Hydrodynamic theory of the Dyakonov-Shur instability in graphene transistors

Abstract

We present a comprehensive theory of the Dyakonov-Shur (DS) plasma instability in currentbiased graphene transistors. Using the hydrodynamic approach, we derive equations describing the DS instability in the two-dimensional electron fluid in graphene at arbitrary values of electron drift velocity. These non-linear equations together with Maxwell's equations are used for numerical analysis of the spatial and temporal evolution of the graphene electron system after the DS instability is triggered by random current fluctuations. We analyze conditions necessary for the onset of the DS instability and the properties of the final stationary state of the graphene electron system. We demonstrate that the instability results in the coherent anharmonic oscillatory state of the electron fluid and calculate both the spatial distribution and the power of the electromagnetic radiation generated by the graphene transistor in the DS instability regime.

Entropy Wave Instability in Dirac and Weyl Semimetals

“…Furthermore, there is an agreement with Refs. [19,22] for Λ ≈ 1 (which is indeed the case for µ ≫ T ) and slow flows [35]. As we see, enforcing the boundary conditions leads to the DSI for u 0 > 0 (for Λ 1).…”

“…In addition to 2D systems, evidence of three-dimensional (3D) relativisticlike hydrodynamic electron transport was reported in the Weyl semimetal tungsten diphosphide WP 2 [17]. Because Dirac and Weyl semimetals provide a suitable platform for investigating electron hydrodynamics in solids, the DSI in graphene received a lot of attention [18][19][20][21][22]. Despite extensive theoretical studies, the generation of THz waves by the DSI was not confirmed experimentally yet.…”

“…Refs. [21,22]). As for the real part, the plasmon frequencies are quantized due to the finite thickness of the slab, where k x → π(l + 1/2)/L.…”