From a spin liquid to a correlated Dirac metal

There is an interesting paper
Theoretical prediction of a strongly correlated Dirac metal 
 I. I. Mazin, Harald O. Jeschke, Frank Lechermann, Hunpyo Lee, Mario Fink, Ronny Thomale, Roser Valentí

The compound Herbertsmithite ZnCu3(OH)6Cl2 has attracted a lot of interest because it is a Mott insulator with a layered crystal structure where the Cu2+ ions (spin 1/2) are arranged in a kagome lattice.
There is some evidence both experimentally and theoretically that the ground state is a spin liquid.
[However, inevitably there are complications such as the role of impurities and the Dzyaloshinskii-Moriya interaction].

In this paper the authors replace the Zn2+ ions with (isoelectronic) Ga3+ ions. This means that in non-interacting electron picture the bands go from half filling (n=1) to two-third filling (n=4/3). This is of particular interest because for a tight-binding model on the kagome lattice there are symmetry protected Dirac points, just like in graphene, at this band filling.

There are subtle interlayer effects because the kagome layers order ABCABC....

This changes the three-dimensional Bravais lattice from hexagonal to rhombohedral and a doped system will have a Fermi surface like that below.

However, one needs to take into account the strong interactions associated with the localised Cu orbitals that lead to a Mott insulator at half filling. The authors use a range of theoretical techniques (rotationally invariant slave bosons, functional RG, Dynamical Cluster Approximation (DMFT)), to investigate instabilities in the associated Hubbard model.
They find a subtle competition between metallicity, charge ordering, ferromagnetism, and f-wave superconductivity.

Hopefully, someone will make this compound soon!

I thank Ben Powell for bringing the paper to my attention. He and Anthony Jacko recently considered an organometallic material with a rich band structure that interpolates between honeycomb and kagome.