  We study Josephson junctions based on InSb nanowires with Sn shells. We
observe skewed critical current diffraction patterns: the maxima in forward and
reverse current bias are at different magnetic flux, with a displacement of
20-40 mT. The skew is greatest when the external field is nearly perpendicular
to the nanowire, in the substrate plane. This orientation suggests that
spin-orbit interaction plays a role. We develop a phenomenological model and
perform tight-binding calculations, both methods reproducing the essential
features of the experiment. The effect modeled is the $\phi$0-Josephson
junction with higher-order Josephson harmonics. The system is of interest for
Majorana studies: the effects are either precursor to or concomitant with
topological superconductivity. Current-phase relations that lack inversion
symmetry can also be used to design quantum circuits with engineered
nonlinearity.
