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The ubiquitous domain wall kinetics under magnetic field or current application describes the dynamic properties in nanostructured magnets. However, when the geometrical size of a nanomagnetic system is constricted to the limiting domain wall length scale, the competing energetics between anisotropy, exchange and dipolar interactions can cause emergent kinetics due to quasiparticle relaxation, similar to bulk magnets of atomic origin. Here, we present a joint experimental and theoretical study to support this argument -- constricted nanomagnets, made of antiferromagnetic and paramagnetic neodymium thin film with honeycomb motif, reveal fast kinetic events at ps time scales due to the relaxation of chiral vortex loop-shaped topological quasiparticles that persist to low temperature in the absence of any external stimuli. Such phenomena are typically found in macroscopic magnetic materials. Our discovery is especially important considering the fact that paramagnets or antiferromagnets have no net magnetization. Yet, the kinetics in neodymium nanostructures is quantitatively similar to that found in ferromagnetic counterparts and only varies with the thickness of the specimen. This suggests that a universal, topological quasiparticle mediated dynamical behavior can be prevalent in nanoscopic magnets, irrespective of the nature of underlying magnetic material., Comment: 26 pages, 11 figures (main text 9 pages, 4 figures; supplementary material 17 pages, 7 figures). arXiv admin note: text overlap with arXiv:2305.00093

The onset of retardation effects in atom-wall interactions is studied. It is shown that the transition range from the 1/z^3 short-range (van der Waals) interaction to the 1/z^4 long-range (Casimir) retarded interaction critically depends on the atomic properties and on the dielectric function of the material. For simple non-alkali atoms (e.g., ground-state hydrogen and ground-state helium) interacting with typical dielectric materials such as intrinsic silicon, the transition to the retarded regime is shown to proceed at a distance of about 10 nm (200 Bohr radii). This is much shorter than typical characteristic absorption wavelengths of solids. Larger transition regimes are obtained for atoms with a large static polarizability such as metastable helium. We present a simple estimate for the critical distance, z_cr=137*(\alpha(0)/Z)^(1/2) atomic units, where alpha(0) is the static polarizability (expressed in atomic units) and Z is the number of electrons of the atom., Comment: 10 pages; RevTeX

The optical properties of monocrystalline, intrinsic silicon are of interest for technological applications as well as fundamental studies of atom-surface interactions. For an enhanced understanding, it is of great interest to explore analytic models which are able to fit the experimentally determined dielectric function $\epsilon(T_\Delta, \omega)$, over a wide range of frequencies and a wide range of the temperature parameter $T_\Delta = (T-T_0)/T_0$, where $T_0 = 293\,{\rm K}$ represents room temperature. Here, we find that a convenient functional form for the fitting of the dielectric function of silicon involves a Lorentz-Dirac curve with a complex, frequency-dependent amplitude parameter, which describes radiation reaction. We apply this functional form to the expression $[\epsilon(T_\Delta, \omega) -1]/[ \epsilon(T_\Delta, \omega)+2]$, inspired by the Clausius-Mossotti relation. With a very limited set of fitting parameters, we are able to represent, to excellent accuracy, experimental data in the (angular) frequency range $0 < \omega < 0.16 \, {\rm a.u.}$ and $0< T_\Delta < 2.83$, corresponding to the temperature range $ 293\,{\rm K} < T < 1123\, {\rm K}$. Using our approach, we evaluate the short-range $C_3$ and the long-range $C_4$ coefficients for the interaction of helium atoms with the silicon surface. In order to validate our results, we compare to a separate temperature-dependent direct fit of $\epsilon(T_\Delta, \omega)$ to the Lorentz-Dirac model., Comment: 18 pages, 9 figures, Version published in PRB

