  In recent experiments, unprecedentedly large values for the conductivity of
electrolytes through carbon nanotubes (CNTs) have been measured, possibly owing
to flow slip and a high pore surface charge density whose origin is still
unknown. By accounting for the coupling between the {quantum} CNT and the
{classical} electrolyte-filled pore capacitances, we study the case where a
gate voltage is applied to the CNT. The computed surface charge and
conductivity dependence on reservoir salt concentration and gate voltage are
intimately connected to the CNT electronic density of states. This approach
provides key insight into why metallic CNTs have larger conductivities than
semi-conducting ones.
