The mid-infrared Hall effect in optimally-doped Bi$_{2}$Sr$_{2}$CaCu$_2$O$_{8+\delta}$

Heterodyne polarometry is used to measure the frequency dependence in the mid IR from 900 to 1100 cm$^-1$ and temperature dependence from 35 to 330 K of the normal state Hall transport in single crystal, optimally doped Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta}$. The results show a simple 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 $\gamma_{xy}$ increases linearly with temperature and has a small, positive, projected intercept at $T=0$. The longitudinal scatter rate, in contrast, is much larger and exhibits very little temperature dependnece. The Hall frequency indicates a carrier mass which is 6.7 times the band mass and which decrease slighly with increasing frequency. These disparate behaviors are consistent with calculations based on the fluctuation-exchange interaction using current vertex corrections (H Kontani, cond-mat/0507664).