Black holes meet condensed matter physics

Progress in science may originate from an original combination of ideas from seemingly very different areas of research. An example of this is given by a recent joint publication in the open-source journal Nature Communications by the groups of Johanna Erdmenger and Ronny Thomale, together with Tim Wehling and Erik van Loon from Bremen University.  In this paper, theoretical methods originating from approaches to quantum gravity are used to calculate transport properties of electrons in quantum materials. This is combined with a proposal for a new material that may display these properties.

A current challenge in condensed matter physics is the realization of strongly coupled, viscous electron fluids. Standard methods such as Fermi liquid theory are not applicable in the strongly coupled regime.  The authors  use the concept of duality, by which a strongly coupled system is equivalently described by  a gravity theory involving a black hole. It was previously predicted using these methods that the ratio of shear viscosity over entropy density  must be very small in strongly coupled systems. In the new publication, the authors provide an extrapolation of this ratio  to intermediate coupling values. Moreover, they propose a new material, Scandium-substituted Herbertsmithite, as a promising candidate to realize viscous hydrodynamic behaviour of electron flows in this coupling regime. This proposed material is based on a hexagonal Kagome lattice structure and the Fermi surface is located exactly at the Dirac point where different electron bands touch, mimicking a relativistic dispersion relation. The effective electron coupling in Scandium-Herbertsmithite is found to be a factor 3.2 larger than in graphene, which at present is one of the most used materials to investigate electron fluids. This renders the Reynolds number sufficiently large, such as to bring even turbulence within reach.