Liquid Crystal Order in Condensed Matter Systems

液晶被定义为介于完全无序各向同性液体和完全有序晶体之间的凝聚态，在自然界中无处不在。首席研究员（PI）将研究液晶相的各种实现及其在新环境中的转变，统一的线索是热和/或量子波动的重要性以及导致普遍相行为的静态异质性。在PI早期关于smic - a和盘状的研究基础上，将研究一类这样的问题，即淬火无序对各种类型液晶有序的影响，如胆甾、smic - c、反铁电等，这些液晶被限制在刚性气凝胶和/或柔性气凝胶的随机矩阵中。这些系统的动力学理论也将发展。另一个重点将是聚合物-液晶复合材料的研究，这种材料将塑料和橡胶的机械性能与传统易碎液晶的电光性能结合起来，具有相当大的技术前景。这类材料，例如液晶弹性体和凝胶，也提出了许多基本的理论问题，这些问题与前面提到的随机基质（如气凝胶）中的液晶问题不无关系，其中随机交联的聚合物基质起着淬火无序的作用。最近发现的显微镜下的非手性弯核（香蕉形）液晶是令人兴奋的，因为它们表现出手性对称性的自发断裂和伴随的自发铁电性。PI将绘制其丰富的相图，探索相，并阐明在定向有序的液体和空间有序的近晶相中这种手性对称性破缺的本质。最近发现的一些“硬”凝聚态体系也表现出液晶的秩序。先前研究的一个例子是假设的铁磁超导体在零场下的自发涡旋固体，因此具有柱状液晶相的对称性。另一个将被研究的例子是假定的“近晶涡旋玻璃”状态，可在ii型超导体中实现，涡旋垂直于平行柱状缺陷的随机阵列。PI将探索这种系统的热波动、钉住和耗散（I-V），目的是解释最近在这种几何结构中令人困惑的实验。部分填充高朗道能级的量子霍尔体系中可能存在的电子液晶态是另一个令人兴奋的研究方向。PI将阐明量子霍尔向列的现象学，旨在从两个互补的角度发展和连接其描述：从有序的一面作为量子熔化的密晶，从无序的一面作为复合费米子的方向有序的费米液体。从平动有序复合费米-液体的角度描述量子霍尔近密态也将被研究，并与先前发展的哈特里-福克近密态联系起来。该研究影响着应用技术的基础性问题。PI积极参与教育活动，包括K-12和公共宣传。液晶，被定义为介于完全无序各向同性液体和完全有序晶体之间的凝聚态，在自然界中无处不在。首席研究员（PI）将研究液晶相的各种实现及其在新环境中的转变，统一的线索是热和/或量子波动的重要性以及导致普遍相行为的静态异质性。该研究影响着应用技术的基础性问题。PI积极参与教育活动，包括K-12和公共宣传

Liquid-crystals, defined as states of condensed matter intermediate in their properties between fully disordered isotropic liquids and fully ordered crystals are ubiquitous in nature. The principal investigator (PI) will study a variety of realizations of liquid crystal phases and transitions between them in novel contexts, with a unifying thread being importance of thermal and/or quantum fluctuations and static heterogeneities that lead to universal phase behavior.One class of such problems that will be studied, building on the PI's earlier work on smectic-A and discotics, is effects of quenched disorder on various types of liquid crystal orders, such as cholesteric, smectic-C, antiferroelectric and others, as realized by liquid crystals confined inside a random matrix of a rigid aerogel and/or a flexible aerosil. A dynamic theory of these systems will also be developed.Another focus will be the study of polymer-liquid crystal composite materials that hold considerable technological promise by combining mechanical properties of plastics and rubber with electro-optic properties of conventional fragile liquid crystals. Such materials, as for example realized by liquid-crystal elastomers and gels, also pose many fundamental theoretical questions, not unrelated to the aforementioned problem of liquid crystals in a random matrix, e.g., aerogel, with the randomly crosslinked polymer matrix playing the role of quenched disorder.Recently discovered microscopically achiral bent-core (banana-shaped) liquid crystals are exciting because they exhibit a spontaneous breaking of chiral symmetry and an accompanying spontaneous ferroelectricity. The PI will work to map out their rich phase diagram, explore phases, and elucidate the nature of this chiral symmetry breaking both in the orientationally ordered liquid and spatially ordered smectic phases.There are a number of recently discovered "hard" condensed matter systems that also appear to exhibit liquid crystal order. A previously studied example is a spontaneous vortex solid in putative ferromagnetic superconductors at zero field, that therefore have a symmetry of a columnar liquid crystal phase. Another example that will be studied is the putative "smectic vortex glass" state realizable in type-II superconductors with vortices running perpendicular to a random array of parallel columnar defects. The PI will explore thermal fluctuations, pinning and dissipation (I-V) of such systems with the goal of explaining recent puzzling experiments in such geometry.Possible electronic liquid crystal states in the quantum Hall regime of partially filled high Landau levels is another exciting direction of research. The PI will elucidate the phenomenology of quantum Hall nematic, aiming to develop and bridge its description from two complementary points of view: from the ordered side as a quantum-melted smectic and from the disordered side as an orientationally-ordered Fermi-liquid of composite fermions. A description of a quantum Hall smectic from the point of view of a translationally-ordered composite Fermi-liquid will also be studied and related to the previously developed Hartree-Fock smectic state.The research affects fundamental issues to applied technology. The PI is active in educational activities including K-12 and public outreach.%%% Liquid-crystals, defined as states of condensed matter intermediate in their properties between fully disordered isotropic liquids and fully ordered crystals are ubiquitous in nature. The principal investigator (PI) will study a variety of realizations of liquid crystal phases and transitions between them in novel contexts, with a unifying thread being importance of thermal and/or quantum fluctuations and static heterogeneities that lead to universal phase behavior.The research affects fundamental issues to applied technology. The PI is active in educational activities including K-12 and public outreach.***