Theory of Locally Crystalline Liquids

该基金支持强关联电子系统性质的理论研究，特别是这些系统中液晶相的行为。 高度相关的电子系统的液晶相具有相当大的局部结晶（电荷）有序性，这一观点得到了强有力的支持。 掺杂莫特绝缘体的各种电子液体和液晶相在理论上是预期的和/或在实验上（特别是从中子衍射和X射线散射实验）已知具有相当大的局部“条纹”顺序。 也有明确的理论和令人信服的，虽然间接的，实验证据表明，有一个很大程度的条纹秩序的各向异性金属态在低温下观察到的量子霍尔系统在更高的朗道水平。 低密度二维电子气的金属相的rs小于，但接近魏格纳结晶的临界密度，预计，理论上，有很大程度的结晶秩序。准一维电荷和自旋密度波绝缘体的正常态长期以来一直被认为具有实质性的（相位无序的）局域密度波序。 即使是普通的量子霍尔液体，特别是那些在非常低的填充因子，是已知的拥有初期的结晶秩序，所示的深磁-旋子最小值的集体模式频谱。 建议对这一说法的含义进行系统的理论研究。 特别是，我们会发现定义的限制情况下，直观的，但模糊的，局部结晶顺序的概念可以精确，并探讨高度相关的电子液体的电子性质的局部结晶度的后果。 将特别注意高温超导体的“波动条纹”相的物理学，这种局部结晶液体的初始玻璃化特性，以及这项研究与经典过冷液体理论的关系。

This grant supports theoretical research on the properties of strongly correlated electron systems; in particular, the behavior of liquid crystalline phases in these systems. There is strong support for the idea that the liquid crystal phases of highly correlated electronic systems have considerable local crystalline (charge) order. Various electronic liquid and liquid crystalline phases of doped Mott insulators are expected on theoretical grounds and/or are known experimentally (especially from neutron diffraction and x-ray scattering experiments) to possess considerable local "stripe" order. There is also clear theoretical and compelling, although indirect, experimental evidence that there is a large degree of stripe order in the anisotropic metallic state observed at low temperatures in quantum Hall systems in higher Landau levels. The metallic phases of the low-density two dimensional electron gas with rs less than, but near to the critical density for Wigner crystallization, are expected, theoretically, to have a large degree of crystalline order. The normal state of quasi-one dimensional charge and spin density wave insulators has long been known to possess substantial (phase disordered) local density wave order. Even ordinary quantum Hall liquids, especially those at very low filling factor, are known to possess incipient crystalline order, as indicated by the deep magneto-roton minimum in the collective mode spectrum. It is proposed to undertake a systematic theoretical study of the implications of this statement. In particular, we will find defined limiting situations in which the intuitive, but vague, notion of local crystalline order can be made precise, and to explore the consequences of local crystallinity on the electronic properties of highly correlated electronic liquids. Special attention will be paid to the physics of the "fluctuating stripe" phases of the high temperature superconductors, to the incipient glassy character of such a locally crystalline liquid, and to the relation of this study to the theory of classical supercooled liquids.%%%