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

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.