Integer Quantum Hall Effect in the Presence of Elastic Backscattering of Electrons

我们小组三年前发现的边缘态电子的非平衡群体，推动了本研究项目。自发现以来，积分量子霍尔效应的一个新的观点出现，在理论理解和实验成果上都取得了显著的发展。本研究项目在研究领域快速、爆炸性增长的各个阶段都做出了实质性的贡献。1)发现了由于非平衡电子分布引起的量子化霍尔电阻的显著偏差。2)理解了电接触在产生和检测非平衡电子分布时所起的作用及其一般公式。3)定量分析了在积分量子霍尔效应的精确测量中接触的影响。4)边态间电子散射的分析及其对温度依赖性的理解。5)与非平衡布居有关的非线性输运效应的分析：特别是对边缘态中反转电子布居的预测。6)提出了一个处理标准霍尔棒样品中非平衡布居的导体的一般模型，并用该模型对实验结果进行了定量解释。7)提出了一种确定整数量子霍尔效应区相干态长度的可能实验。综上所述，本研究项目显著地提高了对强磁场下二维电子气中输运性质的理解。

A nonequilibrium population of electrons in edge states, discovered by our group three years ago, motivated the present research project. Since the discovery, a novel view of integral quantum Hall effects emerged to initiate remarkable developments both in theoretical understanding and in experimental achievements of integral quantum Hall effects. The present research project has made substantial contribution on each stage of the rapid and explosive growth of the research field. The achievements are summarized below :1) Discovery of remarkable deviation of quantized Hall resistance due to nonequilibrium electron distribution.2) Understanding and its general formulation of the role played by electrical contacts -when producing and detecting nonequilibrium electron distribution.3) Quantitative analysis of the effects of contacts in the precision measurements of integral quantum Hall effects.4) Analysis of inter-edge-state electron scattering and the understanding of its dependence on temperature.5) Analysis of nonlinear transport effects associated with the nonequilibrium population : Particularly, a prediction of inverted electron population in edge states.6) Proposal of a general model of conductors that treats nonequilibrium population in standard Hall-bar samples, and the quantitative explanation of experimental results by the model.7) Proposal of a possible experiments to determine phasecoherence length in a regime of integer quantum Hall effects.To summarize, the present research project has achieved remarkably improved understanding of the transport properties in two dimensional electron gas at high magnetic fields.