  Gate-tunable semiconductor-superconductor nanowires with superconducting
leads form exotic Josephson junctions that are a highly desirable platform for
two types of qubits: those with topological superconductivity (Majorana qubits)
and those based on tunable anharmonicity (gatemon qubits). Controlling their
behavior, however, requires understanding their electrostatic environment and
electronic structure. Here we study gated InAs nanowires with epitaxial
aluminum shells. By measuring current-phase relations (CPR) and comparing them
with analytical and numerical calculations, we show that we can tune the number
of modes, determine the transparency of each mode, and tune into regimes in
which electron-electron interactions are apparent, indicating the presence of a
quantum dot. To take into account electrostatic and geometrical effects, we
perform microscopic self-consistent Schrodinger-Poisson numerical simulations,
revealing the energy spectrum of Andreev states in the junction as well as
their spatial distribution. Our work systematically demonstrates the effect of
device geometry, gate voltage and phase bias on mode behavior, providing new
insights into ongoing experimental efforts and predictive device design.
