Theoretical Problems in Condensed Matter and Statistical Physics

该奖项支持理论研究和教育的重点是系统，其中传导电子被强烈地限制在一个或多个方向。研究工作的动机是实验，包括各种有趣的现象。除了增进理解之外，这项研究的一个结果是推进理论技术：纳米级半导体器件，即双量子点，可以用来捕获一对传导电子，并通过按规定顺序向相邻的门施加电势来操纵它们的自旋。电子自旋与宿主材料中的核自旋相互作用，可以用来操纵这些自旋的极化。最近的实验产生了一些相当惊人的结果，这将是本研究的重点之一。PI旨在促进对这种耦合系统的非平衡动力学的理解，这是一项重大挑战，可能具有实际和基本的后果。二维电子系统，如场效应晶体管，在低温强磁场中表现出非常丰富的行为，包括一系列被称为量子霍尔效应的显著现象。当系统处于量子化霍尔态时，它可以沿着样品边缘携带电流，几乎没有能量损失。然而，如果样品中有一个足够窄的收缩，电子可以从一个边缘隧穿到另一个边缘，导致电阻。两个或两个以上的收缩会导致电阻快速振荡，作为磁场强度或施加在样品上的绝缘栅极上的电压的函数。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(？库仑封锁？)或者两者的结合。该项目旨在理清这些效应在现有和未来设备中的重要性。对这些实验的分析将告诉我们真实样品中边缘状态的性质以及量子霍尔系统的基本物理。研究还将集中在振荡上，振荡被认为是源-漏电压的函数，以及个别收缩的电流-电压特性。另一组项目将集中于应用微波辐射引起的明显零电阻状态，这已经在磁场的中间值的二维电子系统中看到。最近一项使用圆极化辐射的实验发现，微波效应与圆极化的符号完全无关，这与所有理论预测相反。该项目将试图理解这一点，以及其他令人困惑的观察结果。该项目还将探索测试预测的设计，即电子密度的不均匀性可以在零电阻状态下引起局部静电势的随时间振荡。最后，PI的目标是分析实验，在这些实验中，电子在控制动量的情况下隧穿到非常薄的？量子线吗?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，包括由于电子-电子相互作用的集体效应，提供重要的见解。该奖项支持理论研究和教育，包括凝聚态和统计物理中的各种现象。本研究的重点是在系统中出现的现象，其中传导电子被强烈地限制在一个或多个维度。PI的目的是解释现有实验中令人困惑的结果，这些实验涉及到非常大的分子大小的原子结构，因此纳米结构？介于材料和电子器件之间，当电子被限制在半导体结构内的一个平面上，并暴露在垂直于平面的非常高的磁场中，就会产生物质的电子态，即量子霍尔态。所有这些实验都探索了一些基本有趣的现象，在这些现象中，电子的波状性质起着至关重要的作用。像这样的现象出现了，随着电子电路元件的尺寸以摩尔的速度缩小到更小的尺寸，对它们的理解变得越来越重要。年代法律。除了推动我们周围世界的基础知识的重要作用外，这项研究还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.