Functional theories of thermoelectric phenomena.

We review the progress that has been recently made in the application of time-dependent density functional theory to thermoelectric phenomena. As the field is very young, we emphasize open problems and fundamental issues. We begin by introducing the formal structure of thermal density functional theory, a density functional theory with two basic variables-the density and the energy density-and two conjugate fields-the ordinary scalar potential and Luttinger's thermomechanical potential. The static version of this theory is contrasted with the familiar finite-temperature density functional theory, in which only the density is a variable. We then proceed to constructing the full time-dependent non equilibrium theory, including the practically important Kohn-Sham equations that go with it. The theory is shown to recover standard results of the Landauer theory for thermal transport in the steady state, while showing greater flexibility by allowing a description of fast thermal response, temperature oscillations and related phenomena. Several results are presented here for the first time, i.e. the proof of invertibility of the thermal response function in the linear regime, the full expression of the thermal currents in the presence of Luttinger's thermomechanical potential, an explicit prescription for the evaluation of the Kohn-Sham potentials in the adiabatic local density approximation, a detailed discussion of the leading dissipative corrections to the adiabatic local density approximation and the thermal corrections to the resistivity that follow from it.

Spin-Orbit Twisted Spin Waves: Group Velocity Control.

We present a theoretical and experimental study of the interplay between spin-orbit coupling (SOC), Coulomb interaction, and motion of conduction electrons in a magnetized two-dimensional electron gas. Via a transformation of the many-body Hamiltonian we introduce the concept of spin-orbit twisted spin waves, whose energy dispersions and damping rates are obtained by a simple wave-vector shift of the spin waves without SOC. These theoretical predictions are validated by Raman scattering measurements. With optical gating of the density, we vary the strength of the SOC to alter the group velocity of the spin wave. The findings presented here differ from that of spin systems subject to the Dzyaloshinskii-Moriya interaction. Our results pave the way for novel applications in spin-wave routing devices and for the realization of lenses for spin waves.

Nonlocal Drag of Magnons in a Ferromagnetic Bilayer.

Quantized spin waves, or magnons, in a magnetic insulator are assumed to interact weakly with the surroundings, and to flow with little dissipation or drag, producing exceptionally long diffusion lengths and relaxation times. In analogy to Coulomb drag in bilayer two-dimensional electron gases, in which the contribution of the Coulomb interaction to the electric resistivity is studied by measuring the interlayer resistivity (transresistivity), we predict a nonlocal drag of magnons in a ferromagnetic bilayer structure based on semiclassical Boltzmann equations. Nonlocal magnon drag depends on magnetic dipolar interactions between the layers and manifests in the magnon current transresistivity and the magnon thermal transresistivity, whereby a magnon current in one layer induces a chemical potential gradient and/or a temperature gradient in the other layer. The largest drag effect occurs when the magnon current flows parallel to the magnetization; however, for oblique magnon currents a large transverse current of magnons emerges. We examine the effect for practical parameters, and find that the predicted induced temperature gradient is readily observable.

Magnetic fluctuations driven insulator-to-metal transition in Ca(Ir(1-x)Rux)O3.

Magnetic fluctuations in transition metal oxides are a subject of intensive research because of the key role they are expected to play in the transition from the Mott insulator to the unconventional metallic phase of these materials, and also as drivers of superconductivity. Despite much effort, a clear link between magnetic fluctuations and the insulator-to-metal transition has not yet been established. Here we report the discovery of a compelling link between magnetic fluctuations and the insulator-to-metal transition in Ca(Ir1-xRux)O3 perovskites as a function of the substitution coefficient x. We show that when the material turns from insulator to metal, at a critical value of x ~ 0.3, magnetic fluctuations tend to change their character from antiferromagnetic, a Mott insulator phase, to ferromagnetic, an itinerant electron state with Hund's orbital coupling. These results are expected to have wide-ranging implications for our understanding of the unconventional properties of strongly correlated electrons systems.

Derivative discontinuity with localized Hartree-Fock potential.

The localized Hartree-Fock potential has proven to be a computationally efficient alternative to the optimized effective potential, preserving the numerical accuracy of the latter and respecting the exact properties of being self-interaction free and having the correct -1/r asymptotics. In this paper we extend the localized Hartree-Fock potential to fractional particle numbers and observe that it yields derivative discontinuities in the energy as required by the exact theory. The discontinuities are numerically close to those of the computationally more demanding Hartree-Fock method. Our potential enjoys a "direct-energy" property, whereby the energy of the system is given by the sum of the single-particle eigenvalues multiplied by the corresponding occupation numbers. The discontinuities c↑ and c↓ of the spin-components of the potential at integer particle numbers N↑ and N↓ satisfy the condition c↑N↑ + c↓N↓ = 0. Thus, joining the family of effective potentials which support a derivative discontinuity, but being considerably easier to implement, the localized Hartree-Fock potential becomes a powerful tool in the broad area of applications in which the fundamental gap is an issue.

