  The intrinsic anomalous Hall effect is one of the most exciting
manifestations of the geometric properties of the electronic wave-function.
Here, we predict that the electronic wave-function's geometric nature also
gives rise to a purely quantum mechanical, {\it intrinsic} (scattering
time-independent) component of the Hall conductivities in the presence of a
magnetic field. We show that the orbital magnetic moment and the anomalous Hall
velocity combine to generate a scattering time-independent contribution to the
Hall effect, in addition to the Lorentz force induced scattering time-dependent
`classical' Hall effect. This dissipation-less Hall effect also manifests in
the thermo-electric and thermal conductivities and is dominant near the band
edges and band-crossings. It gives rise to negative magneto-resistance and it
also leads to an underestimation in the charge carrier density measured in Hall
experiments.
