The dispersion law for plasma oscillations in a two-dimensional electron gas in the hydrodynamic approximation interpolates between Ω ∝ √q and Ω ∝ q 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.
Digital Object Identifier (DOI)
Kolomeisky, Eugene B. and Straley, Joseph P., "Kelvin-Mach Wake in a Two-Dimensional Fermi Sea" (2018). Physics and Astronomy Faculty Publications. 579.