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., Comment: 5 pages

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 figures

Energy gaps are crucial aspects of the electronic structure of finite and extended systems. Whereas much is known about how to define and calculate charge gaps in density-functional theory (DFT), and about the relation between these gaps and derivative discontinuities of the exchange-correlation functional, much less is know about spin gaps. In this paper we give density-functional definitions of spin-conserving gaps, spin-flip gaps and the spin stiffness in terms of many-body energies and in terms of single-particle (Kohn-Sham) energies. Our definitions are as analogous as possible to those commonly made in the charge case, but important differences between spin and charge gaps emerge already on the single-particle level because unlike the fundamental charge gap spin gaps involve excited-state energies. Kohn-Sham and many-body spin gaps are predicted to differ, and the difference is related to derivative discontinuities that are similar to, but distinct from, those usually considered in the case of charge gaps. Both ensemble DFT and time-dependent DFT (TDDFT) can be used to calculate these spin discontinuities from a suitable functional. We illustrate our findings by evaluating our definitions for the Lithium atom, for which we calculate spin gaps and spin discontinuities by making use of near-exact Kohn-Sham eigenvalues and, independently, from the single-pole approximation to TDDFT. The many-body corrections to the Kohn-Sham spin gaps are found to be negative, i.e., single particle calculations tend to overestimate spin gaps while they underestimate charge gaps., Comment: 11 pages, 1 figure, 3 tables

The static conductivity of the dilute magnetic semiconductor GaMnAs is calculated using the memory function formalism and time-dependent density-functional theory to account for impurity scattering and to treat Hartree and exchange interactions within the hole gas. We find that the Coulomb scattering off the charged impurities alone is not sufficient to explain the experimentally observed drop in resistivity below the ferromagnetic transition temperature: the often overlooked scattering off the fluctuations of localized spins is shown to play a significant role.

Optical processes in insulators and semiconductors, including excitonic effects, can be described in principle exactly using time-dependent density-functional theory (TDDFT). Starting from a linearization of the TDDFT semiconductor Bloch equations in a two-band model, we derive a simple formalism for calculating excitonic binding energies. This formalism leads to a generalization of the standard Wannier equation for excitons, featuring a nonlocal effective electron-hole interaction determined by long-range and dynamical exchange-correlation (XC) effects. We calculate excitonic binding energies in several direct-gap semiconductors, using exchange-only and model XC kernels., Comment: 4 pages, 1 figure

The exact exchange-correlation (XC) potential in time-dependent density-functional theory (TDDFT) is known to develop steps and discontinuities upon change of the particle number in spatially confined regions or isolated subsystems. We demonstrate that the self-interaction corrected adiabatic local-density approximation for the XC potential has this property, using the example of electron loss of a model quantum well system. We then study the influence of the XC potential discontinuity in a real-time simulation of a dissociation process of an asymmetric double quantum well system, and show that it dramatically affects the population of the resulting isolated single quantum wells. This indicates the importance of a proper account of the discontinuities in TDDFT descriptions of ionization, dissociation or charge transfer processes., Comment: 17 pages, 6 figures

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 DFT

We study the mapping between time-dependent densities and potentials for noninteracting electronic systems on lattices. As discovered recently by Baer [J. Chem. Phys. 128, 044103 (2008)], there exist well-behaved time-dependent density functions on lattices which cannot be associated with any real time-dependent potential. This breakdown of time-dependent V-representability can be tracked down to problems with the continuity equation which arise from discretization of the kinetic-energy operator. Examples are given for lattices with two points and with N points, and implications for practical numerical applications of time-dependent density-functional theory are discussed. In the continuum limit, time-dependent noninteracting V-representability is restored., Comment: 8 pages, 4 figures

In semiconductors with inversion asymmetry, spin-orbit coupling gives rise to the well-known Dresselhaus and Rashba effects. If one considers quantum wells with two or more conduction subbands, an additional, intersubband-induced spin-orbit term appears whose strength is comparable to the Rashba coupling, and which remains finite for symmetric structures. We show that the conduction band spin splitting due to this intersubband spin-orbit coupling term is negligible for typical III-V quantum wells.

