  We study the physics of the Josephson effect in nematic superconductors with
$E_u$ odd parity in the Ginzburg-Landau approach. Two-component vector
superconducting order parameter makes this effect rather unusual. We get that
the Meissner kernel has off-diagonal components. We derive current-phase
relations for different configurations of the junction, crystallographic axes
of the sample, and nematicity direction. We show that an anomalous Josephson
Hall effect can be observed in such a system without any magnetization. That
is, for definite orientations of the junction and crystal axes, a component of
the Josephson current along the junction is induced by the order parameter
phase difference across the contact. We also calculate the magnetic field
dependence of the maximum current through the junction. We find that the period
of the Fraunhofer oscillations of the maximum Josephson current depends on the
geometry of the junction, direction of the magnetic field, and nematicity
vector.

Superconductivity