Topological and Textured Condensed Matter Systems

该奖项资助低维凝聚态物质的电子特性的理论研究和教育，其中系统状态下的拓扑结构，或直接在哈密顿量中编码，诱导新的行为。当低能电子物理由狄拉克方程控制时，后一种情况就会出现，石墨烯就是一个重要的例子。前者在可以有效地描述为量子磁体的系统中实现。量子霍尔双分子层提供了一个独特的环境来探测这种物理，因为它的拓扑结构携带物理电荷，并且它允许实验探测，这在其他实现中是不可能的。这个项目的重点是这两种系统，作为拓扑结构和纹理如何影响电子特性的范例。石墨烯是一种二维碳网络，在二维电子系统中是不寻常的。在某种程度上，这是由于它的电子特性是由狄拉克方程控制的。量子电动力学可以作一个类比，其中库仑相互作用与动能竞争，以决定系统的物理行为。这些能量尺度的比例表明，库仑相互作用在原始石墨烯中相对较强，在短长度和长长度尺度上都有重要的影响。这项研究将集中在包括无序、掺杂和波动在内的这种物理的后果上，以了解在什么情况下可以观察到库仑相互作用的影响。PI还将研究纳米结构的石墨烯系统，其中的行为在传统的二维电子系统中没有类似的发生。其中包括通过外部电位产生新的狄拉克点，以及在量子环中观察到的“有效时间反转对称性破缺”。未掺杂石墨烯在量子霍尔体系中的显著绝缘行为也将被研究。PI旨在更好地理解无序的影响，它们如何影响系统的状态，它们对边缘状态的影响，并检查最近在双层石墨烯中看到的类似行为。填充因子1附近的量子霍尔双层显示出逆流阻力，在零温度极限下似乎消失，并且在隧道电导中具有强但有限的共振。允许这种不寻常行为出现的潜在状态仍然知之甚少，但很可能以一种亲密的方式涉及混乱。PI将研究由周期势诱导的大量纹理缺陷（介子）会发生什么，作为研究它们的存在如何影响现实无序势下系统相干性的第一步。PI还将考虑从相干双层到不相关层的过渡，因为它们是分离的，以获得一个干净的系统。该方法采用薄圆柱体极限作为起点，与无限二维系统相比，可以以更完整的方式处理波动。石墨烯是新器件技术的重要候选材料。这项研究有助于理解它，并可能使其应用。研究生将参与本研究项目；他们将接受分析凝聚态系统的现代方法的培训，为他们在科学和技术领域的职业生涯做好准备。这项研究将与来自美国和国外的科学家合作进行，加强和丰富我们自己的物理社区。该奖项支持新电子材料的理论研究和教育。电子材料在现代社会中发挥着至关重要的作用，在计算机、光学、电信等领域都有应用。随着时间的推移，对高速度和低功耗的要求越来越高，对满足这些要求的新材料的需求变得越来越迫切。该项目将探索一种新型材料的电子物理，具有传统半导体中无法比拟的特性和行为。其中一些材料的一个显著特征是，在一个重要的意义上，它们的电子表现得好像它们以光速运动，从而产生有趣的现象。这种系统的一个范例是石墨烯，它是一种由碳原子组成的二维蜂窝网络，其特性使其对设备应用具有吸引力。PI将使用理论方法研究石墨烯的基本电子特性，并了解该系统与更传统的半导体表亲之间的异同。PI还将研究当考虑到相互作用的影响时，电子是如何组织自己的。研究观察具有新的导电和光学性质的物质的新电子态的可能性。PI还将关注磁场的影响。磁场可以对被限制在一个平面上的电子的电子特性产生许多显著的影响，包括由量子力学规则固定的可测量电阻和与材料特性无关的基本常数。当两个这样的平面靠得非常近时，会产生另一个惊人的效应：电子似乎会自己组织成一种新的物质状态，这让人想起了超导。超导态对电流没有阻力。PI试图理解这种物质的新状态，它是如何产生的，以及它与超导性有何不同。

TECHNICAL SUMMARYThis award funds theoretical research and education on the electronic properties of low-dimensional condensed matter, where topological structure in the state of the system, or encoded directly in the Hamiltonian, induces novel behavior. The latter case can arise when the low-energy electron physics is controlled by a Dirac equation, of which an important example is that of graphene. The former is realized in systems that may be effectively described as a quantum magnet. The quantum Hall bilayer offers a unique environment to probe this physics because its topological structures carry physical charge, and it allows experimental probes that are not possible in other realizations. This project focuses on these two systems as paradigms for how topological structure and textures can affect electronic properties.Graphene, a two-dimensional carbon network, is unusual among two-dimensional electron systems. In part this is a consequence of the fact that its electronic properties are controlled by a Dirac equation. An analogy may be drawn with quantum electrodynamics, in which Coulomb interactions compete with the kinetic energy to determine the physical behavior of the system. The ratio of these energy scales suggests that Coulomb interactions are relatively strong in pristine graphene, with important consequences both at short and long length scales. The research will focus on the consequences of this physics when disorder, doping, and fluctuations are included, to understand under what circumstances the effects of Coulomb interactions might be observed. The PI will also examine nanostructured graphene systems, where behaviors with no analog in conventional two dimensional electron systems occur. These include the creation of new Dirac points via an external potential, and "effective time-reversal symmetry breaking" as observed in quantum rings. The remarkable insulating behavior of undoped graphene in the quantum Hall regime will also be examined. The PI aims to better understand the effects of disorder, how they