We formulate a time-dependent density functional theory (TDDFT) in terms of the density matrix to study ultrafast phenomena in semiconductor structures. A system of equations for the density matrix components, which is equivalent to the time-dependent Kohn-Sham equation, is derived. From this we obtain a TDDFT version of the semiconductor Bloch equations, where the electronic many-body effects are taken into account in principle exactly. As an example, we study the optical response of a three-dimensional two-band insulator to an external short-time pulsed laser field. We show that the optical absorption spectrum acquires excitonic features when the exchange-correlation potential contains a $1/q^{2}$ Coulomb singularity. A qualitative comparison of the TDDFT optical absorption spectra with the corresponding results obtained within the Hartree-Fock approximation is made.

The exact exchange potential in time-dependent density-functional theory is defined as an orbital functional through the time-dependent optimized effective potential (TDOEP) method. We numerically solve the TDOEP integral equation for the real-time nonlinear intersubband electron dynamics in a semiconductor quantum well with two occupied subbands. By comparison with adiabatic approximations, it is found that memory effects in the exact exchange potential become significant when the electron dynamics takes place in the vicinity of intersubband resonances., Comment: 5 pages, 5 figures

The generator coordinate (GC) method is a variational approach to the quantum many-body problem in which interacting many-body wave functions are constructed as superpositions of (generally nonorthogonal) eigenstates of auxiliary Hamiltonians containing a deformation parameter. This paper presents a time-dependent extension of the GC method as a new approach to improve existing approximations of the exchange-correlation (XC) potential in time-dependent density-functional theory (TDDFT). The time-dependent GC method is shown to be a conceptually and computationally simple tool to build memory effects into any existing adiabatic XC potential. As an illustration, the method is applied to driven parametric oscillations of two interacting electrons in a harmonic potential (Hooke's atom). It is demonstrated that a proper choice of time-dependent generator coordinates in conjunction with the adiabatic local-density approximation reproduces the exact linear and nonlinear two-electron dynamics quite accurately, including features associated with double excitations that cannot be captured by TDDFT in the adiabatic approximation., Comment: 10 pages, 13 figures

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 Physics

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 figures

The Hohenberg-Kohn (HK) theorem is one of the most fundamental theorems of quantum mechanics, and constitutes the basis for the very successful density-functional approach to inhomogeneous interacting many-particle systems. Here we show that in formulations of density-functional theory (DFT) that employ more than one density variable, applied to systems with a degenerate ground state, there is a subtle loophole in the HK theorem, as all mappings between densities, wave functions and potentials can break down. Two weaker theorems which we prove here, the joint-degeneracy theorem and the internal-energy theorem, restore the internal, total and exchange-correlation energy functionals to the extent needed in applications of DFT to atomic, molecular and solid-state physics and quantum chemistry. The joint-degeneracy theorem constrains the nature of possible degeneracies in general many-body systems.

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 figures

Time-dependent density-functional theory (TDDFT) treats dynamical exchange and correlation (xc) via a single-particle potential, Vxc(r,t), defined as a nonlocal functional of the density n(r',t'). The popular adiabatic local-density approximation (ALDA) for Vxc(r,t) uses only densities at the same space-time point (r,t). To go beyond the ALDA, two local approximations have been proposed based on quantum hydrodynamics and elasticity theory: (a) using the current as basic variable (C-TDDFT) [G. Vignale, C. A. Ullrich, and S. Conti, Phys. Rev. Lett. 79, 4878 (1997)], (b) working in a co-moving Lagrangian reference frame (L-TDDFT) [I. V. Tokatly, Phys. Rev. B 71, 165105 (2005)]. This paper illustrates, compares, and analyzes both non-adiabatic theories for simple time-dependent model densities in the linear and nonlinear regime, for a broad range of time and frequency scales. C- and L-TDDFT are identical in certain limits, but in general exhibit qualitative and quantitative differences in their respective treatment of elastic and dissipative electron dynamics. In situations where the electronic density rapidly undergoes large deformations, it is found that non-adiabatic effects can become significant, causing the ALDA to break down., Comment: 15 pages, 15 figures

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.

