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

TL;DR

This study reveals a universal scaling law between Hall and longitudinal resistivities in Hg- and Tl-based superconductors, consistent with theoretical models, across different cleanliness regimes and magnetic field conditions.

Contribution

It demonstrates universal scaling behavior of Hall resistivity in these superconductors, linking experimental results with vortex core midgap state theory.

Findings

Scaling exponent  is 1.9 in clean limit at high field

Scaling exponent  is 1.0 in moderately clean limit at low field

Hall conductivity shows universal behavior across different materials

Abstract

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.