Kinetic Theory of the Dyakonov-Shur Instability

One of the most promising routes to the spontaneous generation of terahertz radiation is the Dyakonov-Shur instability of a two-dimensional electron gas [Dyakonov and Shur, Phys. Rev. Lett. 71, 2465 (1993)]. This instability arises from a non-standard, but experimentally achievable choice of boundary conditions on the electron gas, coupled to a uniform background current flow. Despite much circumstantial evidence for this instability, a clean experimental realization has proven to be difficult, most likely since the instability was implicitly deep in a hydrodynamic regime, where electrons collide with each other at a rate 1/τ_ee much larger than Umklapp or phonon/impurity collisions. In this talk, we will investigate the fate of the instability across the hydrodynamic-to-ballistic transition via semiclassical kinetic theory. While the instability disappears in an intermediate regime of τ_ee, it reappears in the ballistic limit τ_ee → ∞ for certain boundary conditions.