Liquid Crystal Order in Condensed Matter Systems

液晶，定义为在其性质上介于完全无序的各向同性液体和完全有序的晶体之间的凝聚物质状态，在自然界中普遍存在。 主要研究者（PI）将研究液晶相的各种实现及其在新环境中的转变，统一的线索是导致普遍相行为的热和/或量子波动和静态不均匀性的重要性。将研究的一类此类问题，建立在PI早期对smectic-A和discicants的工作基础上，猝灭无序对各种类型的液晶有序的影响，例如，通过限制在刚性气凝胶和/或柔性气溶胶的随机基质内的液晶实现的，如双折射、近晶-C、反铁电等。 此外，还将发展这些系统的动力学理论。另一个重点是研究聚合物-液晶复合材料，该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相结合，具有相当大的技术前景。 例如通过液晶弹性体和凝胶实现的这样的材料也提出了许多基本的理论问题，这些问题与随机矩阵中的液晶的上述问题无关，例如，最近发现的显微镜下非手性的香蕉形液晶是令人兴奋的，因为它们表现出手征对称性的自发破缺和伴随的自发铁电性。 PI将绘制出丰富的相图，探索相，并阐明这种手性对称性破缺在取向有序的液体和空间有序的近晶相中的本质。最近发现的一些“硬”凝聚态系统也表现出液晶有序性。 先前研究的例子是假定的铁磁超导体中的自发涡旋固体在零场，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”状态可实现的第二类超导体与涡流运行垂直于一个随机阵列的平行柱状缺陷。 PI将探索这种系统的热涨落，钉扎和耗散（I-V），目的是解释这种几何结构中最近令人困惑的实验。部分填充高朗道能级的量子霍尔机制中可能的电子液晶态是另一个令人兴奋的研究方向。 PI将阐明量子霍尔效应的现象学，旨在从两个互补的角度发展和桥接其描述：从有序的一面作为量子熔化的近晶相，从无序的一面作为复合费米子的取向有序的费米液体。 从有序复合费米液体的角度对量子霍尔近晶态的描述也将被研究，并与先前开发的Hartree-Fock近晶态相关。 PI积极参与教育活动，包括K-12和公共宣传。液晶，定义为在其性质上介于完全无序的各向同性液体和完全有序的晶体之间的凝聚物质状态，在自然界中普遍存在。 主要研究者（PI）将研究液晶相的各种实现及其在新环境中的转变，统一的线索是导致普遍相行为的热和/或量子波动和静态不均匀性的重要性。该研究影响应用技术的基本问题。 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.***