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

整数量子霍尔效应(QHE)和一维安德森定域化(AL)限制了一种更普遍的现象-定向定域化(DL)的特例，这种现象被预测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等人最近的测量结果。并确定了第一个实验证据的QRR的一般，但到目前为止完全理论，DL制度，统一的QHE和AL。我们已经开始澄清如何无序影响电子转移通过势垒。我们使用递归格林函数技术进行了计算机模拟。我们考虑了一个附加的光滑随机势，它模拟了电子库仑与施主离子在与2DEG相邻的掺杂层中的相互作用。透射峰足够宽，可以解释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。为了进一步探索这一点，我们对边缘通道能量进行了自洽的Hartree计算，并在平均场近似下处理无序效应。通过我们对边缘通道交叉的计算预测的隧道极大值的位置与观测到的微分电导峰值的位置是定量一致的。我们还提出了一个简单的测量方法，它应该能够明确地解决自旋在这个系统中所起的作用这一重要问题。

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.