Electrical Conductivity in Narrow Energy Bands

The electrical conductivity for a system of electrons described by the single-band Hubbard Hamiltonian is studied. An expression for the electrical conductivity that is applicable in the narrow-band regime, i.e., the bandwidth $\Delta$, much smaller than intra-atomic Coulomb repulsion $I$ is derived. It is shown that the conductivity vanishes at $T=0\mathrm{}$ to first order in $\frac{\Delta }{I}$ for one electron per atomic site. For the non-half-filled-band case, the degeneracy of the (atomic limit) ground-state wave function plays a crucial role in yielding a nonzero value for the conductivity. The theory is used to analyze the experimental data in Li-doped NiO. It is demonstrated how, as a consequence of this theory, the contribution to the conductivity from the narrow $3d^8$ band is suppressed in the total conductivity, contrary to an ordinary band-theory approach to the transport properties of this band.