arXiv subjects

S. Pittalis

Publications and source records attributed to S. Pittalis.

35 records · Page 2Linked to original sources

arXiv2009

Orbital-free energy functional for electrons in two dimensions

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.

cond-mat.str-el↗

arXiv2009

Becke-Johnson-type exchange potential for two-dimensional systems

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.

cond-mat.str-el↗

arXiv2009

Gaussian approximations for the exchange-energy functional of current-carrying states: Applications to two-dimensional systems

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.

cond-mat.str-el↗

arXiv2009

Lower Bounds on the Exchange-Correlation Energy in Reduced Dimensions

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 quasi-one 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.

cond-mat.str-el↗

arXiv2009

Multiband superconductivity in Pb, H under pressure and CaBeSi from {\it ab-initio} calculations

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 MgB$_2$, and show how it is possible to describe the superconducting properties of real materials on a fully {\it ab-initio} basis.

cond-mat.supr-con↗

arXiv2009

Electronic exchange in quantum rings

Quantum rings can be characterized by a specific radius and ring width. For this rich class of physical systems, an accurate approximation for the exchange-hole potential and thus for the exchange energy is derived from first principles. Excellent agreement with the exact-exchange results is obtained regardless of the ring parameters, total spin, current, or the external magnetic field. The description can be applied as a density functional outperforming the commonly used local-spin-density approximation, which is here explicitly shown to break down in the quasi-one-dimensional limit. The dimensional crossover, which is of extraordinary importance in low-dimensional systems, is fully captured by our functional.

cond-mat.str-el↗

arXiv2009

Correlation energy of two-dimensional systems: Toward non-empirical and universal modeling

The capability of density-functional theory to deal with the ground-state of strongly correlated low-dimensional systems, such as semiconductor quantum dots, depends on the accuracy of functionals developed for the exchange and correlation energies. Here we extend a successful approximation for the correlation energy of the three dimensional inhomogeneous electron gas, originally introduced by Becke [J. Chem. Phys. {\bf 88}, 1053 (1988)], to the two-dimensional case. The approach aims to non-empirical modeling of the correlation-hole functions satisfying a set of exact properties. Furthermore, the electron current and spin are explicitly taken into account. As a result, good performance is obtained in comparison with numerically exact data for quantum dots with varying external magnetic field, and for the homogeneous two-dimensional electron gas, respectively.

cond-mat.str-el↗

arXiv2008

Density gradients for the exchange energy of electrons in two dimensions

We derive a generalized gradient approximation to the exchange energy to be used in density functional theory calculations of two-dimensional systems. This class of approximations has a long and successful history, but it has not yet been fully investigated for electrons in two dimensions. We follow the approach originally proposed by Becke for three-dimensional systems [Int. J. Quantum Chem. 23, 1915 (1983), J. Chem. Phys. 85, 7184 (1986)]. The resulting functional depends on two parameters that are adjusted to a test set of parabolically confined quantum dots. Our exchange functional is then tested on a variety of systems with promising results, reducing the error in the exchange energy by a factor of 4 with respect to the simple local density approximation.

cond-mat.str-el↗

arXiv2008

Role of Coulomb interaction in the superconducting properties of CaC6 and H under pressure

Superconductivity in intercalated graphite CaC6 and H under extreme pressure, in the framework of superconducting density functional theory, 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. In particular, we discuss the effect on the calculated Tc of the anisotropy of the electron-phonon interaction and of the different approximations for screening the Coulomb repulsion. These results contribute to the understanding of multigap 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.

cond-mat.supr-con↗

arXiv2008

Local correlation functional for electrons in two dimensions

We derive a local approximation for the correlation energy in two-dimensional electronic systems. In the derivation we follow the scheme originally developed by Colle and Salvetti for three dimensions, and consider a Gaussian approximation for the pair density. Then, we introduce an ad-hoc modification which better accounts for both the long-range correlation, and the kinetic-energy contribution to the correlation energy. The resulting functional is local, and depends parametrically on the number of electrons in the system. We apply this functional to the homogeneous electron gas and to a set of two-dimensional quantum dots covering a wide range of electron densities and thus various amounts of correlation. In all test cases we find an excellent agreement between our results and the exact correlation energies. Our correlation functional has a form that is simple and straightforward to implement, but broadly outperforms the commonly used local-density approximation.

cond-mat.str-el↗

arXiv2008

Exchange-correlation orbital functionals in current-density-functional theory: Application to a quantum dot in magnetic fields

