Theory of the nonlinear Rashba-Edelstein effect

It is well known that a current driven through a two-dimensional electron gas with Rashba spin-orbit coupling induces a spin polarization in the perpendicular direction (Edelstein effect). This phenomenon has been extensively studied in the linear response regime, i.e., when the average drift velocity of the electrons is a small fraction of the Fermi velocity. Here we investigate the phenomenon in the nonlinear regime, meaning that the average drift velocity is comparable to, or exceeds the Fermi velocity. This regime is realized when the electric field is very large, or when electron-impurity scattering is very weak. The quantum kinetic equation for the density matrix of noninteracting electrons is exactly and analytically solvable, reducing to a problem of spin dynamics for unpaired electrons near the Fermi surface. The crucial parameter is $gamma=eEL_s/E_F$, where $E$ is the electric field, $e$ is the absolute value of the electron charge, $E_F$ is the Fermi energy, and $L_s = hbar/(2malpha)$ is the spin-precession length in the Rashba spin-orbit field with coupling strength $alpha$. If $gammall1$ the evolution of the spin is adiabatic, resulting in a spin polarization that grows monotonically in time and eventually saturates at the maximum value $n(alpha/v_F)$, where $n$ is the electron density and $v_F$ is the Fermi velocity. If $gamma gg 1$ the evolution of the spin becomes strongly non-adiabatic and the spin polarization is progressively reduced, and eventually suppressed for $gammato infty$. We also predict an inverse nonlinear Edelstein effect, in which an electric current is driven by a magnetic field that grows linearly in time. The conductivities for the direct and the inverse effect satisfy generalized Onsager reciprocity relations, which reduce to the standard ones in the linear response regime.

Current-induced spin polarization at the surface of metallic films: a theorem and an ab initio calculation

The broken inversion symmetry at the surface of a metallic film (or, more generally, at the interface between a metallic film and a different metallic or insulating material) greatly amplifies the influence of the spin-orbit interaction on the surface properties. The best known manifestation of this effect is the momentum-dependent splitting of the surface state energies (Rashba effect). Here we show that the same interaction also generates a spin-polarization of the bulk states when an electric current is driven through the bulk of the film. For a semi-infinite jellium model, which is representative of metals with a closed Fermi surface, we prove as a theorem that, regardless of the shape of the confinement potential, the induced surface spin density at each surface is given by ${bf S} =-gamma hbar {bf hat z}times {bf j}$, where ${bf j}$ is the particle current density in the bulk, ${bf hat z}$ the unit vector normal to the surface, and $gamma=frac{hbar}{4mc^2}$ contains only fundamental constants. For a general metallic solid $gamma$ becomes a material-specific parameter that controls the strength of the interfacial spin-orbit coupling. Our theorem, combined with an {it ab initio} calculation of the spin polarization of the current-carrying film, enables a determination of $gamma$, which should be useful in modeling the spin-dependent scattering of quasiparticles at the interface.

Intrinsic Spin Hall Effect at Oxide Interfaces: a Simple Model

An asymmetric triangular potential well provides the simplest model for the confinement of mobile electrons at the interface between two insulating oxides, such as LaAlO_3 and SrTiO_3 (LAO/STO). These electrons have been recently shown to exhibit a large spin-orbit coupling of the Rashba type, i.e., linear in the in-plane momentum. In this paper we study the intrinsic spin Hall effect due to Rashba coupling in an asymmetric triangular potential well. Besides splitting each subband into two branches of opposite helicity, the spin-orbit interaction causes the wave function in the direction perpendicular to the plane of the quantum well (the z direction) to depend on the in-plane wave vector k. In contrast to the extreme asymmetric case, i.e., the wedge-shaped quantum well, for which the intrinsic spin Hall effect vanishes due to vertex corrections, we find that the asymmetric well supports a non-vanishing intrinsic spin Hall conductivity, which increases in magnitude as the well becomes more symmetric. The spin Hall conductivity is found to be proportional to the square of the spin-orbit coupling constant and, in the limit of low carrier density, depends only on the effective mass renormalization associated with the k-dependence of the wave functions in the z direction. Its origin lies in the non-vanishing matrix elements of the spin current between subbands corresponding to different states of quantized motion perpendicular to the plane of the well.

Comment on Density and Physical Current Density Functional Theory by Xiao-Yin Pan and Viraht Sahni, Int. J. Quant. Chem. 110, 2833 (2010)

This comment criticizes the above paper by Xiao-Yin Pan and Viraht Sahni. It is shown that their formulation of Physical Current Density Functional Theory is, at best, a garbled reformulation of the Vignale-Rasolt current-density functional theory, and, at worst, a potential source of mistakes insofar as it complicates the formulation of the variational principle and prevents the constrained search construction of the universal functional.

On the Causality Paradox of Time-Dependent Density Functional Theory

I show that the so-called causality paradox of time-dependent density functional theory arises from an incorrect formulation of the variational principle for the time evolution of the density. The correct formulation not only resolves the paradox in real time, but also leads to a new expression for the causal exchange-correlation kernel in terms of Berry curvature. Furthermore, I show that all the results that were previously derived from symmetries of the action functional remain valid in the present formulation. Finally, I develop a model functional theory which explicitly demonstrates the workings of the new formulation.