affect the state of the system, their consequences for edge states, and to examine recent analogous behavior seen in bilayer graphene.Quantum Hall bilayers near filling factor 1 display a counterflow resistance that appears to vanish in the zero temperature limit, and a strong but finite resonance in tunneling conductance. The underlying state that allows such unusual behavior to emerge remains poorly understood, but is likely to involve disorder in an intimate way. The PI will examine what happens when large collections of textured defects, merons, are induced by a periodic potential as a first step in examining how their presence affects the coherence of the system in a realistic disorder potential. The PI will also consider the transition from a coherent bilayer to uncorrelated layers as they are separated, for a clean system. The approach adopts the thin cylinder limit as a starting point, for which fluctuations may be handled in a more complete way than is possible for an infinite two-dimensional system.Graphene is an important candidate for new device technologies. This research contributes to it understanding and may enable applications. Graduate students will participate in this research project; they will be trained in modern methods for analyzing condensed matter systems, preparing them for careers in science and technology. This research will be performed in collaboration with scientists from the US and abroad, strengthening and enriching our own physics community.NONTECHNICAL SUMMARYThis award supports theoretical research and education into new electronic materials. Electronic materials play a crucial role in modern society, finding applications in computers, optics, telecommunications and more. As the demands for high speed and low power consumption increase over time, the need for new materials to meet these demands becomes ever-more more pressing. This project will explore the electronic physics of a new of class materials, possessing properties and behaviors with no analog in traditional semiconductors. A remarkable feature of some of these materials is that in an important sense their electrons behave as if they were moving at the speed of light leading to interesting phenomena.A paradigm for such systems is graphene, a two dimensional honeycomb network of carbon atoms with properties that make it attractive for device applications. The PI will use theoretical methods to study the basic electronic properties of graphene and to understand the similarities and differences between this system and its more conventional semiconductor cousins. The PI will also study how the electrons may organize themselves when the effects of interactions are taken into account. The possibility of observing new electronic states of matter which may have novel conduction and optical properties will be investigated. The PI will also focus on effects of magnetic fields. A magnetic field can have many remarkable effects on the electronic properties of electrons confined to a plane, including measurable resistances that are fixed by the rules of quantum mechanics and fundamental constants that are independent of the properties of the material. Another striking effect occurs when two such planes are brought very close together: the electrons appear to organize themselves into a new state of matter that is reminiscent of superconductivity. Superconducting states display no resistance to the flow of electricity. The PI seeks to understand this new state of matter, how it arises, and how it differs from superconductivity.