Transport Through Semiconductor Nanostructures

0086509 Brouwer该基金支持介观体系中半导体量子点传输的理论研究。 所考虑的系统足够小，量子干涉和电子的有限停留时间起着重要作用，而它们足够大，并且具有不规则的形状，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）来描述样本或样本系综。研究包括两个部分：时间相关的传输和通过量子点的共振和非共振路径的干涉。 这两个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表现出来。资助的第一部分围绕最近在实验上实现的绝热量子电子泵。 这个想法是，如果（量子力学）系统的任何两个参数发生变化，直流电流将流过它。在实验中，变化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具有量子干涉性质，因此称为量子泵浦。 电流的方向是随机的，由点的微观细节决定。 实验的基本方面可以从一个简单的散射矩阵公式来理解。 这里要做的研究旨在提高我们对实验的理解（失相的影响），以及性质的预测（电压和电流之间的关系，这似乎不是由点的电导给出的），通过对散射矩阵公式的更详细的分析和扩展，以及通过电子交互进入新的方向，（库仑阻塞）转化为时间的形式主义-第二部分研究了量子点中直接传输路径和共振路径的干涉。 这种干涉在通过点的传输中引起法诺共振。 最近已经观察到Fano共振，并且通过共振宽度和复Fano参数q来描述。 谐振宽度和q在谐振之间随机变化。 本研究的目的是计算一个混沌量子点的q分布。 进一步可能的活动包括研究库仑阻塞的相互作用和相互联系，直接传输路径，退相和近藤效应，这些都发生在同一个系统中。该基金支持介观体系中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。 所考虑的系统足够小，量子干涉和电子的有限停留时间起着重要作用，而它们足够大，并且具有不规则的形状，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）来描述样本或样本系综。研究包括两个部分：时间相关的传输，以及通过量子点的共振和非共振路径的干涉。 这两个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表现出来。 虽然这项研究具有基础科学性质，但其结果也会引起那些对构建纳米级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.***