Properties of the Majorana-state tunneling Josephson junction mediated by an interacting quantum dot

TL;DR

This paper investigates how electron interactions and magnetic fields influence Majorana states and Josephson currents in a topological superconductor-quantum dot system, revealing effects on conductance, spin polarization, and state hybridization.

Contribution

It introduces a detailed model of Majorana-state tunneling in a quantum dot-mediated Josephson junction, highlighting the impact of interactions and magnetic field orientation on observable properties.

Findings

Electron interactions reduce zero bias conductance peaks.

Magnetic field angle controls spin polarization and Majorana leakage.

Phase-biased current exhibits $4\\pi$ periodicity and can switch sign.

Abstract

We consider a model of a Josephson junction of two topological superconducting wires mediated by an interacting quantum dot. An additional normal electrode coupled to the dot from the top allows to probe its density of states. The Majorana states adjacent to the dot hybridize across the junction and from a bound state in the dot. The dot is subjected to the effective magnetic field arising from the superposition of the fields driving each wire into topological states, which, dependent on the angle between the fields, introduces variable Zeeman splitting of the dot active level. We show that electron interactions in the dot diminish the characteristic for Majoranas zero bias peak arising in the transverse conductance through the dot and introduce an overall asymmetry of the conductance. They also renormalize the hybridization between the end-state Majoranas in shorter wires. The Majorana spin polarization is determined by the effective magnetic field in the dot. Phase-biased Josephson current exhibits spin polarization in thermal equilibrium, which possesses characteristic $4\pi$ periodicity, and its sign can be switched when an unpaired Majorana state is present in the junction. We also observe spin-dependent Majorana state "leaking", which can be controlled by the position of the dot level in energy scale.