In electronic many-particle systems, the mapping between densities and spin magnetizations, {n(r), m(r)}, and potentials and magnetic fields, {v(r), B(r)}, is known to be nonunique, which has fundamental and practical implications for spin-density-functional theory (SDFT). This paper studies the nonuniqueness (NU) in SDFT on arbitrary lattices. Two new, non-trivial cases are discovered, here called local saturation and global noncollinear NU, and their properties are discussed and illustrated. In the continuum limit, only some well-known special cases of NU survive., Comment: 4 pages, 1 figure

In time-dependent density-functional theory, exchange and correlation (xc) beyond the adiabatic local density approximation can be described in terms of viscoelastic stresses in the electron liquid. In the time domain, this leads to a velocity-dependent xc vector potential with a memory containing short- and long-range components. The resulting time-dependent Kohn-Sham formalism describes the dynamics of electronic systems including decoherence and relaxation. For the example of collective charge-density oscillations in a quantum well, we illustrate the xc memory effects, clarify the dissipation mechanism, and extract intersubband relaxation rates for weak and strong excitations., Comment: 4 pages, 4 figures

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 figures

In semiconductor heterostructures, bulk and structural inversion asymmetry and spin-orbit coupling induce a k-dependent spin splitting of valence and conduction subbands, which can be viewed as being caused by momentum-dependent crystal magnetic fields. This paper studies the influence of these effective magnetic fields on the intersubband spin dynamics in an asymmetric n-type GaAs/AlGaAs quantum well. We calculate the dispersions of intersubband spin plasmons using linear response theory. The so-called D'yakonov-Perel' decoherence mechanism is inactive for collective intersubband excitations, i.e., crystal magnetic fields do not lead to decoherence of spin plasmons. Instead, we predict that the main signature of bulk and structural inversion asymmetry in intersubband spin dynamics is a three-fold, anisotropic splitting of the spin plasmon dispersion. The importance of many-body effects is pointed out, and conditions for experimental observation with inelastic light scattering are discussed., Comment: 8 pages, 6 figures

In inversion-asymmetric semiconductors, spin-orbit coupling induces a k-dependent spin splitting of valence and conduction bands, which is a well-known cause for spin decoherence in bulk and heterostructures. Manipulating nonequilibrium spin coherence in device applications thus requires understanding how valence and conduction band spin splitting affects carrier spin dynamics. This paper studies the relevance of this decoherence mechanism for collective intersubband spin-density excitations (SDEs) in quantum wells. A density-functional formalism for the linear spin-density matrix response is presented that describes SDEs in the conduction band of quantum wells with subbands that may be non-parabolic and spin-split due to bulk or structural inversion asymmetry (Rashba effect). As an example, we consider a 40 nm GaAs/AlGaAs quantum well, including Rashba spin splitting of the conduction subbands. We find a coupling and wavevector-dependent splitting of the longitudinal and transverse SDEs. However, decoherence of the SDEs is not determined by subband spin splitting, due to collective effects arising from dynamical exchange and correlation., Comment: 10 pages, 4 figures

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)

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 figures

Recent photoabsorption measurements have revealed a rich fine structure in the collective charge-density excitation spectrum of few-electron quantum dots in the presence of magnetic fields. We have performed systematic computational studies of the far-infrared density response of quantum dots, using time-dependent density-functional theory in the linear regime and treating the dots as two-dimensional disks. It turns out that the main characteristics observed in the experiment can be understood in terms of the electronic shell structure of the quantum dots. However, new features arise if a breaking of the circular symmetry of the dots is allowed, leading to an improved description of the experimental results., Comment: 18 pages, 5 figures, submitted to Phys. Rev. B

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, revtex

In the current density functional theory of linear and nonlinear time-dependent phenomena, the treatment of exchange and correlation beyond the level of the adiabatic local density approximation is shown to lead to the appearance of viscoelastic stresses in the electron fluid. Complex and frequency-dependent viscosity/elasticity coefficients are microscopically derived and expressed in terms of properties of the homogeneous electron gas. As a first consequence of this formalism, we provide an explicit formula for the linewidths of collective excitations in electronic systems., Comment: RevTeX, 4 pages