain edges, but is unknown whether coupling them together in networks to perform braiding operations is possible, a question this project will tackle. Then, Cu doped Bi2Se3 as an intrinsic TS will be reexamined. In view of contradicting experimental evidence from surface probes, alternative pairing models will be explored via quasiparticle interference predictions to explain the experimental data. Finally, the edge states of InAs/GaSb quantum wells, which feature an unexpected conductance insensitivity to magnetic fields, will be studied. Once this behaviour is understood, a coupling to a superconductor will be considered to explore transport signatures of Majorana fermions.
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