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ABSTRACT: Recent advances in the creation and modulation of graphene-like systems are
introducing a science of "designer Dirac materials". In its original
definition, artificial graphene is a man-made nanostructure that consists of
identical potential wells (quantum dots) arranged in a adjustable honeycomb
lattice in the two-dimensional electron gas. As our ability to control the
quality of artificial graphene samples improves, so grows the need for an
accurate theory of its electronic properties, including the effects of
electron-electron interactions. Here we determine those effects on the band
structure and on the emergence of Dirac points.
01/2012;
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ABSTRACT: We derive a self-consistent local variant of the Thomas-Fermi approximation
for (quasi-)two-dimensional (2D) systems by localizing the Hartree term. The
scheme results in an explicit orbital-free representation of the electron
density and energy in terms of the external potential, the number of electrons,
and the chemical potential determined upon normalization. We test the method
over a variety 2D nanostructures by comparing to the Kohn-Sham 2D-LDA
calculations up to 600 electrons. Accurate results are obtained in view of the
negligible computational cost. We also assess a local upper bound for the
Hartree energy.
11/2011;
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ABSTRACT: Density-functional theory (DFT) for electrons at finite temperature is increasingly important in condensed matter and chemistry. The exact conditions that have proven crucial in constraining and constructing accurate approximations for ground-state DFT are generalized to finite temperature, including the adiabatic connection formula. We discuss consequences for functional construction.
Physical Review Letters 10/2011; 107(16):163001. · 7.37 Impact Factor
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ABSTRACT: We extend a recent formulation of quantum continuum mechanics [J. Tao et. al,
Phys. Rev. Lett. {\bf 103}, 086401 (2009)] to many-body systems subjected to a
magnetic field. To accomplish this, we propose a modified Lagrangian approach,
in which motion of infinitesimal volume elements of the system is referred to
the "quantum convective motion" that the magnetic field produces already in the
ground-state of the system. In the linear approximation, this approach results
in a redefinition of the elastic displacement field $\uv$, such that the
particle current $\jv$ contains both an electric displacement and a
magnetization contribution: $\jv=\jv_0+n_0\partial_t \uv+\nabla \times
(\jv_0\times \uv)$, where $n_0$ and $\jv_0$ are the particle density and the
current density of the ground-state and $\partial_t$ is the partial derivative
with respect to time. In terms of this displacement, we formulate an "elastic
approximation" analogous to the one proposed in the absence of magnetic field.
The resulting equation of motion for $\uv$ is expressed in terms of
ground-state properties -- the one-particle density matrix and the two-particle
pair correlation function -- and in this form it neatly generalizes the
equation obtained for vanishing magnetic field.
09/2011;
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ABSTRACT: We study the graphite intercalated compound CaC$_6$ by means of Eliashberg
theory, focusing on the anisotropy properties. An analysis of the
electron-phonon coupling is performed, and we define a minimal 6-band
anisotropy structure. Comparing with Superconducting Density Functional Theory
(SCDFT) the condition under which Eliashberg theory is able to reproduce the
SCDFT gap structure is determined, and we discuss the role of Coulomb
interactions. The Engelsberg-Schrieffer polaron structure is computed by
solving the Eliashberg equation on the Matsubara axis and analytically
continuing it to the full complex plane. This reveals the polaronic
quasiparticle bands anisotropic features as well as the interplay with
superconductivity.
Physical Review B 08/2011; 85:184514. · 3.69 Impact Factor
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ABSTRACT: We present a practical and accurate density functional for the exchange-correlation energy of electrons in two dimensions. The exchange part is based on a recent two-dimensional generalized-gradient approximation derived by considering the limits of small and large density gradients. The fully local correlation part is constructed following the Colle-Salvetti scheme and a Gaussian approximation for the pair density. The combination of these expressions is shown to provide an efficient density functional to calculate the total energies of two-dimensional electron systems such as semiconductor quantum dots. Excellent performance of the functional with respect to numerically exact reference data for quantum dots is demonstrated. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010
International Journal of Quantum Chemistry 09/2010; 110(12):2308 - 2314. · 1.36 Impact Factor
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ABSTRACT: In modeling low-dimensional electronic nanostructures, the evaluation of the electron-electron interaction is a challenging task. Here we present an accurate and practical density-functional approach to the two-dimensional many-electron problem. In particular, we show that spin-density functionals in the class of meta-generalized-gradient approximations can be greatly simplified by reducing the explicit dependence on the Kohn-Sham orbitals to the dependence on the electron spin density and its spatial derivatives. Tests on various quantum-dot systems show that the overall accuracy is well preserved, if not even improved, by the modifications.
