Spontaneous Running Waves and Self-Oscillatory Transport in Dirac Fluids

TL;DR

This paper predicts a hydrodynamic instability in Dirac electron fluids that leads to spontaneous oscillations and wave-like transport phenomena, with potential applications in high-frequency electronic devices.

Contribution

It introduces a novel hydrodynamic Turing instability in Dirac fluids, revealing intrinsic, disorder-independent self-oscillatory transport near charge neutrality.

Findings

Instability causes a transition to oscillatory flow with spatial modulation.

Electromagnetic emission occurs at tunable gigahertz frequencies.

The mechanism is intrinsic and analogous to Kapitsa roll waves.

Abstract

We predict hydrodynamic Turing instability of current-carrying Dirac electron fluids that drives spontaneous self-oscillatory transport. The instability arises near charge neutrality, where carrier kinetics make current dissipation strongly density dependent. Above a critical drift velocity, a uniform electronic flow becomes unstable and undergoes a dynamical transition to a state with coupled spatial modulation and temporal oscillations--an electronic analogue of Kapitsa roll waves in viscous films. The transition exhibits two clear signatures: a nonanalytic, second-order-like onset in the time-averaged current and narrow-band electromagnetic emission at a tunable washboard frequency $f=u/\lambda$. Although reminiscent of sliding charge-density waves, the mechanism is intrinsic and disorder independent. Owing to the small effective mass of Dirac carriers, hydrodynamic time scales translate into emission frequencies in the tens to hundreds of gigahertz range, establishing Dirac materials as a platform for high-frequency self-oscillatory electron hydrodynamics.