arXiv subjects

C. A. Ullrich

Publications and source records attributed to C. A. Ullrich.

At least 19 recordsLinked to original sources

arXiv2026

Temperature-Dependent Dielectric Function of Calcium Fluoride

The optical properties of calcium fluoride (fluorspar, CaF2) are mainly determined by a strongly temperature-dependent giant infrared (IR) peak, and a series of nearly temperature-independent ultraviolet (UV) peaks. We find that the temperature dependence of the IR peak can be modeled, to good accuracy, by a radiation-reaction improved coupled-oscillator model (RRCO model), with temperature-dependent parameters. For the UV peaks, we find a convenient functional form which covers both the real as well as the imaginary parts of the dielectric function and provide a comparison to first-principles calculations based on time-dependent density-functional theory (TDDFT). The result is a compact functional form for the dielectric function of undoped CaF2 applicable to wide frequency and temperature ranges (0 < hbar omega < 60 eV, 22C < T < 500C). With the help of the temperature-dependent dielectric function, we obtain temperature-dependent values of the short-range and long-range asymptotics of atom-surface interactions with CaF2, for hydrogen, as well as ground-state and metastable helium. The giant IR absorption peak of CaF2 is shown to lead to a delayed onset of the fully retarded Casimir--Polder limit in the long-range interaction regime. We present arguments supporting a more general applicability of the RRCO model to materials of general interest.

cond-mat.mtrl-sci↗

arXiv2025

Coupled Oscillators and Dielectric Function

A generalized Sellmeier model, also referred to as the Lorentz-Dirac model, has been used for the description of the dielectric function of a number of technologically important materials in the literature. This model represents the frequency-dependent dielectric function as a sum over Green functions of classical damped harmonic oscillators, much in analogy with the functional form used for the dynamic polarizability of an atom, but with one important addition, namely, a complex-valued oscillator strength in the numerator. Here, we show that this generalized functional form can be justified based on the response function of coupled damped oscillators. The encountered analogies suggest an explanation for the generally observed success of the Lorentz--Dirac model in describing the dielectric function of crystals of consummate technological significance.

cond-mat.mtrl-sci↗

arXiv2024

Retardation Effects in Atom-Wall Interactions

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*(α(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.

cond-mat.other↗

arXiv2024

Emergent topological quasiparticle kinetics in constricted nanomagnets

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.

cond-mat.mes-hall↗

arXiv2022

Temperature-dependent dielectric function of intrinsic silicon: Analytic models and atom-surface potentials

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 $ε(T_Δ, ω)$, over a wide range of frequencies and a wide range of the temperature parameter $T_Δ= (T-T_0)/T_0$, 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 $[ε(T_Δ, ω) -1]/[ ε(T_Δ, ω)+2]$, 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 $0 < ω< 0.16 \, {\rm a.u.}$ and $0< T_Δ< 2.83$, 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 $ε(T_Δ, ω)$ to the Lorentz-Dirac model.

cond-mat.mtrl-sci↗

arXiv2012

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.

cond-mat.mtrl-sci↗

arXiv2011

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.

cond-mat.mtrl-sci↗

arXiv2009

Spin gaps and spin-flip energies in density-functional theory

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.

cond-mat.mtrl-sci↗

arXiv2009

Temperature-dependent resistivity of ferromagnetic GaMnAs: Interplay between impurity scattering and many-body effects

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.

cond-mat.mtrl-sci↗

arXiv2009

Time-dependent density-functional approach for exciton binding energies

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.

cond-mat.mtrl-sci↗

arXiv2009

Physical signatures of discontinuities of the time-dependent exchange-correlation potential

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.

cond-mat.mes-hall↗

arXiv2008

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.

cond-mat.mtrl-sci↗

arXiv2008

Time-dependent V-representability on lattice systems

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.

cond-mat.mes-hall↗

arXiv2007

Intersubband spin-orbit coupling and spin splitting in symmetric quantum wells

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.

cond-mat.mtrl-sci↗

arXiv2007

Time-dependent density-functional theory for ultrafast interband excitations

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.

cond-mat.mes-hall↗

arXiv2007

Real-time electron dynamics with exact-exchange time-dependent density-functional theory

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.

cond-mat.mes-hall↗

arXiv2007

The generator coordinate method in time-dependent density-functional theory: memory made simple

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.

cond-mat.mes-hall↗

arXiv2007

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.

cond-mat.mtrl-sci↗