Theory of Charge and Spin Dynamics in Electron Liquids

本基金支持凝聚态物理的理论研究。电子系统中电荷密度激发的时间依赖密度泛函理论（TDFT）目前是一种发展良好的工具，其预测通常与实验测量相比较。然而，该理论在描述(i)杂质效应和（ii）完全或部分自旋极化电子液体中的自旋和耦合自旋电荷动力学方面仍然相对不发达。本研究的主要目标是发展自旋动力学和杂质效应的TDFT，使其达到与普通TDFT相当的复杂水平。从本质上讲，这意味着在存在杂质散射的情况下，对自旋和频率相关的交换相关（xc）场进行精确的近似。为了适当地包括迟滞和弛豫效应，有必要超越绝热的局部自旋密度近似，这可以用自旋电流密度作为基本变量来实现。具有均匀杂质分布的自旋极化电子气体的自旋依赖粘弹性谱在该方法中起着关键作用。这些数量将在Kubo-Mori形式主义的框架内计算。在宏观极限下，该理论应产生电荷和自旋电流的广义流体力学（纳维-斯托克斯）方程。这个理论应该补充和扩展最近提出的绝热自旋动力学。二维电子液体在强磁场下（所有电子都处于最低朗道能级）的粘弹性谱的计算是一个令人着迷的问题。最近的研究表明，用有效弹性理论可以很好地描述不可压缩分数量子霍尔态的电荷动力学。这个理论需要在两个方向上扩展：首先，必须包括能量耗散，因为它对正确描述可压缩态的电荷动力学至关重要；其次，必须考虑电子的自旋。目的是发展一种有效的粘弹性理论，以统一最低朗道能级的自旋和电荷密度激发的处理。该理论将应用于计算分数填充因子下量子霍尔铁磁体的集体激发、拓扑自旋织构的动力学以及自旋边缘波的色散。最近的理论工作强调了在晶体绝缘体介电响应的密度泛函计算中需要超越局部密度近似（LDA）。在这种情况下，将努力将LDA的修正表示为宏观极化的显式函数。这种极化密度泛函理论，如果成功，将允许第一性原理计算的介电性质进行相对容易。本基金支持凝聚态物理的理论研究。这项研究将扩展电子相互作用理论，包括杂质和电子自旋的影响。特别是，在非常高的磁场中相互作用的电子的性质-量子霍尔态-将被研究。这项研究有助于对凝聚态物理的基本认识

This grant supports theoretical research in condensed matter physics. The time-dependent density functional theory (TDFT) of charge-density excitations in electronic systems is by now a well developed tool, whose predictions are routinely compared to experimental measurements. However, the theory is still relatively underdeveloped with regard to its ability to describe (i) impurity effects and (ii) spin and coupled spin-charge dynamics in fully or partly spin-polarized electron liquids. The primary goal of this research is to develop the TDFT of spin dynamics and impurity effects to a level of sophistication comparable to what has been reached by ordinary TDFT. In essence, this means developing accurate approximations for the spin- and frequency-dependent exchange-correlation (xc) fields in the presence of impurity scattering. In order to properly include retardation and relaxation effects it is necessary to go beyond the adiabatic local spin-density approximation, and this can be done using the spin-current density as the basic variable. A key role in this approach is played by the spin-dependent visco-elastic spectra of the spin-polarized electron gas with a uniform distribution of impurities. These quantities will be calculated within the framework of the Kubo-Mori formalism. In the macroscopic limit the theory should yield generalized hydrodynamics (Navier-Stokes) equations for charge and spin currents. This theory should complement and extend the recently proposed adiabatic spin dynamics.The calculation of the visco-elastic spectra of a two-dimensional electron liquid at high magnetic field (such that all the electrons are in the lowest Landau level) poses a fascinating problem. It has been recently shown that the charge dynamics of incompressible fractional quantum Hall states are well described by an effective elasticity theory. This theory needs to be extended in two directions: first, energy dissipation must be included, since it is essential to correctly describe the charge dynamics of compressible states; second, the spin of the electron must be taken into account. The objective is to develop an effective visco-elastic theory to unify the treatment of spin and charge density excitations in the lowest Landau level. The theory will be applied to the calculation of the collective excitations of quantum Hall ferromagnets at fractional filling factors, the dynamics of topological spin textures, and the dispersion of spin edge waves.Recent theoretical work has highlighted the need to go beyond the local density approximation (LDA) in density-functional calculations of the dielectric response of crystalline insulators. In this context an effort will be made to express the correction to LDA as an explicit functional of the macroscopic polarization. This polarization density functional theory, if successful, will allow first-principles calculations of dielectric properties to be carried out with relative ease.%%% This grant supports theoretical research in condensed matter physics. The research will extend the theory of interacting electrons to include the effects of impurities and electron spin. In particular, the properties of interacting electrons in very high magnetic fields - the quantum Hall state - will be studied. The research contributes to fundamental understanding in condensed matter physics.***