Point-contact conductances at the quantum Hall transition
Point-contact conductances at the quantum Hall transition
复制标题
量子霍尔跃迁处的点接触电导
DOI：
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发表时间：
1998
期刊：
影响因子：
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通讯作者：
M. Zirnbauer
中科院分区：
文献类型：
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作者：
M. Janssen;Marcus Metzler;M. Zirnbauer
在Chalker-Coddington网络模型的基础上，对整数量子霍尔体系点接触电导的统计特性进行了数值和解析研究。在霍尔平台区的点接触电导反映了强烈的本地化的电子，而附近的平台过渡，他们表现出强烈的介观波动。通过将网络模型映射到具有GL（2|（2）对称性，并根据共形场论的规则，假定两点相关器，导出了临界态电导分布的显式表达式。只有一个自由参数，即典型电导的幂律指数。其数值计算为X_t = 0.640 +/- 0.009。预测的电导分布与数值结果吻合较好。当两个接触点之间的距离较大时，其分布可以用一个由X_t唯一决定的多重分形谱来描述。我们的研究结果表明，多重分形可以显示在适当的传输实验。
On the basis of the Chalker-Coddington network model, a numerical and analytical study is made of the statistics of point-contact conductances for systems in the integer quantum Hall regime. In the Hall plateau region the point-contact conductances reflect strong localization of the electrons, while near the plateau transition they exhibit strong mesoscopic fluctuations. By mapping the network model on a supersymmetric vertex model with GL(2|2) symmetry, and postulating a two-point correlator in keeping with the rules of conformal field theory, we derive an explicit expression for the distribution of conductances at criticality. There is only one free parameter, the power law exponent of the typical conductance. Its value is computed numerically to be X_t = 0.640 +/- 0.009. The predicted conductance distribution agrees well with the numerical data. For large distances between the two contacts, the distribution can be described by a multifractal spectrum solely determined by X_t. Our results demonstrate that multifractality can show up in appropriate transport experiments.