Theoretical Condensed Matter Physics

技术综述：该奖项支持软量子物质的理论研究和教育。PI将使用软物质物理的思想和技术，包括广义弹性和流体力学，以及驱动非平衡系统的物理，来理解二维电子系统在量子化磁场中的固体和液晶相，以及超固态的现象学。在许多软凝聚物质系统中，排斥的长程相互作用和吸引的短程相互作用之间的竞争通过形成空间不均匀的中间相来解决，例如条状或气泡相。例子包括铁磁性薄膜和I型超导体的中间态。这一建议集中在二维电子系统中的这类相，其中库仑相互作用提供长程排斥，而量子力学交换相互作用提供短程吸引。在过去的六年里，对这类系统的一些输运和微波传导性实验已经提供了电子“条状”相以及晶格相的证据，包括维格纳晶体和气泡晶体。这项拟议的研究将研究不同晶体相之间可能的结构相变以及这些相的弹性性质。这些弹性性质将被用作研究这些晶体在垂直和倾斜磁场中的钉扎模式的输入。还将研究驱动维格纳晶体和气泡晶体，特别是它们的去钉扎转变和非线性IV特性。超稠度是一种被提出的物质状态，在这种状态下，玻色-爱因斯坦凝聚与固体的结晶顺序共存。最近在固体氦上的扭转振荡器实验声称观察到了这种新的物质状态，受此启发，PI将研究超固体的现象学。PI将进一步发展他最近提出的正常-固体到超固体转变的朗道模型，目的是提出新的实验，可能为超固体相提供额外的证据。PI还将研究超固体模型的流体动力学，并推导出其密度-密度关联函数，该函数可以在光散射实验中测量。在进行研究工作的同时，还将对本科生和研究生的教育做出坚定的承诺。REU计划与这项研究直接相关。非技术总结：该奖项支持在量子世界中发现和理解新的物质状态的理论研究和教育。这项研究的重点之一是物质的新状态，以及当电子被限制在平面上并暴露在强磁场中时可能发生的变化。这项工作的另一个重点是确定实验是否在氦中看到了一种物质状态，这种物质已经凝固并冷却到最低温度。这种奇怪的状态很久以前就被提出了，但一直没有被发现，直到最近进行了旋转一大块固体氦的实验。它们表明，一小部分原子仍然处于静止状态，对于一个表面上看起来是固体的物体来说，这是一个奇怪的性质。PI将进行研究，旨在找到实验特征，帮助确定物质的这种神秘状态是否真的被看到。物质的新状态的发现和对其性质的了解导致了新的技术，我们都从中受益。例如，超导电性的发现，曾经是实验室的好奇，导致了强大的磁铁，用于核磁共振机器，现在常规用于医学。按照类似的传统，这项研究可能会为未来技术的智力基础做出贡献，这些技术将造福社会，有助于保持美国的竞争力。

TECHNICAL SUMMARY:This award supports theoretical research and education on soft quantum matter. The PI will use ideas and techniques of soft matter physics, including generalized elasticity and hydrodynamics, and the physics of driven, nonequilibrium systems, to understand the solid and liquid-crystalline phases of two-dimensional electron systems in a quantizing magnetic field, and the phenomenology of supersolids.In many soft condensed matter systems, a competition between repulsive long range interactions and attractive short range interactions is resolved through the formation of a spatially inhomogeneous mesophase, such as a stripe or bubble phase. Examples include thin ferromagnetic films and the intermediate state of type-I superconductors. This proposal focuses on such phases in two-dimensional electron systems, where the Coulomb interaction provides the long range repulsion and the quantum-mechanical exchange interaction the short-range attraction. Over the past six years a number of transport and microwave conductivity experiments on such systems have provided evidence for electronic "stripe" phases as well lattice phases, including Wigner and bubble crystals. The proposed research will study possible structural phase transitions between different crystal phases and the elastic properties of those phases. These elastic properties will be used as the input for a study of the pinning modes of these crystals in both perpendicular and tilted magnetic fields. Driven Wigner and bubble crystals, specifically their depinning transitions and nonlinear IV characteristics, will also be studied. Supersolidity is a proposed state of matter in which Bose-Einstein condensation coexists with the crystalline order of a solid. Motivated by recent torsional oscillator experiments on solid helium that claim to have observed this novel state of matter, the PI will study the phenomenology of supersolids. The PI will further develop his recently proposed Landau model for the normal-solid to supersolid transition with the objective of suggesting new experiments that might provide additional evidence for a supersolid phase. The PI will also study the hydrodynamics of a model supersolid and derive its density-density correlation function, which could be measured in a light-scattering experiment.A strong commitment to education of undergraduate and graduate researchers is accomplished in parallel with the research efforts. The REU program is directly tied to this research.NON-TECHNICAL SUMMARY:This award supports theoretical research and education on the discovery and understanding of new states of matter in the quantum world. One focus of the research is on new states of matter and the transformations that may occur among them that might arise when electrons that are confined to a plane and exposed to a high magnetic field. Another focus of the work is to identify whether experiments are seeing a state of matter in helium that has been solidified and cooled to the lowest temperatures. This curious state was proposed long ago but has remained unseen until recent experiments were performed that rotate a chunk of solid helium. They suggest a fraction of the atoms remain at rest; a curious property for an apparently solid body. The PI will carry out research that aims to find experimental signatures that will aid in the determination of whether this enigmatic state of matter has actually been seen.The discovery of new states of matter and understanding their properties has led to new technologies from which we all benefit. For example, the discovery of superconductivity, once a laboratory curiosity, has led to the powerful magnets that are used in MRI machines that are now routinely used in medicine. In a similar tradition, this research may contribute to the intellectual foundations of future technology that will benefit society and help keep America competitive.