Volt-ampere characteristic of the superconductive nanostructure with the Andreev reflection induced by the Majorana fermions

Abstract

One of the modern quantum mechanical nanostructures in which the appearance and detection of Majorana fermions takes place was considered. There are a lot of propositions onhow to create and to detect the Majorana modes. Some various structures were investigated for this purpose. The two-terminal device where a superconducting island was deposited on a three dimensional topological insulator was investigated. The branch of chiral Majorana particles was located at the interface between the semiconductor and the ferromagnetic material. In this structure, it was possible to realize the Andreev reflection induced by the Majorana fermions. To control the Majorana modes one must be able only not to create them but also to tune the resulting current-voltage characteristic of the given structure. One of the simplest models which allowed to analyz the relevant characteristics and propose the additional possibilities to tune the superconducting current was considered. In this model, an incident from the lead electron was converted into a backscattered hole with probability equal to one. Such a process may be called as a Majorana particle induced Andreev reflection. On the basis of the simplified Hamiltonian, the expressions for the transmission coefficient and the volt-ampere dependence of this structure were calculated and analyzed. It is shown that these characteristics can be flexibly adjusted using certain structure parameters, in particular, by changing the Fermi velocity of quasielectrons. Two Majorana bound states may encode a single qubit nonlocally. Such a qubit can be robust against the local source of decoherence and hence can provide a good building block for topological quantum computations. Since Majorana particles are non-Abelion fermions they may be useful in the potential applications for quantum computations free from decoherence.