Gate-controlled supercurrent (GCS) in superconducting nanobridges has recently attracted attention as a means to create superconducting switches. Despite the clear advantages for applications, the microscopic mechanism of this effect is still under debate. In this work, we realize GCS for the first time in a highly crystalline superconductor epitaxially grown on an InAs nanowire. We show that the supercurrent in the epitaxial Al layer can be switched to the normal state by applying ≃±23 V on a bottom gate insulated from the nanowire by a crystalline hBN layer. Our extensive study of the temperature and magnetic field dependencies suggests that the electric field is unlikely to be the origin of GCS in our device. Though hot electron injection alone cannot explain our experimental findings, a very recent non-equilibrium phonons based picture is compatible with most of our results.

Various promising qubit concepts have been put forward recently based on engineered superconductor (SC) subgap states like Andreev bound states, Majorana zero modes or the Yu-Shiba-Rusinov (Shiba) states. The coupling of these subgap states via a SC strongly depends on their spatial extension and is an essential next step for future quantum technologies. Here we investigate the spatial extension of a Shiba state in a semiconductor quantum dot coupled to a SC for the first time. With detailed transport measurements and numerical renormalization group calculations we find a remarkable more than 50 nm extension of the zero energy Shiba state, much larger than the one observed in very recent scanning tunneling microscopy (STM) measurements. Moreover, we demonstrate that its spatial extension increases substantially in magnetic field.Superconductor nanostructures are the most advanced platforms for quantum computational architectures thanks to the macroscopic coherent wavefunction and the robust protection by the superconducting gap. Recently, various novel qubit concepts like the Andreev (spin) qubits [1-5], Majorana box qubits [6-8], braiding with Majorana zero modes in a Majorana or a Shibachain [9-18] have been put forward or even implemented. All these qubits are based on their associated sub-gap states such as Andreev bound states [19], Majorana zero modes [18,[20][21][22][23][24][25][26] or Shiba states [27][28][29][30]. The Shiba state is formed when a magnetic adatom or its artificial version (quantum dot) is coupled to a superconductor and the localized magnetic moment creates a subgap state by binding an anti-aligned quasiparticle from the superconductor. Depending on the coupling strength between the superconductor and the magnetic moment, the ground state can be either the screened local moment with singlet character or the unscreened doublet states.The coupling of these sub-gap states via a superconductor is an essential next step towards 2-qubit operations or state engineering, e.g. an Andreev molecule [31][32][33] or a Majorana-chain, which consists of series of adatoms or quantum dots interlinked by the superconductor [9][10][11][12][13][14][15][16][17][18]. Obviously, the coupling between such subgap states strongly depends on their spatial extension into the superconductor, so it is required for these localized states to extend as much as possible.So far, the spatial extent and structure of the Shiba states was investigated by STM measurements on mag-netic adatoms deposited on the surface of a superconductor [34][35][36][37] and, interestingly, it revealed that the dimensionality plays a crucial role [36]. In a three dimensional isotropic s-wave superconductor, it was found that the Shiba states decay over a very short distance of the order of ∼ 1 nm [34,35], but extends one order of magnitude further, as far as ∼ 10 nm, if the impurity is placed on the surface of a two-dimensional superconductor [36,38].In this work, we investigate the spatial extension of the Shiba state formed when an artificial ...