  Gate-tunable semiconductor nanowires with superconducting leads have great
potential for quantum computation and as model systems for mesoscopic Josephson
junctions. The supercurrent, $I$, versus the phase, $\phi$, across the junction
is called the current-phase relation (CPR). It can reveal not only the
amplitude of the critical current, but also the number of modes and their
transmission. We measured the CPR of many individual InAs nanowire Josephson
junctions, one junction at a time. Both the amplitude and shape of the CPR
varied between junctions, with small critical currents and skewed CPRs
indicating few-mode junctions with high transmissions. In a gate-tunable
junction, we found that the CPR varied with gate voltage: Near the onset of
supercurrent, we observed behavior consistent with resonant tunneling through a
single, highly transmitting mode. The gate dependence is consistent with
modeled subband structure that includes an effective tunneling barrier due to
an abrupt change in the Fermi level at the boundary of the gate-tuned region.
These measurements of skewed, tunable, few-mode CPRs are promising both for
applications that require anharmonic junctions and for Majorana readout
proposals.
