# Kelvin-Helmholtz instability of the Dirac fluid of charge carriers on graphene

## TL;DR

This paper provides numerical evidence of Kelvin-Helmholtz instability in the Dirac fluid of electrons in graphene, proposing experimental detection methods and developing a specialized lattice Boltzmann simulation technique.

## Contribution

It introduces a novel numerical approach to simulate the instability in graphene's electron fluid and suggests experimental setups for its detection.

## Key findings

- Kelvin-Helmholtz instability occurs in graphene's Dirac fluid under certain conditions.
- The instability can be detected via electric potential differences across an obstacle.
- Whirlpools similar to previous observations are formed due to the instability.

## Abstract

We provide numerical evidence that a Kelvin-Helmholtz instability occurs in the Dirac fluid of electrons in graphene and can be detected in current experiments. This instability appears for electrons in the viscous regime passing though a micrometer-scale obstacle and affects measurements on the time scale of nanoseconds. A possible realization with a needle-shaped obstacle is proposed to produce and detect this instability by measuring the electric potential difference between contact points located before and after the obstacle. We also show that, for our setup, the Kelvin-Helmholtz instability leads to the formation of whirlpools similar to the ones reported in Bandurin et al. [Science 351, 1055 (2016)]. To perform the simulations, we develop a lattice Boltzmann method able to recover the full dissipation in a fluid of massless particles.