09/2010;
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ABSTRACT: The exchange-correlation potentials stemming from the local-density approximation and several generalized-gradient approximations are known to have incorrect asymptotic decay. This failure is independent of the dimensionality, but so far the problem has been corrected -- within the mentioned approximations -- only in three dimensions. Here we provide a cured exchange-correlation potential in two dimensions, where the applications have a continuously increasing range in, e.g., semiconductor physics. The given potential is a generalized-gradient approximation, which is as easy to apply as the local-density approximation. We demonstrate that the corrected potential agrees very well with the analytic result of a two-electron quantum dot in the asymptotic regime, and yields plausible exchange-correlation potentials for larger two-dimensional systems.
08/2010;
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ABSTRACT: Finite temperature density functional theory provides, in principle, an exact
description of the thermodynamical equilibrium of many-electron systems. In
practical applications, however, the functionals must be approximated.
Efficient and physically meaningful approximations can be developed if relevant
properties of the exact functionals are known and taken into consideration as
constraints. In this work, derivations of exact properties and scaling
relations for the main quantities of finite temperature density functional
theory are presented. In particular, a coordinate scaling transformation at
finite temperature is introduced and its consequences are elucidated.
08/2010;
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ABSTRACT: We express the high-frequency (antiadiabatic) limit of the exchange-correlation (xc) kernels of an inhomogeneous electron gas in terms of the following equilibrium properties: the ground-state density, the xc kinetic stress tensor, the pair-correlation function and the ground-state xc 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 antiadiabatic xc kernels will be useful in calculations of excitation energies by time-dependent density-functional theory in atoms, molecules, and solids, and provide a solid basis for interpolation between the low- and high-frequency limits of the xc kernels.
Phys. Rev. B. 03/2010; 81(24).
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ABSTRACT: Accurate treatment of the electronic correlation in inhomogeneous electronic systems, combined with the ability to capture the correlation energy of the homogeneous electron gas, allows to reach high predictive power in the application of density-functional theory. For two-dimensional systems we can achieve this goal by generalizing our previous approximation [Phys. Rev. B 79, 085316 (2009)] to a parameter-free form, which reproduces the correlation energy of the homogeneous gas while preserving the ability to deal with inhomogeneous systems. The resulting functional is shown to be very accurate for finite systems with an arbitrary number of electrons with respect to numerically exact reference data.
02/2010;
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ABSTRACT: The Becke-Johnson exchange potential [A. D. Becke and E. R. Johnson, J. Chem. Phys. 124, 221101 (2006)] has been successfully used in electronic structure calculations within density-functional theory. However, in its original form, the potential may dramatically fail in systems with non-Coulombic external potentials, or in the presence of external magnetic or electric fields. Here, we provide a system-independent correction to the Becke-Johnson approximation by (i) enforcing its gauge-invariance and (ii) making it exact for any single-electron system. The resulting approximation is then better designed to deal with current-carrying states and recovers the correct asymptotic behavior for systems with any number of electrons. Tests of the resulting corrected exchange potential show very good results for a hydrogen chain in an electric field and for a four-electron harmonium in a magnetic field.
The Journal of chemical physics 01/2010; 132(4):044112. · 3.09 Impact Factor
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ABSTRACT: The Becke-Johnson exchange potential [J. Chem. Phys. 124, 221101 (2006)] has been successfully used in electronic structure calculations within density-functional theory. However, in its original form the potential may dramatically fail in systems with non-Coulombic external potentials, or in the presence of external magnetic or electric fields. Here, we provide a system-independent correction to the Becke-Johnson approximation by (i) enforcing its gauge invariance and (ii) making it exact for any single-electron system. The resulting approximation is then better designed to deal with current-carrying states, and recovers the correct asymptotic behavior for systems with any number of electrons. Tests of the resulting corrected exchange potential show very good results for a Hydrogen chain in an electric field and for a four-electron harmonium in a magnetic field.
