# Emission of plasmons by drifting Dirac electrons: where hydrodynamics matters

## TL;DR

This paper demonstrates that drifting Dirac electrons in hydrodynamic regimes can emit plasmons via Cerenkov radiation, with the effect characterized through analytical conductivity models and instability growth rates in graphene-based setups.

## Contribution

It reveals high-frequency hydrodynamic Cerenkov plasmon emission in Dirac materials and provides analytical tools to characterize this phenomenon across the hydrodynamic-to-ballistic transition.

## Key findings

- Cerenkov emission occurs only in the hydrodynamic regime due to reduced plasmon velocity.
- Analytical high-frequency non-local conductivity across the crossover is derived.
- Hydrodynamic plasmon instabilities are shown to grow in specific graphene configurations.

## Abstract

Direct current in clean semiconductors and metals was recently shown to obey the laws of hydrodynamics in a broad range of temperatures and sample dimensions. However, the determination of frequency window for hydrodynamic phenomena remains challenging. Here, we reveal a phenomenon being a hallmark of high-frequency hydrodynamic transport, the Cerenkov emission of plasmons by drifting Dirac electrons. The effect appears in hydrodynamic regime only due to reduction of plasmon velocity by electron-electron collisions below the velocity of carrier drift. To characterize the Cerenkov effect quantitatively, we analytically find the high-frequency non-local conductivity of drifting Dirac electrons across the hydrodynamic-to-ballistic crossover. We find the growth rates of hydrodynamic plasmon instabilities in two experimentally relevant setups: parallel graphene layers and graphene covered by subwavelength grating, further showing their absence in ballistic regime. We argue that the possibility of Cerenkov emission is linked to singular structure of non-local conductivity of Dirac materials and is independent on specific dielectric environment.