Non-Galilean response of Rashba coupled Fermi gases

We consider the effect of a momentum kick on the ground state of a non-interacting two-dimensional Fermi gas subject to Rashba spin-orbit coupling. Although the total momentum is a constant of motion, the gas does not obey the rules of Galilean relativity. Upon imprinting a small overall velocity to the non-interacting gas, we find that the Fermi sea is deformed in a non-trivial way. We also consider a weakly repulsive Fermi gas, and find, from its Hartree shift, that the total ground state of the system may change into a deformed, finite momentum ground state as the repulsion is increased beyond a critical value, without the need of any external Zeeman fields. We also discuss possible experimental signatures of these effects.