Density-functional theory of thermoelectric phenomena.

We introduce a nonequilibrium density-functional theory of local temperature and associated local energy density that is suited for the study of thermoelectric phenomena. The theory rests on a local temperature field coupled to the energy-density operator. We identify the excess-energy density, in addition to the particle density, as the basic variable, which is reproduced by an effective noninteracting Kohn-Sham system. A novel Kohn-Sham equation emerges featuring a time-dependent and spatially varying mass which represents local temperature variations. The adiabatic contribution to the Kohn-Sham potentials is related to the entropy viewed as a functional of the particle and energy density. Dissipation can be taken into account by employing linear response theory and the thermoelectric transport coefficients of the electron gas.

Microscopic theory of the inverse Edelstein effect.

We provide a precise microscopic definition of the recently observed inverse Edelstein effect in which a nonequilibrium spin accumulation in the plane of a two-dimensional (interfacial) electron gas drives an electric current perpendicular to its own direction. The drift-diffusion equations that govern the effect are presented and applied to the interpretation of the experiments.

Collective spin Hall effect for electron-hole gratings.

We show that an electric field parallel to the wave fronts of an electron-hole grating in a GaAs quantum well generates, via the electronic spin Hall effect, a spin grating of the same wave vector and with an amplitude that can exceed 1% of the amplitude of the initial density grating. We refer to this phenomenon as the "collective spin Hall effect." A detailed study of the coupled spin-charge dynamics for quantum wells grown in different directions reveals rich features in the time evolution of the induced spin density, including the possibility of generating a helical spin grating.

Interacting drift-diffusion theory for photoexcited electron-hole gratings in semiconductor quantum wells.

Phase-resolved transient grating spectroscopy in semiconductor quantum wells has been shown to be a powerful technique for measuring the electron-hole drag resistivity ρ(eh), which depends on the Coulomb interaction between the carriers. In this Letter we develop the interacting drift-diffusion theory, from which ρ(eh) can be determined, given the measured mobility of an electron-hole grating. From this theory we predict a crossover from a high-excitation-density regime, in which the mobility has the "normal" positive value, to a low-density regime, in which Coulomb drag dominates and the mobility becomes negative. At the crossover point, the mobility of the grating vanishes.

Short-time spin dynamics in strongly correlated few-fermion systems.

The nonequilibrium spin dynamics of a one-dimensional system of repulsively interacting fermions is studied by means of density-matrix renormalization group simulations. We focus on the short-time decay of the oscillation amplitudes of the centers of mass of spin-up and spin-down fermions. Because of many body effects, the decay is found to evolve from quadratic to linear in time, and eventually back to quadratic as the strength of the interaction increases. The characteristic rate of the decay increases linearly with the strength of repulsion in the weak-coupling regime, while it is inversely proportional to it in the strong-coupling regime. Our predictions can be tested in experiments on tunable ultracold few-fermion systems in one-dimensional traps.

Electron-electron interactions in artificial graphene.

Recent advances in the creation and modulation of graphenelike systems are introducing a science of "designer Dirac materials". In its original definition, artificial graphene is a man-made nanostructure that consists of identical potential wells (quantum dots) arranged in an adjustable honeycomb lattice in the two-dimensional electron gas. As our ability to control the quality of artificial graphene samples improves, so grows the need for an accurate theory of its electronic properties, including the effects of electron-electron interactions. Here we determine those effects on the band structure and on the emergence of Dirac points.

Probing the topological exciton condensate via Coulomb drag.

The onset of exciton condensation in a topological insulator thin film was recently predicted. We calculate the critical temperature for this transition, taking into account screening effects. Furthermore, we show that the proximity to this transition can be probed by measuring the Coulomb drag resistivity between the surfaces of the thin film as a function of temperature. This resistivity shows an upturn upon approaching the exciton-condensed state.

Optics of semiconductors from meta-generalized-gradient-approximation-based time-dependent density-functional theory.

