Spin-resolved Andreev levels and parity crossings in hybrid superconductor–semiconductor nanostructures

The physics and operating principles of hybrid superconductor–semiconductor devices rest ultimately on the magnetic properties of their elementary subgap excitations, usually called Andreev levels. Here we report a direct measurement of the Zeeman effect on the Andreev levels of a semiconductor quantum dot with large electron g -factor, strongly coupled to a conventional superconductor with a large critical magnetic field. This material combination allows spin degeneracy to be lifted without destroying superconductivity. We show that a spin-split Andreev level crossing the Fermi energy results in a quantum phase transition to a spin-polarized state, which implies a change in the fermionic parity of the system. This crossing manifests itself as a zero-bias conductance anomaly at finite magnetic field with properties that resemble those expected for Majorana modes in a topological superconductor. Although this resemblance is understood without evoking topological superconductivity, the observed parity transitions could be regarded as precursors of Majorana modes in the long-wire limit. A study of the magnetic fine structure of the electronic states in a semiconductor quantum dot coupled to a superconducting contact highlights important elements that should be taken into account in the search for Majorana modes in the solid state.