Statistical fluxes and the sodium cobaltate Curie-Weiss metal

A central pursuit in the study of quantum matter is whether non Fermi liquid states exist, as invoked in trying to explain e.g. high-$T_{c}$ superconductivity. A quite different context is the search for thermodynamic materials in energy applications, which require at the same time a very large thermopower and a low resistivity. Here we predict a new state of matter that descends from a strongly interacting microscopy described by a t-J model on a triangular lattice. Due to the altered role of quantum statistics the spins are ``localized'' in statistical Landau orbits, while the charge carriers form a Bose metal that feels the spins through random gauge fields. In contrast to the Fermi-liquid state, this state naturally exhibits a Curie-Weiss susceptibility, large thermopower, and linear-temperature resistivity, explaining the physics of \textrm{Na}$_{x}$\textrm {CoO}$_{2}$ at $x>0.5.$ A ``smoking gun'' prediction for neutron scattering is presented.