Theory of Charge and Spin Dynamics in Electron Liquids

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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.***