arXiv subjects

V. U. Nazarov

Publications and source records attributed to V. U. Nazarov.

At least 19 recordsLinked to original sources

arXiv2016

Exact "exact exchange" potential of two- and one-dimensional electron gases beyond the asymptotic limit

The exchange-correlation potential experienced by an electron in the free space adjacent to a solid surface or to a low-dimensional system defines the fundamental image states and is generally important in surface- and nano-science. Here we determine the potential near the two- and one-dimensional electron gases (EG), doing this analytically at the level of the exact exchange of the density-functional theory (DFT). We find that, at $r_\perp\gg k_F^{-1}$, where $r_\perp$ is the distance from the EG and $k_F$ is the Fermi radius, the potential obeys the already known asymptotic $-e^2/r_\perp$, while at $r_\perp \lesssim k_F^{-1}$, but {\em still in vacuum}, qualitative and quantitative deviations of the exchange potential from the asymptotic law occur. The playground of the excitations to the low-lying image states falls into the latter regime, causing significant departure from the Rydberg series. In general, our analytical exchange potentials establish benchmarks for numerical approaches in the low-dimensional science, where DFT is by far the most common tool.

cond-mat.mes-hall↗

arXiv2015

Role of the kinematics of probing electrons in electron energy-loss spectroscopy of solid surfaces

Inelastic scattering of electrons incident on a solid surface is determined by the two properties: (i) electronic response of the target system and (ii) the detailed quantum-mechanical motion of the projectile electron inside and in the vicinity of the target. We emphasize the equal importance of the second ingredient, pointing out the fundamental limitations of the conventionally used theoretical description of the electron energy-loss spectroscopy (EELS) in terms of the ``energy-loss functions''. Our approach encompasses the dipole and impact scattering as specific cases, with the emphasis on the quantum-mechanical treatment of the probe electron. Applied to the high-resolution EELS of Ag surface, our theory largely agrees with recent experiments, while some instructive exceptions are rationalized.

cond-mat.mtrl-sci↗

arXiv2015

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 $c_\uparrow$ and $c_\downarrow$ of the spin-components of the potential at integer particle numbers $N_\uparrow$ and $N_\downarrow$ satisfy the condition $c_\uparrow N_\uparrow+c_\downarrow N_\downarrow=0$. 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.

quant-ph↗

arXiv2014

Energy bands in graphene: Comparison between the tight-binding model and {\it ab initio} calculations

We compare the classification of the electron bands in graphene, obtained by group theory algebra in the framework of tight-binding model (TBM), with that calculated in the density-functional theory (DFT) framework. Identification in the DFT band-structure of all eight energy bands (four valence and four conduction bands) corresponding to the TBM-derived energy bands is performed and corresponding analysis is presented. The four occupied (three $σ$- and one $π$-like) and three unoccupied (two $σ$- and one $π$-like) bands given by DFT closely correspond to those predicted by TBM, both by their symmetry and their dispersion law. However, the two lowest lying at the $Γ$-point unoccupied bands (one of them of a $σ$-like type and the other of a $π$-like one), are not of TBM type. According both to their symmetry and to the electron density these bands are plane waves orthogonal to the TBM valence bands; dispersion of these states can be determined unambiguously up to the Brillouin zone borders. On the other hand, the fourth unoccupied band given by the TBM, can be identified among those given by the DFT band calculations; it is situated rather high with respect to energy. The interaction of this band with the free-electron states is so strong, that it exists only in a part of $k$-space.

cond-mat.mes-hall↗

arXiv2013

Coupled plasmon - phonon excitations in extrinsic monolayer graphene

The existence of an acoustic plasmon in extrinsic (doped or gated) monolayer graphene was found recently in an {\it ab initio} calculation with the frozen lattice [M. Pisarra {\it et al.}, arXiv:1306.6273, 2013]. By the {\em fully dynamic} density-functional perturbation theory approach, we demonstrate a strong coupling of the acoustic plasmonic mode to lattice vibrations. Thereby, the acoustic plasmon in graphene does not exist as an isolated excitation, but it is rather bound into a combined plasmon-phonon mode. We show that the coupling provides a mechanism for the {\em bidirectional} energy exchange between the electronic and the ionic subsystems with fundamentally, as well as practically, important implications for the lattice cooling and heating by electrons in graphene.

