Mean-Field Study of Normal Metal-Quantum Dot-Superconductor System in the Presence of External Magnetic Field

TL;DR

This study investigates how external magnetic fields influence the spectral and transport properties of a quantum dot coupled to normal and superconducting leads, revealing Zeeman splitting and quantum phase transitions.

Contribution

It introduces a mean-field Green's function approach to analyze magnetic field effects on Andreev bound states in a N-QD-S system, highlighting the impact of Coulomb interactions and magnetic fields.

Findings

Zeeman splitting causes ABSs to cross the Fermi level.

Quantum phase transition linked to fermion parity change.

Conductance varies with Zeeman energy and Coulomb interactions.

Abstract

In this paper, we have analyzed the spectral and transport properties of a weakly correlated single-level quantum dot hybridized with one normal conducting and another Bardeen-Cooper-Schrieffer (BCS) superconducting lead (N-QD-S system) in the presence of an external magnetic field. We have employed Green's function equation of motion (EOM) approach within a self-consistent Hartree-Fock (HF) mean-field approximation to analyze the Hamiltonian. We studied the effect of on-dot Coulomb correlation and an external magnetic field on the sub-gap Andreev levels of a quantum dot, strongly coupled to a conventional s-wave superconductor as a function of impurity parameters. We have shown that for a finite magnetic field, the Andreev bound states (ABSs) split into a spin-up and spin-down contribution (i.e. Zeeman splitting) and cross the Fermi energy level, resulting in a quantum phase transition, which is an indication of a change in the fermion parity of the ground state. Further, within the non-linear regime, we discuss the total electrical conductance for various values of Zeeman energy and on-dot Coulomb interactions. We have compared our results with the existing experimental and theoretical results.