Current Distribution in the Quantum Hall Effect

在分布磁场中测量了低迁移率和高迁移率GaAs/AlGaAs异质结中相邻量子霍尔平台之间过渡区的霍尔电阻随温度和电流的变化关系。随着温度或电流的增加，相邻量子霍尔平台之间的过渡区向高磁场方向移动。我们用Bi_2Sr_2CaCu_2O_（8+ δ）高温超导体单晶片制作了一个分布磁场。使用多探头霍尔装置测量磁场分布轮廓。在适当的电流分布下，结合测量磁场的计算结果再现了过渡区位移随温度和电流的变化关系。结果表明，在低温（电流）下，电流分布集中在样品边缘附近，随着温度（电流）的升高，电流分布向体区扩展，在高迁移率样品中，电子自旋向上和自旋向下时的朗道能级随温度的变化规律不同.这是首次观察到整数量子霍尔效应是自旋相关的。

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.