Probing Fractional Statistics and Correlated States in Cleaved-Edge Devices

* 非技术性摘要 * 当被限制在比我们所熟悉的三维空间更小的空间维度时，由电子与其他电子相互作用组成的系统的行为会发生巨大的变化。 例如，在二维世界中，将相互作用的电子置于非常强的磁场中会产生不寻常的物质，其中包含具有一小部分电子电荷的新实体。 此外，这些被称为“准粒子”的新实体既不像光的粒子（光子），也不像电子。 光子是玻色子，玻色子喜欢聚集，这使得制造激光器成为可能。 然而，电子喜欢避开彼此，导致了已知的固体（如导体、半导体和绝缘体）的量子力学行为。新的准粒子既不是玻色子也不是费米子，并且服从一种称为分数统计的新型量子统计行为。 使用专门创建的半导体器件，该项目将探测这些独特系统的导电特性。 一个相关的主题将是研究具有新型排序的新物质状态，这种排序与熟悉的排序（如自旋对齐）非常不同，这是铁磁性的原因。 了解这些新行为可能使我们能够设计新型超导体，并为更强大的量子计算机铺平道路，这些计算机对环境干扰的敏感性要低得多。 此外，非常窄的一维超导导线将被调查，以确定其鲁棒性，提供了一个更好的理解其潜在的应用程序作为超密集电路中的互连。 从事这些项目的研究生和本科生将接受最先进的半导体加工和超灵敏电气测量方面的培训，为他们在学术界或工业界的职业生涯做好准备。 同时，外展部分将向K-12学生介绍重要的概念，如电荷，电流，自旋，超导性和粒子统计。技术摘要 * 该计划旨在阐明相关电子系统在减少尺寸的不寻常属性。 这种系统是在半导体晶体的劈裂边缘的特殊装置中产生的。 新的属性，如分数带电准粒子的分数统计，和相关态的不寻常的潜在量子秩序的出现，将被调查。 在二维分数量子霍尔态中，测量从单个相干源注入到不同集电极的电流中的噪声的时间相关性，预计将产生分数统计的证据，介于三维系统中常见的玻色子和费米子统计之间，分别用于光子和电子。 或者，研究Aharonov-Bohm量子干涉调制的磁场周期可以揭示Pfronov分数量子霍尔态波函数中不寻常的拓扑量子序。 揭示这些性质有助于更好地理解一种被称为“任意子超导性”的新型超导性，并可能使未来实现拓扑量子计算，这是一种基本上不受退相干效应影响的方案。 此外，非常窄的一维超导导线将被调查，以探测新的量子相变的存在。 研究超窄超导导线的行为将有助于更好地理解其作为超密集电路互连线的潜在应用。 研究生和本科生将接受最先进的半导体加工和超灵敏电气测量方面的培训。 接受的培训将为他们在学术界或工业界的职业生涯做好准备。 同时，外展部分将向大学预科学生介绍量子力学和粒子统计等现代概念。

****NON-TECHNICAL ABSTRACT****The behavior of systems composed of electrons interacting with other electrons can change dramatically when confined to spatial dimensions less than the familiar three dimensions in which we live. For example, in a two-dimensional world, placing the interacting electrons in a very strong magnetic field creates unusual matter, which contains new entities with a fraction of the electron charge. Moreover these new entities, called "quasi-particles," behave neither as particles of light (photons) nor as electrons. Photons are bosons, and bosons like to aggregate, making it possible to build lasers. However, electrons like to avoid each other; leading to the known quantum-mechanical behaviors of solids such as conductors, semiconductors, and insulators. The new quasi-particles are neither bosons nor fermions, and obey a new type of quantum statistical behavior called fractional statistics. Using specially created semiconductor devices this project will probe the electrical conduction properties of these unique systems. A related topic will be the study of new states of matter with a new type of ordering, very different from familiar ordering such as the alignment of spins, responsible for the magnetism in iron. Understanding these new behaviors may enable us to design new types of superconductors, and pave the way to more robust quantum computers, which are much less sensitive to environmental interference. Additionally very narrow one-dimensional superconducting wires will be investigated to ascertain their robustness, providing a better understanding of their potential application as interconnects in ultra dense circuitry. Graduate and undergraduate students working on these projects will be trained in state-of-the-art semiconductor processing, and on ultra sensitive electrical measurements, to prepare them for careers in academia or industry. At the same time, the outreach component will introduce K-12 students to important concepts such as charge, current, spins, superconductivity, and statistics of particles.**** TECHNICAL ABSTRACT****This program seeks to elucidate unusual properties of correlated electronic systems in reduced dimensions. Such systems are created in special devices on the cleaved-edge of semiconductor crystals. The emergence of new properties, such as fractional statistics of fractionally-charged quasi-particles, and unusual underlying quantum orders of correlated states, will be investigated. In the two-dimensional fractional quantum Hall states, measuring the temporal correlation of the noise in the electrical currents injected into different collectors from a single coherent source is expected to yield evidence indicative of fractional statistics, intermediate between the familiar bosonic and fermionic statistic in three-dimensional systems for photons and electrons, respectively. Alternatively, studying the magnetic field period of the Aharonov-Bohm quantum interference modulation could reveal unusual topological quantum orders in the wave functions of the Pfaffian fractional quantum Hall states. Uncovering such properties helps bring a greater understanding of a new type of superconductivity termed "anyon superconductivity," and may enable future realization of topological quantum computation, a scheme largely free from decoherence effects. Additionally, very narrow one-dimensional superconducting wires will be investigated to probe the existence of new quantum phase transitions. Investigating the behaviors of ultra narrow superconducting wires will provide a better understanding for their potential application as interconnects in ultra dense circuitry. Graduate students and undergraduate students will be trained in state-of-the-art semiconductor processing and ultra sensitive electrical measurements. The training received will prepare them for careers in academia or industry. At the same time, the outreach component will introduce pre-college students to modern concepts such as quantum mechanics and statistics of particles.