Liquid Crystal Order in Condensed Matter Systems

液晶是性质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态，在自然界中无处不在。首席研究员(PI)将在新的背景下研究液晶相的各种实现以及它们之间的转变，统一的线索是导致普遍相行为的热和/或量子涨落和静态不均匀的重要性。这类问题将被研究的一类问题，建立在PI早期关于近晶-A和毒品的工作基础上，是猝灭无序对各种类型的液晶有序的影响，如胆固相、近晶-C、反铁电和其他，如限制在刚性气凝胶和/或柔性气凝胶随机矩阵中的液晶所实现的。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，例如由液晶弹性体和凝胶实现的，也提出了许多基本的理论问题，与前面提到的随机基质中的液晶问题无关，例如气凝胶，其中随机交联的聚合物基质起到猝灭无序的作用。最近发现的非手性弯曲核(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破缺和伴随的自发铁电性。PI将致力于绘制其丰富的相图，探索相，并阐明在取向有序的液体相和空间有序的近晶相中手性对称性破坏的本质。最近发现的一些“硬”凝聚态系统似乎也显示出液晶有序。以前研究的一个例子是在零场假设的铁磁超导体中的自发涡旋固体，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设的“近晶涡旋玻璃”状态可以在第二类超导体中实现，其涡旋垂直于平行柱状缺陷的随机阵列。PI将探索这类系统的热涨落、钉扎和耗散(I-V)，目的是解释最近在这种几何结构中令人困惑的实验。部分填充的高Landau能级量子霍尔区中可能的电子液晶态是另一个令人兴奋的研究方向。PI将阐明量子霍尔向列相的现象学，旨在从两个互补的角度来发展和沟通它的描述：从有序面作为量子熔化的近晶相和从无序面作为复合费米子的定向有序费米液体。还将从平移有序复合费米液体的角度描述量子霍尔近晶态，并将其与先前发展的Hartree-Fock近晶态相联系。这项研究影响到应用技术的基本问题。PI活跃在教育活动中，包括K-12和公众宣传。%的液晶，定义为性质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态。首席研究员(PI)将在新的背景下研究液晶相的各种实现以及它们之间的转变，一个统一的线索是导致普遍相行为的热和/或量子涨落和静态不均匀的重要性。这项研究影响到应用技术的基本问题。国际和平协会积极参与包括K-12和公众宣传在内的教育活动。

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.***