Study of Tunneling Phenomena and Electron Correlation Effects on Transport in a Very Small Semiconductor

整数量子霍尔效应（QHE）和一维安德森局域化（AL）限制了一种更普遍现象的特殊情况，定向局域化（DL），预测会发生在被称为“量子轨道”（QRR）的无序一维波导中。我们研究了Kang等人最近对二维电子系统边缘之间电子转移的测量结果，并确定了QRR的第一个实验证据，但到目前为止完全是理论上的，统一了QHE和al的DL制度。我们首先阐明了无序如何影响电子通过势垒的转移。我们已经用递归格林函数技术做了计算机模拟。我们考虑了一个额外的光滑随机电位系统，该系统模拟了电子与邻近2DEG的掺杂层中的供体离子的库仑相互作用。发现透射峰足够宽，可以解释所观察到的电导峰的持久性。这一结果与数据中没有自旋特征是一致的。还解释了峰结构的温度依赖性。为了进一步探讨这一点，我们对边缘通道能量进行了自洽哈特里计算，在平均场近似中处理无序的影响。我们计算的边缘通道交叉点所预测的隧道最大值的位置与观测到的差分电导峰的位置在数量上是一致的。我们还提出了一种简单的测量方法，它应该能够明确地解决自旋在这个系统中所起作用的重要问题。

The integer quantum Hall effect (QHE) and one-dimensional Anderson localization (AL) are limiting special cases of a more general phenomenon, directed localization (DL), predicted to occur in disordered one-dimensional wave guides called "quantum railroads" (QRR). We have investigated the results of recent measurements by Kang et al. of electron transfer between edges of two-dimensional electron systems and identify the first experimental evidence of QRR's in the general, but until now entirely theoretical, DL regime that unifies the QHE and AL.We have begun by clarifying how disorder affects electron transfer through the barrier. We have done our computer simulations using a recursive Green's function technique. We consider the system with an additional smooth random potential that models the electron Coulomb interaction with donor ions in the doped layer adjacent to the 2DEG's. The transmission peak is found to be sufficiently broad to explain the observed persistence of the conductance peaks. This results are consistent with the absence of features of spin in the data. Temperature dependence of the peak structure is also explained.To explore this further we performed self-consistent Hartree calculations of the edge channel energies, treating the effects of disorder in a mean-field approximation. The locations of the tunneling maxima predicted by our calculations of the edge channel crossings are in quantitative agreement with the observed positions of the differential conductance peaks.We have also proposed a simple measurement that should be able to settle unambiguously important issue of the role that spin plays in this system.