Universal scaling of Hall resistivity in clean and moderately clean limits for Hg- and Tl-based superconductors

The mixed-state Hall resistivity and the longitudinal resistivity in HgBa_{2}CaCu_{2}O_{6}, HgBa_{2}Ca_{2}Cu_{3}O_{8}, and Tl_{2}Ba_{2}CaCu_{2}O_{8} thin films have been investigated as functions of the magnetic field up to 18 T. We observe the universal scaling behavior between \rho_{xy} and \rho_{xx} in the regions of the clean and the moderately clean limit. The scaling exponent \beta is 1.9 in the clean limit at high field and low temperature whereas \beta is 1.0 in the moderately clean limit at low field and high temperature, consistent with a theory based on the midgap states in the vortex cores. This finding implies that the Hall conductivity is also universal in Hg- and Tl-based superconductors.