Correlated Electron Transport in One-dimensional Channels

一维通道中的相关电子输运-本项目的目标是建立一个理论结构，在该结构中处理具有相互作用电子的系统的量子输运，特别是在门控半导体异质结构中形成的窄通道。电子之间的库仑排斥在低电子密度下变得至关重要，导致远程相互作用和相关态。我们将研究两个强相关电子系统的模型。在第一个模型中，在反转层内形成通道的静电势的波动被认为比电子-电子相互作用小得多。第二个模型将考虑电势的强烈波动和由此形成的几乎孤立的量子点。这些模型将与实验结果进行比较。半导体结构制造的最新进展，包括电子束光刻和相邻表面上的MBE生长，使得亚微米尺度上量子输运的系统实验研究成为可能。现有的理论准确地描述了电子在狭窄通道中移动时散射很少的情况，以及相反的情况，电子被紧紧地冻结在原地。然而，存在一种中间状态，通过改变电子密度，单个样品可以从金属变为绝缘体。这种更有趣的状态不能用传统模型来处理，因为它们没有适当地包括电子-电子相互作用。本研究项目建议为这种中间过渡制度建立模型。这样的理解是非常重要的，因为这类效应已经被提出作为下一代超小型电子设备的基础。

Correlated Electron Transport in One-Dimensional Channels - The object of this project is to build a theoretical structure within which to treat quantum transport for a system with interacting electrons, in particular for narrow channels formed in gated semiconductor heterostructures. Coulomb repulsion between electrons becomes crucially important at low electron density, resulting in long-range interactions and correlated states. Two models for a strongly correlated system of electrons will be investigated. In the first model fluctuations of the electrostatic potential that forms the channel within the inversion layer is taken as much smaller than the electron-electron interaction. The second model will take account of strong fluctuations in the potential and the resulting formation of almost isolated quantum dots. These models will be compared with experimental results. %%% Recent progress in fabrication of semiconductor structures, including electron beam lithography and MBE growth on vicinal surfaces, has allowed the systematic experimental study of quantum transport on submicron length scales. Existing theories accurately describe the case where the electrons in a narrow channel move with very little scattering, and the opposite case where the electrons are frozen tightly in place. There is, however and intermediate regime where a single sample can be changed from a metal to an insulator simply by changing the electron density. This much more interesting regime cannot be treated using conventional models, because they do not include electron-electron interactions properly. This research project proposes to develop models for this intermediate transition regime. Such understanding is quite important, as this class of effects have been proposed as the basis for the next generation of ultra-small electronic devices.