We calculate the optical spectra of silicon, germanium, and zinc blende semiconductors in the adiabatic time-dependent density-functional formalism, making use of kinetic energy density-dependent [meta-generalized-gradient-approximation (GGA)] exchange-correlation functionals. We find excellent agreement between theory and experiment. The success of the theory on this notoriously difficult problem is traced to the fact that the exchange-correlation kernel of meta-GGA supports a singularity of the form α/q(2) (where q is the wave vector and α is a constant), whereas previously employed approximations (e.g., local-density and generalized gradient approximations) do not. Thus, the use of the adiabatic meta-GGA opens a new path for handling the extreme nonlocality of the time-dependent exchange-correlation potential in solid-state systems.

Persistent spin oscillations in a spin-orbit-coupled superconductor.

Quasi-two-dimensional superconductors with tunable spin-orbit coupling are very interesting systems with properties that are also potentially useful for applications. In this Letter we demonstrate that these systems exhibit undamped collective spin oscillations that can be excited by the application of a supercurrent. We propose to use these collective excitations to realize persistent spin oscillators operating in the frequency range of 10 GHz-1 THz.

Electric control of spin currents and spin-wave logic.

Spin waves in insulating magnets are ideal carriers for spin currents with low energy dissipation. An electric field can modify the dispersion of spin waves, by directly affecting, via spin-orbit coupling, the electrons that mediate the interaction between magnetic ions. Our microscopic calculations based on the superexchange model indicate that this effect of the electric field is sufficiently large to be used to effectively control spin currents. We apply these findings to the design of a spin-wave interferometric device, which acts as a logic inverter and can be used as a building block for room-temperature, low-dissipation logic circuits.

Two-dimensional Mott-Hubbard electrons in an artificial honeycomb lattice.

Artificial crystal lattices can be used to tune repulsive Coulomb interactions between electrons. We trapped electrons, confined as a two-dimensional gas in a gallium arsenide quantum well, in a nanofabricated lattice with honeycomb geometry. We probed the excitation spectrum in a magnetic field, identifying collective modes that emerged from the Coulomb interaction in the artificial lattice, as predicted by the Mott-Hubbard model. These observations allow us to determine the Hubbard gap and suggest the existence of a Coulomb-driven ground state.

Spin drag in an ultracold fermi gas on the verge of ferromagnetic instability.

Recent experiments [Jo, Science 325, 1521 (2009)] have presented evidence of ferromagnetic correlations in a two-component ultracold Fermi gas with strong repulsive interactions. Motivated by these experiments we consider spin drag, i.e., frictional drag due to scattering of particles with opposite spin, in such systems. We show that when the ferromagnetic state is approached from the normal side, the spin drag relaxation rate is strongly enhanced near the critical point. We also determine the temperature dependence of the spin diffusion constant. In a trapped gas the spin drag relaxation rate determines the damping of the spin dipole mode, which therefore provides a precursor signal of the ferromagnetic phase transition that may be used to experimentally determine the proximity to the ferromagnetic phase.

Many-body orbital paramagnetism in doped graphene sheets.

The orbital magnetic susceptibility of a gas of noninteracting massless Dirac fermions is zero when the Fermi energy is away from the Dirac point. Making use of diagrammatic perturbation theory, we calculate exactly the orbital magnetic susceptibility of massless Dirac fermions to first order in the Coulomb interaction demonstrating that it is finite and positive. Doped graphene sheets are thus unique systems in which the orbital magnetic susceptibility is completely controlled by many-body effects.

Coulomb-induced Rashba spin-orbit coupling in semiconductor quantum wells.

In the absence of an external field, the Rashba spin-orbit interaction (SOI) in a two-dimensional electron gas in a semiconductor quantum well arises entirely from the screened electrostatic potential of ionized donors. We adjust the wave functions of a quantum well so that electrons occupying the first (lowest) subband conserve their spin projection along the growth axis (s(z)), while the electrons occupying the second subband precess due to Rashba SOI. Such a specially designed quantum well may be used as a spin relaxation trigger: electrons conserve s(z) when the applied voltage (or current) is lower than a certain threshold V*; higher voltage switches on the Dyakonov-Perel spin relaxation.

Communications: On the relation between the scalar and tensor exchange-correlation kernels of the time-dependent density-functional theory.

The scalar f(xc) and tensor f(xc) exchange-correlation (xc) kernels are key ingredients of the time-dependent density functional theory and the time-dependent current density functional theory, respectively. We derive a comparatively simple relation between these two kernels under the assumption that the dynamic xc can be considered "weak." A calculation of the frequency-dependent dielectric function of silicon using this relation in conjunction with Vignale-Kohn f(xc) demonstrates a potential of our method to account for the dynamic many-body effects within the rigorous scheme of time-dependent density functional theory. Our formula provides a bridge between the scalar f(xc), which directly enters many applications, and the tensor f(xc) which, due to its locality in space, is much easier to approximate.