Dynamo Effect and Turbulence in Hydrodynamic Weyl Metals

TL;DR

This paper explores the potential for observing the dynamo effect in hydrodynamic Weyl semimetals, deriving relevant equations, estimating key parameters, and showing how the chiral anomaly influences dynamo thresholds.

Contribution

It introduces a theoretical framework for realizing the dynamo effect in solid-state Weyl semimetals, expanding experimental possibilities beyond traditional fluids.

Findings

Hydrodynamic Weyl semimetals can achieve large magnetic Reynolds numbers.

The chiral anomaly reduces the threshold for dynamo instability.

Derived magneto-hydrodynamic equations for Weyl electron-hole plasma.

Abstract

The dynamo effect is a class of macroscopic phenomena responsible for generation and maintaining magnetic fields in astrophysical bodies. It hinges on hydrodynamic three-dimensional motion of conducting gases and plasmas that achieve high hydrodynamic and/or magnetic Reynolds numbers due to large length scales involved. The existing laboratory experiments modeling dynamos are challenging and involve large apparatuses containing conducting fluids subject to fast helical flows. Here we propose that electronic solid-state materials -- in particular, hydrodynamic metals -- may serve as an alternative platform to observe some aspects of the dynamo effect. Motivated by recent experimental developments, this paper focuses on hydrodynamic Weyl semimetals, where the dominant scattering mechanism is due to interactions. We derive Navier-Stokes equations along with equations of magneto-hydrodynamics that describe transport of Weyl electron-hole plasma appropriate in this regime. We estimate the hydrodynamic and magnetic Reynolds numbers for this system. The latter is a key figure of merit of the dynamo mechanism. We show that it can be relatively large to enable observation of the dynamo-induced magnetic field bootstrap in experiment. Finally, we generalize the simplest dynamo instability model -- Ponomarenko dynamo -- to the case of a hydrodynamic Weyl semimetal and show that the chiral anomaly term reduces the threshold magnetic Reynolds number for the dynamo instability.