The description of interacting many-electron systems in external magnetic fields is considered in the framework of the optimized effective potential method extended to current-spin-density functional theory. As a case study, a two-dimensional quantum dot in external magnetic fields is investigated. Excellent agreement with quantum Monte Carlo results is obtained when self-interaction corrected correlation energies from the standard local spin-density approximation are added to exact-exchange results. Full self-consistency within the complete current-spin-density-functional framework is found to be of minor importance.

cond-mat.mtrl-sci↗

arXiv2007

Exchange-energy functionals for finite two-dimensional systems

Implicit and explicit density functionals for the exchange energy in finite two-dimensional systems are developed following the approach of Becke and Roussel [Phys. Rev. A 39, 3761 (1989)]. Excellent agreement for the exchange-hole potentials and exchange energies is found when compared with the exact-exchange reference data for the two-dimensional uniform electron gas and few-electron quantum dots, respectively. Thereby, this work significantly improves the availability of approximate density functionals for dealing with electrons in quasi-two-dimensional structures, which have various applications in semiconductor nanotechnology.

cond-mat.str-el↗

arXiv2007

Orbital currents in the Colle-Salvetti correlation energy functional and the degeneracy problem

Popular density functionals for the exchange-correlation energy typically fail to reproduce the degeneracy of different ground states of open-shell atoms. As a remedy, functionals which explicitly depend on the current density have been suggested. We present an analysis of this problem by investigating functionals that explicitly depend on the Kohn-Sham orbitals. Going beyond the exact-exchange approximation by adding correlation in the form of the Colle-Salvetti functional we show how current-dependent terms enter the Colle-Salvetti expression and their relevance is evaluated. A very good description of the degeneracy of ground-states for atoms of the first and second row of the periodic table is obtained.

cond-mat.mtrl-sci↗

arXiv2007

Comparison of exact-exchange calculations for solids in current-spin-density- and spin-density-functional theory

The relative merits of current-spin-density- and spin-density-functional theory are investigated for solids treated within the exact-exchange-only approximation. Spin-orbit splittings and orbital magnetic moments are determined at zero external magnetic field. We find that for magnetic (Fe, Co and Ni) and non-magnetic (Si and Ge) solids, the exact-exchange current-spin-density functional approach does not significantly improve the accuracy of the corresponding spin-density functional results.

cond-mat.mtrl-sci↗

arXiv2007

First-principles approach to Non-Collinear Magnetism: towards Spin-dynamics

A description of non-collinear magnetism in the framework of spin-density functional theory is presented for the exact exchange energy functional which depends explicitly on two-component spinor orbitals. The equations for the effective Kohn-Sham scalar potential and magnetic field are derived within the optimized effective potential (OEP) framework. With the example of a magnetically frustrated Cr monolayer it is shown that the resulting magnetization density exhibits much more non-collinear structure than standard calculations. Furthermore, a time-dependent generalization of the non-collinear OEP method is well suited for an ab-initio description of spin dynamics. We also show that the magnetic moments of solids Fe, Co and Ni are well reproduced.

cond-mat.mtrl-sci↗

arXiv2006

Optimized Effective Potential Method in Current-Spin Density Functional Theory

Current-spin density functional theory (CSDFT) provides a framework to describe interacting many-electron systems in a magnetic field which couples to both spin- and orbital-degrees of freedom. Unlike in usual (spin-) density functional theory, approximations to the exchange-correlation energy based on the model of the uniform electron gas face problems in practical applications. In this work, explicitly orbital-dependent functionals are used and a generalization of the Optimized Effective Potential (OEP) method to the CSDFT framework is presented. A simplifying approximation to the resulting integral equations for the exchange-correlation potentials is suggested. A detailed analysis of these equations is carried out for the case of open-shell atoms and numerical results are given using the exact-exchange energy functional. For zero external magnetic field, a small systematic lowering of the total energy for current-carrying states is observed due to the inclusion of the current in the Kohn-Sham scheme. For states without current, CSDFT results coincide with those of spin density functional theory.

cond-mat.mtrl-sci↗

arXiv2006

On the degeneracy of atomic states within exact-exchange (spin-) density functional theory

The problem of degenerate ground states of open-shell atoms is investigated in spin-restricted and unrestricted density functional theory using the exact exchange energy functional. For the spin-unrestricted case, spurious energy splittings of the order of 2 to 3 kcal/mol are found for atoms of the second and third period which is larger than the splittings obtained from recently proposed approximate exchange functionals depending explicitly on the current density. In remarkable contrast, for spin-restricted calculations the degeneracy of different atomic ground states is recovered to within less than 0.6 kcal/mol.

physics.atom-ph↗