Theoretical Problems in Condensed Matter and Statistical Physics

该奖项支持理论研究和教育，重点是传导电子被强烈限制在一个或多个方向的系统。这项研究工作的动机是实验，包括各种有趣的现象。除了增进理解，这项研究的一个结果是推进理论技术。纳米级半导体器件，被称为双量子点，可以用来捕获一对导电电子，并通过按规定的顺序向相邻的栅极施加电势来操纵它们的自旋。电子自旋与主体材料中的核自旋相互作用，并且可以用于操纵这些自旋的极化。最近的实验产生了一些相当令人惊讶的结果，这将是本研究的重点之一。PI寻求加深对这个耦合系统的非平衡动力学的理解，这是一个重大挑战，可能会产生实际和根本性的后果。二维电子系统，如场效应晶体管，在低温下的强磁场中表现出非常丰富的行为，包括一组被称为量子霍尔效应的显着现象。当系统处于量子化霍尔态时，它可以沿着样本边缘携带电流，几乎没有能量损失。然而，如果样品中有足够窄的收缩，电子可以从一个边缘隧穿到另一个边缘，导致电阻。两个或多个收缩可导致电阻作为施加到样品上的绝缘栅极的磁场强度或电压的函数而快速振荡。这种振荡可以源于量子力学干涉效应，电子-电子相互作用效应（？库仑阻塞？）或两者的组合。PI旨在整理出这些影响在现有和未来设备中的重要性。对这些实验的分析应该告诉我们关于真实的样品中边缘态的性质以及量子霍尔系统的基本物理。研究还将集中于已被视为源极-漏极电压的函数的振荡，以及个别收缩的电流-电压特性，另一组项目将集中于由外加微波辐射引起的表面上为零的电阻状态，这种状态已在中等磁场值的二维电子系统中观察到。最近的一个实验使用圆偏振辐射发现微波效应是完全独立的符号的圆偏振，与所有的理论预测。该项目将试图理解这一点，以及其他令人困惑的观察结果。该项目还将探讨设计用于测试的预测，在电子密度的不均匀性可以引起，在零电阻状态下，随时间变化的振荡，在当地的静电potential.Finally，PI的目的是分析实验中的电子隧道，控制动量，到一个非常薄的？量子线或者进入量子霍尔态的二维电子系统的边缘。这些实验应该对这些系统的物理学，包括电子-电子相互作用引起的集体效应，提供重要的见解。非技术性总结该奖项支持凝聚态物理和统计物理中各种现象的理论研究和教育。这项研究的重点是在传导电子被强烈限制在一个或多个维度的系统中出现的现象。PI的目的是解释令人费解的结果，从现有的实验，涉及结构的原子的大小非常大的分子，使？纳米结构？介于材料和电子器件之间，实验涉及物质的电子态，当电子被限制在半导体结构内的平面上并暴露于垂直于平面的非常高的磁场时，量子霍尔态。所有这些实验都从根本上探索了有趣的现象，其中电子的波动性质起着至关重要的作用。 随着电子电路元件的尺寸以摩尔？s定律。 除了推进我们周围世界的基础知识的重要作用，这项研究有助于新技术的知识基础，有助于保持电子技术的快速发展。

TECHNICAL SUMMARYThis award supports theoretical research and education focused on systems where conduction electrons are strongly confined in one or more directions. The research effort is motivated by experiment and encompasses a variety of intriguing phenomena. Apart from advancing understanding, a consequence of the research is to advance theoretical techniquesNanoscale semiconductor devices, known as double quantum dots, can be used to trap a pair of conduction electrons, and to manipulate their spins by applying electric potentials to adjacent gates in a prescribed sequence. The electron spins interact with nuclear spins in the host material, and can be used to manipulate the polarization of those spins. Recent experiments have produced some quite surprising results, which will be one focus of this research. The PI seeks to advance understanding of the non-equilibrium dynamics of this coupled system, a major challenge which could have practical as well as fundamental consequences. Two-dimensional electron systems, such as field effect transistors, exhibit very rich behavior in strong magnetic fields at low temperatures, including a remarkable set of phenomena known as the quantum Hall effects. When a system is in a quantized Hall state, it can carry electric currents along the sample edges, with almost no energy loss. However, if there is a sufficiently narrow constriction in the sample, electrons can tunnel from one edge to another, leading to electrical resistance. Two or more constrictions can lead to resistance that oscillates rapidly as a function of magnetic field strength or of voltages applied to insulated gates on the sample. Such oscillations can originate from quantum mechanical interference effects, from electron-electron interaction effects (?Coulomb blockade?) or a combination of the two. The PI aims to sort out the importance of these effects in existing and future devices. Analysis of these experiments should tell us about the nature of edge states in real samples as well as the fundamental physics of quantum Hall systems. Research will also focus on oscillations that have been seen as a function of source-drain voltage, and on the current-voltage characteristics of individual constrictions.Another set of projects will focus on the state of apparently zero electrical resistance induced by applied microwave radiation, which has been seen in two-dimensional electron systems at intermediate values of the magnetic field. A recent experiment using circularly polarized radiation found the microwave effect to be completely independent of the sign of the circular polarization, in contrast to all theoretical predictions. The project will try to understand this, as well as other puzzling observations. The project will also explore designs for testing a prediction that nonuniformity in the electron density can give rise, in the zero-resistance state, to time-dependent oscillations in the local electrostatic potential.Finally, the PI aims to analyze experiments in which an electron tunnels, with controlled momentum, into a very thin ?quantum wire? or into the edge of a two-dimensional electron system in a quantum Hall state. The experiments should give important insights into the physics of these systems, including collective effects due to electron-electron interactions.NON-TECHNICAL SUMARYThis award supports theoretical research and education that encompasses a variety of phenomena in condensed matter and statistical physics. This research is focused on phenomena that arise in systems where conduction electrons are strongly confined in one or more dimensions. The PI aims to explain puzzling results from existing experiments that involve structures of atoms the size of very large molecules so that the ?nanostructures? lie between being a material and an electronic device, and experiments involving electronic states of matter that arise when electrons are confined to a plane within a semiconductor structure and exposed to a very high magnetic field perpendicular to the plane, quantum Hall states. All these experiments probe fundamentally interesting phenomena in which the wave-like nature of electrons plays a crucial role. Phenomena like these appear and their understanding becomes increasingly important as the size of electronic circuit elements shrink to ever smaller dimensions at the pace of Moore?s law. Apart from the important role of advancing fundamental knowledge of the world around us, this research contributes to the intellectual foundations of new technologies that help to preserve the rapid advance of electronics technologies.