Theory of Locally Crystalline Liquids

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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.%%%