SCALING BEHAVIOR OF THE LONGITUDINAL AND HALL RESISTIVITIES IN INDIUMFILMS

We have made simultaneous measurements of the longitudinal rho(xx) and Hall rho(xy) resistivities for granular films of indium with differen t thicknesses ((t) over bar = 12, 20, and 60 nm) and the normal-state resistivities (rho(xxn) = 2-5x10(-5) Omega m) at temperatures T down t o 0.5 K and in fields B up to 7 T. A striking scaling behavior express ed as rho(xy)(T)=A rho(xx)(T)(beta) has been observed for all the film s studied irrespective of (t) over bar and rho(xxn) at fixed fields wh ich are not close to a critical field B-C. In the mixed state (B<B-C a nd T<T-C, where T-C is the transition temperature), the coefficient A and exponent beta (=2-3) are nearly independent of the field strength B and the film thickness (t) over bar. In the vicinity of the field-dr iven superconductor-insulator transition, we have found the unusual in sulating region B-xxC<B<B-xyC, where B-xxC and B-xyC represent critica l fields determined by rho(xx) and rho(xy), respectively, which tends to grow with increasing rho(xxn) and/or decreasing (t) over bar, This region is similar to one found previously by Paalanen, Hebard, and Rue l in amorphous InOx thin films, and the present result is consistent w ith their notion that the insulating region corresponds to the Bose-gl ass insulator.