Direct measurement of critical exponents in the quantum Hall regime

We have studied the magnetoresistance of AlGaAs/GaAs-heterojunctions at millikelvin temperatures in small Hall bar and Corbino geometries with different sizes. Below a characteristic temperature T_c which increases with decreasing sample width, the phase-breaking length L_in is larger than the sample size. Under these conditions the half width ΔB of the longitudinal magnetoresistance no longer depends upon temperature but only upon size. By varying the size it is thus possible to directly investigate the localization transition in the integer quantum Hall regime and to measure the critical exponent v of the localization length ξ α |B - B_c|^-v. Our results show a universal behaviour in the three lowest Landau levels. This is in agreement w universality statement of the field-theoretic approach to the metal-insulator transition in the quantum Hall effect. By studying the characteristic temperature T_c for different widths, the temperature exponent p 2 of the inelastic scattering length can also be measured.