Kelvin-Mach Wake in a Two-Dimensional Fermi Sea

The dispersion law for plasma oscillations in a two-dimensional electron gas in the hydrodynamic approximation interpolates between Ωq and Ωq dependences as the wave vector q increases. As a result, downstream of a charged impurity in the presence of a uniform supersonic electric current flow, a wake pattern of induced charge density and potential is formed whose geometry is controlled by the Mach number M. For 1<M≤2, the wake consists of transverse wave fronts confined within a sector, whose angle is given by the classic Mach condition. An additional wake of a larger angle resembling the Kelvin ship wake, and consisting of both transverse and diverging wave fronts, is found outside the Mach sector for M>2. These wakes also trail an external charge, traveling supersonically, a fixed distance away from the electron gas.