Current Distribution in the Quantum Hall Effect

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The temperature and the current dependence of the Hall resistance in a transition region between the adjacent quantum Hall plateaus has been measured in a distributed magnetic field using a low and a high mobility GaAs/AlGaAs heterostructures. A shift fo the transition region between the adjacent quantum Hall plateaus to higher magnetic field was observed when the temperature or the current was increased. We used a single crystal platelet of Bi_2Sr_2CaCu_2O_<8+delta> high temperatur superconductor to make a distributed magnetic field. The magnetic field distribution profile was measured using a multi-probe Hall device. Results of calculation assuming appropriate current distribution combined with the measured magnetic field have reproduced the temperature and the current dependence of the shift of the transition region. These results reveal that the current distribution is concentrated near the sample edge at low temperature (current) and spread out to the bulk region as the temperature (current) is increased.The results in the high mobility sample have shown a different temperature dependence between the Landau levels with the electron spin up and that with the spin down. This is the first observation that the integer quantum Hall effect is spin dependent.