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

Response properties of III-V dilute magnetic semiconductors: interplay of disorder, dynamical electron-electron interactions and band-structure effects

A theory of the electronic response in spin and charge disordered media is developed with the particular aim to describe III-V dilute magnetic semiconductors like GaMnAs. The theory combines a detailed k.p description of the valence band, in which the itinerant carriers are assumed to reside, with first-principles calculations of disorder contributions using an equation-of-motion approach for the current response function. A fully dynamic treatment of electron-electron interaction is achieved by means of time-dependent density functional theory. It is found that collective excitations within the valence band significantly increase the carrier relaxation rate by providing effective channels for momentum relaxation. This modification of the relaxation rate, however, only has a minor impact on the infrared optical conductivity in GaMnAs, which is mostly determined by the details of the valence band structure and found to be in agreement with experiment.Comment: 15 pages, 9 figure

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

Enhanced carrier scattering rates in dilute magnetic semiconductors with correlated impurities

In III-V dilute magnetic semiconductors (DMSs) such as Ga$_{1-x}$Mn$_x$As, the impurity positions tend to be correlated, which can drastically affect the electronic transport properties of these materials. Within the memory function formalism we have derived a general expression for the current relaxation kernel in spin and charge disordered media and have calculated spin and charge scattering rates in the weak-disorder limit. Using a simple model for magnetic impurity clustering, we find a significant enhancement of the charge scattering. The enhancement is sensitive to cluster parameters and may be controllable through post-growth annealing.Comment: 4 pages, 3 figure

Ultra-nonlocality in density functional theory for photo-emission spectroscopy

We derive an exact expression for the photo-current of photo-emission spectroscopy using time-dependent current density functional theory (TDCDFT). This expression is given as an integral over the Kohn-Sham spectral function renormalized by effective potentials that depend on the exchange-correlation kernel of current density functional theory. We analyze in detail the physical content of this expression by making a connection between the density-functional expression and the diagrammatic expansion of the photo-current within many-body perturbation theory. We further demonstrate that the density functional expression does not provide us with information on the kinetic energy distribution of the photo-electrons. Such information can, in principle, be obtained from TDCDFT by exactly modeling the experiment in which the photo-current is split into energy contributions by means of an external electromagnetic field outside the sample, as is done in standard detectors. We find, however, that this procedure produces very nonlocal correlations between the exchange-correlation fields in the sample and the detector.Comment: 11 pages, 11 figure

Time-dependent density functional theory on a lattice

A time-dependent density functional theory (TDDFT) for a quantum many-body system on a lattice is formulated rigorously. We prove the uniqueness of the density-to-potential mapping and demonstrate that a given density is $v$-representable if the initial many-body state and the density satisfy certain well defined conditions. In particular, we show that for a system evolving from its ground state any density with a continuous second time derivative is $v$-representable and therefore the lattice TDDFT is guaranteed to exist. The TDDFT existence and uniqueness theorem is valid for any connected lattice, independently of its size, geometry and/or spatial dimensionality. The general statements of the existence theorem are illustrated on a pedagogical exactly solvable example which displays all details and subtleties of the proof in a transparent form. In conclusion we briefly discuss remaining open problems and directions for a future research.Comment: 12 pages, 1 figur

Time-resolved X-ray microscopy of nanoparticle aggregates under oscillatory shear

Of all current detection techniques with nanometer resolution, only X-ray microscopy allows imaging nanoparticles in suspension. Can it also be used to investigate structural dynamics? When studying response to mechanical stimuli, the challenge lies in applying them with precision comparable to spatial resolution. In the first shear experiments performed in an X-ray microscope, we accomplished this by inserting a piezo actuator driven shear cell into the focal plane of a scanning transmission X-ray microscope (STXM). Thus shear-induced reorganization of magnetite nanoparticle aggregates could be demonstrated in suspension. As X-ray microscopy proves suitable for studying structural change, new prospects open up in physics at small length scales.Comment: submitted to J. Synchrot. Radia