Turing instability and current-driven self-sustained waves in Dirac fluids

Hydrodynamic instability of a steady flow in thin viscous films flowing down an incline can result in self-sustained running waves, known as Kapitsa roll waves. This talk will describe a prediction of current-driven runing waves for Dirac materials such as graphene monolayers and multilayers, where electron–hole scattering in Dirac plasma near charge neutrality renders momentum relaxation rate highly sensitive to carrier density. Spatial and temporal oscillations arise through a second-order transition once the flow velocity u exceeds a critical value. Experimentally observable signatures of this behavior include: an abrupt increase in time-averaged current at the instability threshold and narrow-band emission at the characteristic “washboard” frequency f=u/λ where λ is modulation wavelength. This behavior parallels the Lee-Fukuyama-Rice description of AC and DC conductivity in sliding charge-density waves, albeit arising from a totally different, intrinsic mechanism unrelated to disorder. Estimates suggest that the emission frequency f, tunable by current, spans a broad range, highlighting Dirac bands as a promising platform for exploring high-frequency dynamics in electron fluids.