Spin-dependent coupling between quantum dots and topological quantum wires

Abstract

Considering Rashba quantum wires with a proximity-induced superconducting gap as physical realizations of Majorana bound states and quantum dots, we calculate the overlap of the Majorana wave functions with the local wave functions on the dot. We determine the spin-dependent tunneling amplitudes between these two localized states and show that we can tune into a fully spin polarized tunneling regime by changing the distance between dot and Majorana bound state. Upon directly applying this to the tunneling model Hamiltonian, we calculate the effective magnetic field on the quantum dot flanked by two Majorana bound states. The direction of the induced magnetic field on the dot depends on the occupation of the nonlocal fermion formed from the two Majorana end states which can be used as a readout for such a Majorana qubit.

The Spin‐Dependent Coupling in the Hybrid Quantum Dot–Majorana Wire System

“…Weakness of each of the transport channels of QD will depend on the asymmetry in spin tunneling between the QD and MBS. As Klinovaja and co‐authors shown, the spin up and down tunneling amplitudes between MBS and quantum dot depend on the spin–orbit interaction length. The change of distance between the dot and topological section hosting MBS causes the oscillations of tunneling amplitudes and especially it can lead to the full‐polarization of tunneling amplitudes.…”

“…The dot electron hybridizes also with Majorana wire giving the coupling parameter where ρ dσ is the density of states of the quantum dot. In our considerations we assume that the Majorana coupling parameter is dependent on the spin direction of dot electron where t m0 is phenomenological constant describing the maximum tunneling between the quantum dot and Majorana wire.…”

“…The competition (coexistence) between Majorana bound states and the Kondo effect can be examined using the quantum dot‐Majorana nanowire system. This system was analyzed experimentally and theoretically for different configurations of a quantum dot, Majorana nanowire, and the external leads. In our work, we examine the competition between Majorana bound states and the Kondo effect using the tunneling setup, in which the quantum dot is placed between two metallic leads (N‐QD‐N) and additionally it is side‐coupled to the Majorana nanowire (see Figure ) .…”

“…In our analysis we will focus on the influence of the Majorana bound states on the transport properties of the N‐QD‐N system, so we will assume that the s‐wave superconductor substrate does not interact with QD. The influence of the QD coupling with the SC substrate was analyzed previously . The connection of quantum dot with metallic lead leads to the Kondo effect, which produces the Kondo resonance pinned to the Fermi level of the metallic leads.…”

“…We will focus on the analysis of the N‐QD‐N system with Majorana wire, in which both the spin directions of the quantum dot are coupled with Majorana wire . In our model we assume that the Majorana wire is side‐connected to the quantum dot, so the MBS, through the interference effects, will influence the current flowing through the QD.…”