Topological Fermi liquids from Coulomb interactions in the doped   Honeycomb lattice
  We get an anomalous Hall metallic state in the Honeycomb lattice with nearest neighbors only arising as a spontaneously broken symmetry state from a local nearest neighbor Coulomb interaction V . The key ingredient is to enlarge the unit cell to host six atoms that permits Kekul\'e distortions and supports self-consistent currents creating non trivial magnetic configurations with total zero flux. We find within a variational mean field approach a metallic phase with broken time reversal symmetry (T) very close in parameter space to a Pomeranchuk instability. Within the T broken region the predominant configuration is an anomalous Hall phase with non zero Hall conductivity, a realization of a topological Fermi liquid. A T broken phase with zero Hall conductivity is stable in a small region of the parameter space for lower values of V . 
Eduardo V. Castro, Adolfo G. Grushin, Bel\'en Valenzuela, Mar\'ia A.   H. Vozmediano, Alberto Cortijo and Fernando de Juan
cond-mat.str-el cond-mat.other