Mixed-State Hall Conductivity in High-TcSuperconductors: Direct Evidence of Its Independence on Disorder

We studied the Hall effect in a ${\mathrm{Tl}}_2{\mathrm{Ba}}_2{\mathrm{CaCu}}_2{O}_8$ epitaxial film and in an ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_7$ single crystal in the mixed state before and after irradiation with high energy Pb ions. Pinning enhancement due to irradiation-induced columnar defects leads to the decrease in magnitude of the longitudinal and Hall resistivities, but does not modify the behavior of the Hall conductivity. This result is valid independent of the sign of the Hall effect in the pinned region (positive for ${\mathrm{Tl}}_2{\mathrm{Ba}}_2{\mathrm{CaCu}}_2{O}_8$ and negative for ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_7$). The present work proves straightforwardly that the mixed-state Hall conductivity does not depend on the pinning strength, in agreement with theory. This result is a dual analog of the behavior of 2D electronic systems where the Hall resistivity remains unaffected by disorder.