a Spin down (blue) and up (red) QP density of states (DOS) in the superconductor in an in-plane magnetic field, which induces both a Zeeman splitting and orbital depairing. The blue and red shaded regions are proportional to, respectively, the number of spin down and spin up non-equilibrium quasiparticles (as in Eq. (1)) near the first detector. (A spin down excitation is a spin down electron-like or a spin up hole-like quasiparticle.) This was calculated with the density of states in a, the reservoir distribution function in e and the injection voltage (Vinj) indicated on the left. For clarity, the imbalance between the number of electron-like QPs and the number of hole-like QPs (the charge imbalance, i.e. the odd component of N(E)), has been multiplied by five. This imbalance can be seen to occur in a specific energy range, Δ − EZ ≤ ∣E∣ ≤ Δ + EZ. b Zoom in of a. It can be seen more clearly here that there are more quasiparticles of one spin (blue) than the other (red). c Predicted spin down (blue) and up (red) QP distribution functions at the indicated distance from the injector. The distribution functions show peaks at the superconducting gap edge, as well as a step-like cutoff at eVinj. d Farther than an electron–electron interaction length (≈1 μm) from the injector, we expect the quasiparticle distribution function to be spin-independent and close to an effective temperature. The trace shown here is an illustration, not a calculation. e QPs are assumed to be at equilibrium at the reservoir. f False colour scanning electron micrograph of the device, and a schematic drawing of the spectroscopy measurement setup. The horizontal superconducting wire is 6 nm Al. The injector (100 nm Cu, cyan) and the detectors (8 nm Al/0.1 nm Pt, red) form tunnel junctions with the wire, with the latter’s native oxide as the barrier. Scale bar: 1 μm.