Transport Through Semiconductor Nanostructures

这笔赠款支持介观条件下半导体量子点输运的理论研究。当量子干涉和电子的有限驻留时间足够大，并且形状不规则时，量子干涉和电子的有限驻留时间起着重要的作用，因此(经典)动力学是混沌的，需要使用统计方法，如随机矩阵理论来描述一个样本或一个样本系综。研究包括两个部分：依赖于时间的输运以及共振和非共振路径通过量子点的干涉。两部分的一个统一主题是混沌动力学、量子干涉和电子-电子相互作用的相互作用。研究的主要焦点是，在量子点中，电子-电子相互作用如何通过库仑阻塞和退相来表现出来。第一部分拨款集中在最近实验上实现的绝热量子电子泵。这个想法是，如果一个(量子力学)系统的任何两个参数发生变化，一个DC。电流会流过它。在实验中，可变的参数是控制量子点形状的栅极电压。在这种情况下，可以证明泵浦电流完全是量子干涉性质的，因此得名量子泵浦。电流的方向是随机的，由网点的微观细节设定。实验的基本方面可以从一个简单的散射矩阵公式中理解。通过对散射矩阵公式进行更详细的分析和扩展，以及将电子相互作用(库仑阻塞)引入含时输运的形式，旨在提高我们对实验(退相效应)的理解和对性质(电压和电流之间的关系，似乎不是由点的电导给出)的预测。研究的第二部分是关于通过量子点的直接传输和共振路径的干扰。这种干扰在通过网点的传输中引起Fano共振。最近观察到了Fano共振，并用一个共振宽度和一个复数Fano参数Q来描述。共振宽度和Q都是随机变化的。这项研究的目的是计算混沌量子点的Q分布。其他可能的活动包括研究库仑阻塞、直接传输路径、退相和近藤效应的相互作用和相互联系，这些都发生在同一个系统中。%这笔赠款支持介观区域内半导体量子点输运的理论研究。这一研究领域与当前对纳米技术的兴趣有关。当量子干涉和电子的有限驻留时间足够大，并且形状不规则时，量子干涉和电子的有限驻留时间起着重要的作用，因此(经典)动力学是混沌的，需要使用统计方法，如随机矩阵理论来描述一个样本或一个样本系综。研究包括两个部分：依赖于时间的输运，以及共振和非共振路径通过量子点的干涉。两部分的一个统一主题是混沌动力学、量子干涉和电子-电子相互作用的相互作用。这项研究的主要焦点是，在量子点中，电子-电子相互作用如何通过库仑阻塞和退相来表现出来。虽然这项研究是基础科学性质的，但其结果也将引起那些对构建纳米设备感兴趣的人的极大兴趣。

0086509BrouwerThis grant supports theoretical research on transport through semiconductor quantum dots in the mesoscopic regime. The systems under consideration are small enough that quantum interference and the finite dwell time of the electrons play an important role, while they are big enough, and with irregular shape, so that the (classical) dynamics is chaotic and statistical methods, such as random matrix theory, need to be used to describe a sample, or an ensemble of samples.The research consists of two parts: time-dependent transport and the interference of resonant and non-resonant paths through quantum dots. A unifying theme of both parts is the interplay of chaotic dynamics, quantum interference, and electron-electron interactions. The primary focus of the research is how, in quantum dots, electron-electron interactions manifest themselves through Coulomb blockade and dephasing.The first part of the grant is centered around the adiabatic quantum electron pump which has recently been realized experimentally. The idea is that if any two parameters of a (quantum mechanical) system are varied, a d.c. current will flow through it. In the experiment, the parameters that are varied are gate voltages that control the shape of the quantum dot. In this case, one can show that the pumped current is entirely of a quantum interference nature, hence the name quantum pump. The current flow is in a random direction, set by microscopic details of the dot. Basic aspects of the experiment can be understood from a simple scattering matrix formula. The research to be done here is aimed at improvement in our understanding of the experiment (effect of dephasing), and to prediction of properties (relationship between voltage and current, which appears not to be given by the dot's conductance), through a more detailed analysis and extension of the scattering matrix formula, as well as entering new directions by inclusion of electronic interactions (Coulomb blockade) into formalism for time-dependent transport.The second part of the research is about interference of direct transmitting and resonant paths through a quantum dot. This interference gives rise to Fano resonances in the transmission through the dot. Fano resonances have been observed recently and are described by a resonance width and by a complex Fano parameter q. Both the resonance width and q vary randomly from resonance to resonance. This research aims at a calculation of the distribution of q for a chaotic quantum dot. Further possible activities include the study of the interplay and mutual connection of Coulomb blockade, direct transmitting paths, dephasing, and the Kondo effect, which all occur in one and the same system.%%%This grant supports theoretical research on transport through semiconductor quantum dots in the mesoscopic regime. This area of research is related to the current interest in nanotechnology. The systems under consideration are small enough that quantum interference and the finite dwell time of the electrons play an important role, while they are big enough, and with irregular shape, so that the (classical) dynamics is chaotic and statistical methods, such as random matrix theory, need to be used to describe a sample, or an ensemble of samples.The research consists of two parts: time-dependent transport, and the interference of resonant and non-resonant paths through quantum dots. A unifying theme of both parts is the interplay of chaotic dynamics, quantum interference, and electron-electron interactions. The primary focus of the research is how, in quantum dots, electron-electron interactions manifest themselves through Coulomb blockade and dephasing. While the research is of a fundamental scientifc nature, the results will also be of great interest to those interested in constructing nanoscale devices.***