Fig. 2: Singlet–doublet phase transitions.

a, Charge stability diagram of V_RB versus V_PG at V_SD = 80 μV, V_LB = −1.108 V and V_HG = −1.000 V. A cross-capacitance between the electrostatic gate V_RB and the QD results in simultaneous tuning of Γ_S and ϵ₀. We note that we expect the QD system to be in the multi-hole regime. b–d, Bottom panels show bias spectroscopy at decreasing values of V_RB corresponding to the square, circle and triangle icons in a. Upper panels portray phase diagrams for the singlet and doublet phases, computed using a minimal ZBW model of the expected ground state character of the hybrid system. Here, ϵ₀ is the electrochemical potential of the QD with respect to the grounded SCs, and U is the charging energy of the QD; the phase diagram was computed assuming U = 1.6 meV and Δ = 71 μeV. As the SC–QD coupling Γ_S is increased, the doublet state becomes energetically unfavourable, as seen by the merging of charge transitions (magenta dashed lines). Γ_S is roughly estimated, by modelling the sub-gap spectrum in the bottom panels (Supplementary Section V), to be 70 μeV, 110 μeV and 150 μeV from b–d, respectively, as indicated by the red dashed lines.