Hall conductivity in ${\mathrm{Tl}}_2$${\mathrm{Ba}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_8$ films in the mixed state

We present data on the Hall conductivity ${\mathrm{\sigma }}_{\mathit{x}\mathit{y}}$ in ${\mathrm{Tl}}_2$ ${\mathrm{Ba}}_2$ ${\mathrm{CaCu}}_2$ ${\mathrm{O}}_8$ thin films. It has been found that the Hall conductivity consists of two terms. The first one is inversely proportional to the magnetic field strength, in agreement with theories for motion of a single vortex. This term changes sign from negative near ${\mathit{T}}_{\mathit{c}}$ to a positive value at low temperatures. The second term is field independent and has been attributed to be due to the normal Hall effect in the vortex cores.