Theory of Locally Crystalline Liquids

本基金支持强相关电子系统性质的理论研究；特别是这些体系中液晶相的行为。高度相关电子系统的液晶相具有相当大的局部晶体（电荷）顺序，这一观点得到了强有力的支持。掺杂Mott绝缘体的各种电子液体和液晶相在理论和/或实验（特别是从中子衍射和x射线散射实验）上被期望具有相当大的局部“条纹”秩序。虽然间接，但也有明确的理论和令人信服的实验证据表明，在较高朗道能级的量子霍尔系统中，在低温下观察到的各向异性金属态中存在很大程度的条纹有序。低密度二维电子气体的金属相，其rs小于但接近维格纳结晶的临界密度，理论上被期望具有很大程度的结晶有序。准一维电荷和自旋密度波绝缘子的正常状态长期以来一直被认为具有大量（相无序）的局部密度波序。即使是普通的量子霍尔液体，特别是那些填充系数非常低的量子霍尔液体，也具有早期结晶秩序，这一点可以从集体模式光谱中的深磁转子最小值中看出。建议对这句话的含义进行系统的理论研究。特别是，我们将找到明确的限制情况，在这种情况下，直观但模糊的局部晶体秩序概念可以精确地实现，并探索局部结晶度对高度相关电子液体的电子性质的影响。将特别注意高温超导体的“波动条纹”相的物理性质，这种局部结晶液体的初始玻璃性质，以及本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.%%%