The infrared Hall conductivity in optimally-doped BSCCO

he frequency dependence in the mid IR from 900 to 1100 cm$^{-1}$ and far IR at 84 cm$^{-1}$ and temperature dependence from 35 to 330 K of the normal state Hall transport is reported in single crystal, optimally doped Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$. The results show a nearly Drude behavior in the Hall conductivity $\sigma_{xy}$, which stands in contrast to the more complex extended Drude behavior for the longitudinal conductivity $\sigma_{xx}$. The mid IR Hall scattering rate increases linearly with temperature and has a small, positive, projected intercept of 200 cm$^{-1}$ at T=0. In contrast, the longitudinal scattering rate is much larger and exhibits very little temperature dependence. The spectral weight of $\sigma_{xy}$ is suppressed to 0.09 times the band value, whereas the spectral weight of $\sigma_{xx}$ is 0.33 times the band value. These disparate behaviors are consistent with calculations based on the fluctuation-exchange interaction when current vertex corrections are included.