cond-mat.mes-hall↗

arXiv2013

Optics of semiconductors and insulators: Role of local-field effects revised

We show that by nullifying the short-wave response to the long-wave excitation (local-field-effects), the adiabatic time-dependent density-functional theory (TDDFT) of optics of semiconductors and insulators can be brought into excellent agreement with experiment. This indicates that the wing elements [($\Gv,\0v)$ and $(\0v,\Gv)$, $\Gv\ne\0v$] of both the Kohn-Sham (KS) density-response function $χ^s$ and the exchange-correlation kernel $f^{xc}$ are greatly overestimated by the existing approximations to the static DFT and TDDFT, respectively, to the extent that zero is a better approximation for them than the corresponding values provided by current theories. The head element of $f^{xc}$ is thereby fixed by the static macroscopic dielectric constant $ε_M$. Our method yields accurate optical spectra including both the weakly and strongly bound excitons, while its computational cost is extremely low, since only the head element of the KS response matrix and the static dielectric constant are needed.

cond-mat.mtrl-sci↗

arXiv2013

Space Group Symmetry Classification of Energy Bands in Graphene and Destruction of Dirac Points by Supercell Potential

In the previous publications (E. Kogan and V. U. Nazarov, Phys. Rev. B {\bf 85}, 115418 (2012) and E. Kogan, Graphene {\bf 2}, 74 (2013)) we presented point group symmetry classification of energy bands in graphene. In the present note we generalize classification by considering the space group symmetry. Also in the framework of group theory we describe destruction of the Dirac points in graphene by a supercell potential.

cond-mat.mes-hall↗

arXiv2013

Non-adiabatic time-dependent density functional theory of the impurity resistivity of metals

We make use of the time-dependent density functional theory to derive a new formally exact expression for the dc resistivity of metals with impurities. This expression takes fully into account the dynamics of electron-electron interactions. Correction to the conventional $T$-matrix (phase-shifts) theory is treated within hydrodynamics of inhomogeneous viscous electron liquid. As a first application, we present calculations of the residual resistivity of aluminum as a function of the atomic number of the impurities. We show that the inclusion of many-body corrections considerably improves the agreement between theory and experiment.

cond-mat.str-el↗

arXiv2013

Time-dependent localized Hartree-Fock potential

By minimizing the difference between the left- and the right-hand sides of the many-body time-dependent Schrödinger equation with the Slater-determinant wave-function, we derive a non-adiabatic and self-interaction free time-dependent single-particle effective potential which is the generalization to the time-dependent case of the localized Hartree-Fock potential. The new potential can be efficiently used within the framework of the time-dependent density-functional theory as we demonstrate by the evaluation of the wave-vector and frequency dependent exchange kernel $f_x(q,ω)$ and the exchange shear modulus $μ_x$ of the homogeneous electron gas.

quant-ph↗

arXiv2012

Scattering resonances in graphene

We address the two-dimensional band-structure of graphene above the vacuum level in the context of discrete states immersed in the three-dimensional continuum. Scattering resonances are discovered that originate from the coupling of the in-plane and perpendicular motions, as elucidated by the analysis of an exactly solvable model. Some of the resonances turn into true bound states at high-symmetry $\kv$ vectors. {\it Ab initio} scattering theory verifies the existence of the resonances in realistic graphene and shows that they lead to a total reflection of the incident electron below and total transmission above the resonance energy.

cond-mat.mes-hall↗

arXiv2012

Symmetry classification of energy bands in graphene

We present the results of the first principle calculations of the energy bands in graphene and their symmetry classification. The valence bands and four lowest conduction bands are classified according to their symmetry at the points $Γ$ and $K$. Merging of the bands is interpreted in the framework of the group theory.

cond-mat.mes-hall↗

arXiv2011

Optics of semiconductors from meta-GGA-based time-dependent density-functional theory

We calculate the optical spectra of silicon and germanium in the adiabatic time-dependent density functional formalism, making use of kinetic energy density-dependent (meta-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 non-locality of the time-dependent exchange-correlation potential in solid-state systems.

cond-mat.str-el↗

arXiv2010

Anti-adiabatic limit of the exchange-correlation kernels of an inhomogeneous electron gas

