Hydrodynamic theory of the Dyakonov-Shur instability in graphene transistors

TL;DR

This paper develops a hydrodynamic theory for the Dyakonov-Shur plasma instability in graphene transistors, analyzing its onset, evolution, and electromagnetic radiation output using numerical simulations.

Contribution

It introduces a comprehensive hydrodynamic model for the DS instability in graphene, including nonlinear equations and numerical analysis of the instability's dynamics and radiation.

Findings

Instability leads to coherent anharmonic oscillations in the electron fluid.

Conditions for the onset of the DS instability are identified.

The spatial distribution and power of emitted radiation are calculated.

Abstract

We present a comprehensive theory of the Dyakonov-Shur (DS) plasma instability in current-biased 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 nonlinear 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.