  When both inversion and time-reversal symmetries are broken, the critical
current of a superconductor can be nonreciprocal. In this work we show that in
certain classes of two-dimensional superconductors with antisymmetric
spin-orbit coupling, Cooper pairs acquire a finite momentum upon the
application of an in-plane magnetic field, and as a result, critical currents
in the direction parallel and antiparallel to the Cooper pair momentum become
unequal. This supercurrent diode effect is also manifested in the
polarity-dependence of in-plane critical fields induced by a supercurrent.
These nonreciprocal effects may be found in polar SrTiO$_3$ film, few-layer
MoTe$_2$ in the $T_d$ phase, and twisted bilayer graphene in which the valley
degrees of freedom plays the role analogous to spin.
