This thesis consists of two original studies about Majorana fermions in topological superconductors (TS). The first chapter is an introduction to topological superconductors. In Chapter 2, we find that Majorana fermions induce selective equal spin Andreev reflection (SESAR), in which incoming electrons with certain spin polarization in the lead are reflected as counter-propagating holes with the same spin. The spin polarization direction of the electrons of this Andreev reflected channel is selected by the Majorana fermions. Moreover, electrons with opposite spin polarization are always reflected as electrons with unchanged spin. As a result, the charge current in the lead is spin-polarized. Therefore, a topological superconductor which supports Majorana fermions can be used as...[ Read more ]

This thesis consists of two original studies about Majorana fermions in topological superconductors (TS). The first chapter is an introduction to topological superconductors. In Chapter 2, we find that Majorana fermions induce selective equal spin Andreev reflection (SESAR), in which incoming electrons with certain spin polarization in the lead are reflected as counter-propagating holes with the same spin. The spin polarization direction of the electrons of this Andreev reflected channel is selected by the Majorana fermions. Moreover, electrons with opposite spin polarization are always reflected as electrons with unchanged spin. As a result, the charge current in the lead is spin-polarized. Therefore, a topological superconductor which supports Majorana fermions can be used as a novel device to create fully spin-polarized currents in paramagnetic leads. We point out that SESARs can also be used to detect Majorana fermions in topological superconductors. The appendices includes all the detailed calculations. In Chapter 3, we propose a new type of topological superconductors which can be used as a novel source of correlated spin currents. We show that inducing superconductivity on an AIII class topological insulator wire, which respects a chiral symmetry and supports protected fermionic end states, will result in a topological superconductor. This topological superconductor supports two topological phases with one or two Majorana fermion end states respectively. In the phase with two Majorana fermions, the superconductor can split Cooper pairs efficiently into electrons in two spatially separated leads due to Majorana induced resonant crossed Andreev reflections. The resulting currents in the leads are correlated and spin-polarized. Importantly, the proposed topological superconductors can be realized using quantum anomalous Hall insulators in proximity to superconductors.