  The hybrid combination of superconductors and low-dimensional semiconductors
offers a versatile ground for novel device concepts, such as sources of
spin-entangled electrons, nanoscale superconducting magnetometers, or recently
proposed qubits based on topologically protected Majorana fermions. The
underlying physics behind such hybrid devices ultimately rely on the magnetic
properties of sub-gap excitations, known as Andreev levels. Here we report the
Zeeman effect on the Andreev levels of a semiconductor nanowire quantum dot
(QD) strongly coupled to a conventional superconductor. The combination of the
large QD g-factor with the large superconductor critical magnetic field allows
spin degeneracy to be lifted without suppressing superconductivity. We show
that a Zeeman-split Andreev level crossing the Fermi energy signals a quantum
phase transition in the ground state of the superconductivity-induced QD,
denoting a change in the fermionic parity of the system. This transition
manifests itself as a zero-bias conductance anomaly appearing at a finite
magnetic field, with properties that resemble those expected for Majorana
fermions in a topological superconductor. Although the herein reported
zero-bias anomalies do not hold any relation with topological
superconductivity, the observed parity transitions can be regarded as
precursors of Majorana modes in the long-wire limit.
