Time-dependent density-functional theory for electronic excitations in materials: basics and perspectives

Time-dependent density-functional theory (TDDFT) is widely used to describe electronic excitations in complex finite systems with large numbers of atoms, such as biomolecules and nanocrystals. The first part of this paper will give a simple and pedagogical explanation, using a two-level system, which shows how the basic TDDFT formalism for excitation energies works. There is currently an intense effort underway to develop TDDFT methodologies for the charge and spin dynamics in extended systems, to calculate optical properties of bulk and nanostructured materials, and to study transport through molecular junctions. The second part of this paper highlights some challenges and recent advances of TDDFT in these areas. Two examples are discussed: excitonic effects in insulators and intersubband plasmon excitations in doped semiconductor quantum wells.Comment: 15 pages, 2 figures, International Conference on Materials Discovery and Databases: Materials Informatics and DF

Time-dependent density-functional theory beyond the adiabatic approximation: insights from a two-electron model system

Most applications of time-dependent density-functional theory (TDDFT) use the adiabatic local-density approximation (ALDA) for the dynamical exchange-correlation potential Vxc(r,t). An exact (i.e., nonadiabatic) extension of the ground-state LDA into the dynamical regime leads to a Vxc(r,t) with a memory, which causes the electron dynamics to become dissipative. To illustrate and explain this nonadiabatic behavior, this paper studies the dynamics of two interacting electrons on a two-dimensional quantum strip of finite size, comparing TDDFT within and beyond the ALDA with numerical solutions of the two-electron time-dependent Schroedinger equation. It is shown explicitly how dissipation arises through multiple particle-hole excitations, and how the nonadiabatic extension of the ALDA fails for finite systems, but becomes correct in the thermodynamic limit.Comment: 10 pages, 7 figure

Time-dependent current density functional theory for the linear response of weakly disordered systems

This paper develops a quantitatively accurate first-principles description for the frequency and the linewidth of collective electronic excitations in inhomogeneous weakly disordered systems. A finite linewidth in general has intrinsic and extrinsic sources. At low temperatures and outside the region where electron-phonon interaction occurs, the only intrinsic damping mechanism is provided by electron-electron interaction. This kind of intrinsic damping can be described within time-dependent density-functional theory (TDFT), but one needs to go beyond the adiabatic approximation and include retardation effects. It was shown previously that a density-functional response theory that is local in space but nonlocal in time has to be constructed in terms of the currents, rather than the density. This theory will be reviewed in the first part of this paper. For quantitatively accurate linewidths, extrinsic dissipation mechanisms, such as impurities or disorder, have to be included. In the second part of this paper, we discuss how extrinsic dissipation can be described within the memory function formalism. We first review this formalism for homogeneous systems, and then present a synthesis of TDFT with the memory function formalism for inhomogeneous systems, to account simultaneously for intrinsic and extrinsic damping of collective excitations. As example, we calculate frequencies and linewidths of intersubband plasmons in a 40 nm wide GaAs/AlGaAs quantum well.Comment: 20 pages, 3 figure

Degeneracy in Density Functional Theory: Topology in v- and n-Space

This paper clarifies the topology of the mapping between v- and n-space in fermionic systems. Density manifolds corresponding to degeneracies g=1 and g>1 are shown to have the same mathematical measure: every density near a g-ensemble-v-representable (g-VR) n(r) is also g-VR (except ``boundary densities'' of lower measure). The role of symmetry and the connection between T=0 and T=0+ are discussed. A lattice model and the Be-series are used as illustrations.Comment: 4 pages, 4 figures (1 color

Memory function formalism approach to electrical conductivity and optical response of dilute magnetic semiconductors

A combination of the memory function formalism and time-dependent density-functional theory is applied to transport in dilute magnetic semiconductors. The approach considers spin and charge disorder and electron-electron interaction on an equal footing. Within the weak disorder limit and using a simple parabolic approximation for the valence band we show that Coulomb and exchange scattering contributions to the resistivity in GaMnAs are of the same order of magnitude. The positional correlations of defects result in a significant increase of Coulomb scattering, while the suppression of localized spin fluctuations in the ferromagnetic phase contributes substantially to the experimentally observed drop of resistivity below T_c. A proper treatment of dynamical screening and collective excitations is essential for an accurate description of infrared absorption.Comment: Proceedings of the 13th Brazilian Workshop on Semiconductors Physic

