Theoretical Problems in Condensed Matter and Statistical Physics

技术总结该奖项支持专注于传导电子在一个或多个方向上受到强烈限制的系统的理论研究和教育。这项研究工作是以实验为动力的，包含了各种有趣的现象。除了加深理解，这项研究的一个结果是推进了理论技术--被称为双量子点的纳米级半导体器件可以用来捕获一对传导电子，并通过按规定的顺序向相邻的栅极施加电压来操纵它们的自旋。电子自旋与主体材料中的核自旋相互作用，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令人惊讶的结果，这将是本研究的重点之一。PI试图促进对这一耦合系统的非平衡动态的理解，这是一个可能具有实际和根本后果的重大挑战。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，包括一系列引人注目的被称为量子霍尔效应的现象。当系统处于量子化霍尔态时，它可以沿样本边缘携带电流，几乎没有能量损失。然而，如果样品中有足够窄的收缩，电子可以从一条边隧道到另一条边，导致电阻。两个或两个以上的收缩可以导致作为磁场强度或施加到样品上的绝缘栅的电压的函数而快速振荡的电阻。这种振荡可能源于量子力学干涉效应、电子-电子相互作用效应(库仑阻塞)。或者是两者的结合。PI旨在理清这些效应在现有和未来设备中的重要性。对这些实验的分析应该告诉我们真实样品中的边态的性质，以及量子霍尔系统的基本物理。研究还将集中在被视为源漏电压函数的振荡，以及单个收缩的电流-电压特性。另一组项目将集中在外加微波辐射引起的明显零电阻状态，这已经在磁场中间值的二维电子系统中看到。最近一项使用圆偏振辐射的实验发现，微波效应与圆偏振的符号完全无关，这与所有的理论预测相反。该项目将试图理解这一点，以及其他令人费解的观察结果。该项目还将探索用于测试这一预测的设计，该预测认为，在零阻状态下，电子密度的不均匀可以引起局部静电势随时间变化的振荡。最后，PI旨在分析在这些实验中，具有受控动量的电子通过隧道进入非常细的量子线？或者进入处于量子霍尔态的二维电子系统的边缘。这些实验应该为这些系统的物理提供重要的见解，包括电子-电子相互作用产生的集体效应。非技术总结该奖项支持涵盖凝聚态和统计物理中各种现象的理论研究和教育。这项研究集中在传导电子在一个或多个维度上受到强烈限制的系统中出现的现象。PI旨在解释现有实验中令人费解的结果，这些实验涉及非常大分子大小的原子结构，从而使纳米结构？介于作为一种材料和一种电子设备之间，以及涉及物质的电子态的实验，这种电子态是当电子被限制在半导体结构中的一个平面上并暴露在垂直于该平面的非常高的磁场-量子霍尔态-时产生的。所有这些实验都从根本上探索了一些有趣的现象，其中电子的波状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定律的速度缩小到越来越小的尺寸，这样的现象出现了，对它们的理解变得越来越重要。除了促进我们周围世界的基本知识的重要作用外，这项研究还为有助于保持电子技术快速进步的新技术的智力基础做出了贡献。

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.