(a) False-coloured scanning electron micrograph of a device identical to that under study, defined by selective removal of the Al (blue), exposing the semiconductor below (pink). Gates (yellow) and flux-bias lines (purple) were deposited on a uniform dielectric layer (not visible). Bias voltage VSD, gate voltages Vα (α ∈ {TL, TR, Probe, Switch, G}), left (right) flux-bias line current IL(R) and external magnetic flux threading the left (right) superconducting loop ΦL(R) are indicated. (b) Schematic representation of the device and the measurement setup. (c) Zoom-in of a near the three-terminal Josephson junction (3TJJ) region. (d), (e) Differential conductance G between tunnelling probe and 3TJJ measured as a function of the currents IL and IR injected into the flux-bias lines, at fixed voltage bias VSD = − 170 μV. In (d) (e), the switch junction is in the ON (OFF) state, VSwitch = 0 (VSwitch = − 1.5 V). The directions of the black arrows indicate the periodicity axes, along which the external magnetic fluxes ΦL and ΦR vary independently. Each black arrow represents the addition of one superconducting flux quantum Φ0 = h/2e (where h is the Planck constant and e the elementary charge) to the corresponding flux. The dotted yellow line follows a ΦL-dependent resonance in d and is replicated in (e) to highlight the slope difference. The coloured arrows labelled γ1-6 define the linecuts shown in Fig. 2 of the main text.

Phase-engineering the Andreev band structure of a three-terminal Josephson junction

In hybrid Josephson junctions with three or more superconducting terminals coupled to a semiconducting region, Andreev bound states may form unconventional energy band structures, or Andreev matter, which are engineered by controlling superconducting phase differences. Here we report tunnelling spectroscopy measurements of three-terminal Josephson junctions realised in an InAs/Al heterostructure. The three terminals are connected to form two loops, enabling independent control over two phase differences and access to a synthetic Andreev band structure in the two-dimensional phase space. Our results demonstrate a phase-controlled Andreev molecule, originating from two discrete Andreev levels that spatially overlap and hybridise. Signatures of hybridisation are observed in the form of avoided crossings in the spectrum and band structure anisotropies in the phase space, all explained by a numerical model. Future extensions of this work could focus on addressing spin-resolved energy levels, ground state fermion parity transitions and Weyl bands in multiterminal geometries.

M. Coraiola, D. Z. Haxell, D. Sabonis, H. Weisbrich, A. E. Svetogorov, M. Hinderling, S. C. ten Kate, E. Cheah, F. Krizek, R. Schott, W. Wegscheider, J. C. Cuevas, W. Belzig, and F. Nichele
Nat. Commun. 14, 6784 (2023)