09/2009;
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ABSTRACT: We consider density functionals for exchange and correlation energies in two-dimensional systems. The functionals are constructed by making use of exact constraints for the angular averages of the corresponding exchange and correlation holes, respectively, and assuming proportionality between their characteristic sizes. The electron current and spin are explicitly taken into account, so that the resulting functionals are suitable to deal with systems exhibiting orbital currents and/or spin polarization. Our numerical results show that in finite systems the proposed functionals outperform the standard two-dimensional local spin-density approximation, still performing well also in the important limit of the homogeneous two-dimensional electron gas.
09/2009;
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ABSTRACT: We study the properties of the lower bound on the exchange-correlation energy in two dimensions. First we review the derivation of the bound and show how it can be written in a simple density-functional form. This form allows an explicit determination of the prefactor of the bound and testing its tightness. Next we focus on finite two-dimensional systems and examine how their distance from the bound depends on the system geometry. The results for the high-density limit suggest that a finite system that comes as close as possible to the ultimate bound on the exchange-correlation energy has circular geometry and a weak confining potential with a negative curvature.
09/2009;
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ABSTRACT: We extend the Becke-Johnson approximation [J. Chem. Phys. 124, 221101 (2006)] of the exchange potential to two dimensions. We prove and demonstrate that a direct extension of the underlying formalism may lead to divergent behavior of the potential. We derive a cure to the approach by enforcing the gauge invariance and correct asymptotic behavior of the exchange potential. The procedure leads to an approximation which is shown, in various quasi-two-dimensional test systems, to be very accurate in comparison with the exact exchange potential, and thus a considerable improvement over the commonly applied local-density approximation. Comment: submitted to Phys. Rev. B on July 9th, 2009
09/2009;
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ABSTRACT: We derive a non-empirical, orbital-free density functional for the total energy of interacting electrons in two dimensions. The functional consists of a local formula for the interaction energy, where we follow the lines introduced by Parr for three-dimensional systems [R. G. Parr, J. Phys. Chem. 92, 3060 (1988)], and the Thomas-Fermi approximation for the kinetic energy. The freedom from orbitals and from the Hartree integral makes the proposed approximation numerically highly efficient. The total energies obtained for confined two-dimensional systems are in a good agreement with the standard local-density approximation within density-functional theory, and considerably more accurate than the Thomas-Fermi approximation.
08/2009;
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ABSTRACT: Electronic structure calculations are routinely carried out within the framework of density-functional theory, often with great success. For electrons in reduced dimensions, however, there is still a need for better approximations to the exchange-correlation energy functional. Furthermore, the need for properly describing current-carrying states represents an additional challenge for the development of approximate functionals. In order to make progress along these directions, we show that simple and efficient expressions for the exchange energy can be obtained by considering the short-range behavior of the one-body spin-density matrix. Applications to several two-dimensional systems confirm the excellent performance of the derived approximations, and verify the gauge-invariance requirement to be of great importance for dealing with current-carrying states.
07/2009;
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ABSTRACT: Bounds on the exchange-correlation energy of many-electron systems are derived and tested. By using universal scaling properties of the electron-electron interaction, we obtain the exponent of the bounds in three, two, one, and quasione dimensions. From the properties of the electron gas in the dilute regime, the tightest estimate to date is given for the numerical prefactor of the bound, which is crucial in practical applications. Numerical tests on various low-dimensional systems are in line with the bounds obtained and give evidence of an interesting dimensional crossover between two and one dimensions.
Physical Review Letters 06/2009; 102(20):206406. · 7.37 Impact Factor
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C Bersier,
A Floris,
P Cudazzo,
G Profeta,
A Sanna,
F Bernardini,
M Monni, S Pittalis,
S Sharma,
H Glawe,
A Continenza,
S Massidda,
E K U Gross
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ABSTRACT: Superconductivity in Pb, H under extreme pressure and CaBeSi, in the framework of the density functional theory for superconductors, is discussed. A detailed analysis on how the electron–phonon and electron–electron interactions combine together to determine the superconducting gap and critical temperature of these systems is presented. Pb, H under pressure and CaBeSi are multigap superconductors. We will address the question under which conditions does a system exhibits this phenomenon. The presented results contribute to the understanding of multiband and anisotropic superconductivity, which has received a lot of attention since the discovery of MgB2, and show how it is possible to describe the superconducting properties of real materials on a fully ab initio basis.
Journal of Physics Condensed Matter 03/2009; 21(16):164209. · 2.55 Impact Factor