Coherent control of intersubband optical bistability in quantum wells

We present a study of the nonlinear intersubband (ISB) response of conduction electrons in a GaAs/AlGaAs quantum well to strong THz radiation, using a density-matrix approach combined with time-dependent density-functional theory. We demonstrate coherent control of ISB optical bistability, using THz control pulses to induce picosecond switching between the bistable states. The switching speed is determined by the ISB relaxation and decoherence times, T1 and T2.Comment: 3 pages, 3 figure

Dissipation through spin Coulomb drag in electronic spin dynamics

Spin Coulomb drag (SCD) constitutes an intrinsic source of dissipation for spin currents in metals and semiconductors. We discuss the power loss due to SCD in potential spintronics devices and analyze in detail the associated damping of collective spin-density excitations. It is found that SCD contributes substantially to the linewidth of intersubband spin plasmons in parabolic quantum wells, which suggests the possibility of a purely optical quantitative measurement of the SCD effect by means of inelastic light scattering

A minimal model for excitons within time-dependent density-functional theory

The accurate description of the optical spectra of insulators and semiconductors remains an important challenge for time-dependent density-functional theory (TDDFT). Evidence has been given in the literature that TDDFT can produce bound as well as continuum excitons for specific systems, but there are still many unresolved basic questions concerning the role of dynamical exchange and correlation (xc). In particular, the role of the long spatial range and the frequency dependence of the xc kernel $f_{\rm xc}$ for excitonic binding are still not very well explored. We present a minimal model for excitons in TDDFT, consisting of two bands from a one-dimensional Kronig-Penney model and simple approximate xc kernels, which allows us to address these questions in a transparent manner. Depending on the system, it is found that adiabatic xc kernels can produce a single bound exciton, and sometimes two bound excitons, where the long spatial range of $f_{\rm xc}$ is not a necessary condition. It is shown how the Wannier model, featuring an effective electron-hole interaction, emerges from TDDFT. The collective, many-body nature of excitons is explicitly demonstrated.Comment: 12 pages, 11 figure

Collective intersubband transitions in quantum wells: a comparative density-functional study

We use time-dependent (current) density functional theory to study collective transitions between the two lowest subbands in GaAs/AlGaAs quantum wells. We focus on two systems where experimental results are available: a wide single and a narrow asymmetric double well. The aim is to calculate frequency and linewidth of collective electronic modes damped via electron-electron interaction only. Since Landau damping is not effective here, the dominant damping mechanism involves dynamical exchange-correlation effects such as multipair production. To capture these effects, one has to go beyond the widely used adiabatic local density approximation (ALDA) and include retardation. We perform a comparative study of two approaches which fall in this category: the dynamical extension of the ALDA by Gross and Kohn, and a more recent method which treats exchange and correlation beyond the ALDA as viscoelastic stresses in the electron liquid. We find that the former method is more robust: it performs similarly for strongly different degrees of collectivity of the electronic motion. Results for quantum wells compare reasonably to experiment, with a tendency towards overdamping. By contrast, the viscoelastic approach is superior for systems where the electron dynamics is predominantly collective, but breaks down if the local velocity field is too rapidly varying, as in the case of a single-electron-like behavior such as tunneling through a potential barrier.Comment: 23 pages, 6 ps-figures, revte

Dissipation through spin Coulomb drag in electronic spin transport and optical excitations

Spin Coulomb drag (SCD) constitutes an intrinsic source of dissipation for spin currents in metals and semiconductors. We discuss the power loss due to SCD in potential spintronics devices and analyze in detail the associated damping of collective spin-density excitations. It is found that SCD contributes substantially to the linewidth of intersubband spin plasmons in semiconductor quantum wells, which suggests the possibility of a purely optical quantitative measurement of the SCD effect in a parabolic well through inelastic light scattering