We predict a new state of matter in the triangular $t-J$ model in a high doping regime. 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 Na${}_x$CoO${}_2$ at $x>0.5.$ A “smoking gun” prediction for neutron scattering is presented.

• Received 5 September 2011

DOI:https://doi.org/10.1103/PhysRevB.84.113113