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We studied the Hall effect in a T128a2CaCu20& epitaxial film and in an YBa2Cu307 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 T12BaqCaCuqOs and negative for YBa2Cu&07). 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. The Hall effect in high-T, superconductors in the mixed state is a subject of great recent interest. The data on the Hall resistivity show an unusual sign change in the vicinity of the transition temperature T, [1 -9] which has also been observed in conventional superconductors [7,10]. Another issue that has attracted special attention is the scaling dependence between the Hall and longitudinal resistivities, p~a nd p, respectively, in the pinned regime: p,~-p~, as first observed by Luo et al. [11]in epitaxial YBa2Cu307 films (P = 1.7~0.2) and by one of us [12] in Bi2Sr2CaCu20s single crystals (p = 2~0.1) (see also Refs. [13] and [14]). Vinokur et al. [15] have shown that the scaling law with p = 2 is a universal feature of any vortex state with disorder-dominated dynamics.It is important to note that the main result of theory [15] is stronger than just to say that p should equal 2 in the pinned regime. The conclusion about the scaling law is a consequence of the more general statement that the Hall conductivity does not depend on the pinning strength. This statement has not yet been verified directly by experiment.It is, in fact, the purpose of the present Letter. We enhanced pinning in an YBa2Cu307 single crystal and in a c-axis-oriented T12Ba2CaCu20& film by means of inclusions of columnar defects induced by high energy Pb ion irradiation.The irradiation dose (see below) was chosen to satisfy two conflicting conditions: First, the transition temperature and the normal-state p~a nd p should not be substantially modified by radiation damage and second, pinning should be enhanced due to the irradiationinduced defects. While the mixed-state longitudinal and Hall resistivities drastically decreased in magnitude after the irradiation, the Hall conductivity of both compounds remained unchanged within experimental accuracy. A good quality twinned YBa2Cu307 single crystal was grown using the standard Aux method. The sample was a plate of typical dimensions 1 X 1 X 0.03 mm3. Good electrical contacts (below 1 0) were made by sticking Pt wires with silver paste followed by annealing at 300'C in room atmosphere for 1 h. The 300-nm-thick c-axis oriented Tl~Ba2CaCu20q film was that used in our previous work [16]. A 3.5 X 0.75 mm2 strip with gold cov...

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