We express the high-frequency (anti-adiabatic) limit of the exchange-correlation kernels of an inhomogeneous electron gas in terms of the following equilibrium properties: the ground-state density, the kinetic stress tensor, the pair-correlation function, and the ground-state exchange-correlation potential. Of these quantities, the first three are amenable to exact evaluation by Quantum Monte Carlo methods, while the last can be obtained from the inversion of the Kohn-Sham equation for the ground-state orbitals. The exact scalar kernel, in this limit, is found to be of very long range in space, at variance with the kernel that is used in the standard local density approximation. The anti-adiabatic xc kernels should be useful in calculations of excitation energies by time-dependent DFT in atoms, molecules, and solids, and provides a solid basis for interpolation between the low- and high-frequency limits of the xc kernels.

cond-mat.str-el↗

arXiv2010

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

The scalar $f_{xc}$ and tensor $\hat{f}_{xc}$ 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". We expect our formula to serve as a convenient bridge between the scalar $f_{xc}$ which directly enters many applications and the tensor $\hat{f}_{xc}$ which, due to its locality in space, is much easier to approximate.

cond-mat.str-el↗

arXiv2008

Exact dynamical exchange-correlation kernel of a weakly inhomogeneous electron gas

The dynamical exchange-correlation kernel $f_{xc}$ of a non-uniform electron gas is an essential input for the time-dependent density functional theory of electronic systems. The long-wavelength behavior of this kernel is known to be of the form $f_{xc}= α/q^2$ where $q$ is the wave vector and $α$ is a frequency-dependent coefficient. We show that in the limit of weak non-uniformity the coefficient $α$ has a simple and exact expression in terms of the ground-state density and the frequency-dependent kernel of a {\it uniform} electron gas at the average density. We present an approximate evaluation of this expression for Si and discuss its implications for the theory of excitonic effects.

cond-mat.mtrl-sci↗

arXiv2008

Time-dependent current-density functional theory for the friction of ions in an interacting electron gas

Due to the strongly nonlocal nature of $f_{xc}({\bf r},{\bf r}',ω)$ the {\em scalar} exchange and correlation (xc) kernel of the time-dependent density-functional theory (TDDFT), the formula for Q the friction coefficient of an interacting electron gas (EG) for ions tends to give a too large value of Q for heavy ions in the medium- and low-density EG, if we adopt the local-density approximation (LDA) to $f_{xc}({\bf r},{\bf r}',ω)$, even though the formula itself is formally exact. We have rectified this unfavorable feature by reformulating the formula for Q in terms of the {\em tensorial} xc kernel of the time dependent current-density functional theory, to which the LDA can be applied without intrinsic difficulty. Our numerical results find themselves in a considerably better agreement with the experimental stopping power of Al and Au for slow ions than those previously obtained within the LDA to the TDDFT.

cond-mat.mtrl-sci↗

arXiv2007

Resolving the wave-vector and the refractive index from the coefficient of reflectance

We resolve the existing controversy concerning the selection of the sign of the normal-to-the-interface component of the wave-vector $k_z$ of an electromagnetic wave in an active (gain) medium. Our method exploits the fact that no ambiguity exists in the case of a {\em film} of the active medium since its coefficient of reflectance is invariant under the inversion of the sign of $k_z$. Then we show that the limit of the infinite film thickness determines a unique and physically consistent choice of the wave-vector and the refractive index. Practically important implications of the theory are identified and discussed.

physics.optics↗

arXiv2007

Including nonlocality in exchange-correlation kernel from time-dependent current density functional theory: Application to the stopping power of electron liquids

We develop a scheme for building the scalar exchange-correlation (xc) kernel of time-dependent density functional theory (TDDFT) from the tensorial kernel of time-dependent {\em current} density functional theory (TDCDFT) and the Kohn-Sham current density response function. Resorting to the local approximation to the kernel of TDCDFT results in a nonlocal approximation to the kernel of TDDFT, which is free of the contradictions that plague the standard local density approximation (LDA) to TDDFT. As an application of this general scheme, we calculate the dynamical xc contribution to the stopping power of electron liquids for slow ions to find that our results are in considerably better agreement with experiment than those obtained using TDDFT in the conventional LDA.

cond-mat.mtrl-sci↗