Fig. 1
From: Parity transitions in the superconducting ground state of hybrid InSb–Al Coulomb islands
Hybrid semiconducting–superconducting island and its energy spectrum. a False-colour scanning electron microscope image of the device consisting of an InSb nanowire (green) with an 800–900 nm long Al-shell (light-blue) covering the top facet and one side facet. Inset: schematic cross-section at the centre of the plunger gate (PG) indicated by the yellow line. The Si/SiOx substrate contains a global back gate that we keep at zero voltage. The InSb wire is contacted by Cr/Au leads (yellow) and then covered by a 30 nm-thick dielectric layer of SiNx (light-grey). Ti/Au top gates (blue) that wrap around the wire allow for local electrostatic control of the electron density. Two gates are used to induce tunnel barriers (TG) and one plunger gate (PG) controls the electron number on the island. The scale bar indicates 500 nm. b dI/dVb vs. tunnel gate voltage and Vb showing 2e-periodic Coulomb diamonds (one diamond is outlined by yellow dashed lines). The lower panel shows horizontal linecuts with 2e-periodic Coulomb oscillations at Vb = 0 (black trace) and 1e-periodic oscillations at Vb = 150 μV (red trace). The panel on the right shows a vertical linecut through the Coulomb peak at the degeneracy point (blue trace) and through the centre of the Coulomb diamond (purple trace). Below are four scenarios for the B-dependence of a single Andreev level (c–f), the resulting energies as a function of the induced charge, Ng (g–j), and the Coulomb oscillations (k–n). In panels c–f, the grey regions represent the continuum of states above ∆. The coloured traces represent the energy, E0, of the lowest-energy subgap state. Panels g–j show the energies of the island with N excess electrons, E(Ng) = Ec(Ng − N)2 + pNE0, where Ng is the gate-induced charge, N is the electron occupancy number, and pN = 0 (1) for N = even (odd). Parabolas for N = even are shown in black, while parabolas for N = odd are shown in colours in correspondence to the colours in the other rows. Crossings in the lowest-energy parabolas correspond to Coulomb peaks as sketched in panels k–n, again with the same colour coding. Labels in the Coulomb valleys between the peaks indicate the GS parity being either even (e) or odd (o)
