Abstract

In this thesis, after giving an introduction to topology in electronic systems and topological superconductors, I first discuss the additional transport properties Majoranas induce — that is, spin transport. I show that the Andreev reflection processes induce non-trivial spin properties when a Majorana is present, which can be tested as an additional experimental signature of Majoranas or can be used for spintronics. We further generalize this property to systems with Majorana flat bands. Then, I discuss a case where two Majoranas coexist, protected by a chiral symmetry. Interestingly, the local Andreev reflection is suppressed at zero bias due to the interferences between the two Majoranas. Consequently, crossed Andreev reflection probability can be enhanced to a value as large as unity (resonant). This can happen in realistic systems of quantum anomalous Hall insulators in proximity to superconductors, where Majorana chiral modes appear. Very recently, an experiment has nicely shown the existence of such Majorana chiral modes which manifest themselves in conductance plateaus quantized at $\frac{1}{2} \frac{e^2}{h}$. I show that our numerical simulation with domain walls further explain the data and the results support the claim that the plateaus are due to Majorana chiral modes.