Turbulent hydrodynamics in strongly correlated Kagome metals

TL;DR

This paper proposes Kagome metals, especially Scandium Herbertsmithite, as promising platforms for studying viscous electron fluids and turbulence, using holography to estimate their fluid properties and suggesting experimental feasibility.

Contribution

It introduces Kagome systems as superior platforms over graphene for exploring viscous electron fluids and turbulence, with holographic estimates of fluid properties.

Findings

Enhanced Coulomb interactions in Sc-Herbertsmithite compared to graphene.

Holographic estimates suggest lower shear viscosity to entropy ratio in Sc-Herbertsmithite.

Turbulent flow regimes are experimentally accessible in these materials.

Abstract

A current challenge in condensed matter physics is the realization of strongly correlated, viscous electron fluids. These fluids are not amenable to the perturbative methods of Fermi liquid theory, but can be described by holography, that is, by mapping them onto a weakly curved gravitational theory via gauge/gravity duality. The canonical system considered for realizations has been graphene, which possesses Dirac dispersions at low energies as well as significant Coulomb interactions between the electrons. In this work, we show that Kagome systems with electron fillings adjusted to the Dirac nodes of their band structure provide a much more compelling platform for realizations of viscous electron fluids, including non-linear effects such as turbulence. In particular, we find that in stoichiometric Scandium (Sc) Herbertsmithite, the fine-structure constant, which measures the effective Coulomb interaction and hence reflects the strength of the correlations, is enhanced by a factor of about 3.2 as compared to graphene, due to orbital hybridization. We employ holography to estimate the ratio of the shear viscosity over the entropy density in Sc-Herbertsmithite, and find it about three times smaller than in graphene. These findings put, for the first time, the turbulent flow regime described by holography within the reach of experiments.