  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.
