arXiv subjects

C. R. Proetto

Publications and source records attributed to C. R. Proetto.

At least 19 recordsLinked to original sources

arXiv2022

Semilocal approximations to the Kohn-Sham exchange potential as applied to a metal surface

Several semilocal exchange potentials usually employed in the framework of density-functional theory (DFT) are tested and compared with their exact counterpart, the exchange Optimized Effective Potential (OEP), as applied to the jellium-slab model of a metal-vacuum interface. Driven by their explicit dependence on the ground-state density, its gradient, and its kinetic-energy density, the three analyzed semilocal exchange potentials approach their respective asymptotic limits faster than in the case of the OEP, all of them having an asymptotic scaling of the form $-α\,e^2/z + V_{\infty}$, with $α< 1$. Here we provide the leading analytic asymptotics of the three model potentials under study, and we find that none of them exhibits the exact OEP slab asymptotics $-\;e^2/z$. While the so-called Becke-Roussel potential's leading asymptote is close to its exact OEP counterpart, the other two model potentials under study approach a material-dependent positive constant value far into the vacuum, resulting in considerably overestimated ionization potentials.

cond-mat.str-el↗

arXiv2021

Asymptotics of the metal-surface Kohn-Sham exact exchange potential revisited

The asymptotics of the Kohn-Sham (KS) exact exchange potential $V_x(z)$ of a jelliumlike semi-infinite metal is investigated, in the framework of the optimized-effective-potential formalism of density-functional theory. Our numerical calculations clearly show that deep into the vacuum side of the surface $V_x(z) \propto e^2 \ln(az) / z$, with $a$ being a system-dependent constant, thus confirming the analytical calculations reported in Phys. Rev. B {\bf 81}, 121106(R) (2010). A criticism of this work published in Phys. Rev. B {\bf 85}, 115124 (2012) is shown to be incorrect. Our rigorous exchange-only results provide strong constraints both for the building of approximate exchange functionals and for the determination of the still unknown KS correlation potential.

cond-mat.str-el↗

arXiv2019

Exact factorization-based density functional theory of electron-phonon systems

Density functional theory is generalized to incorporate electron-phonon coupling. A Kohn-Sham equation yielding the electronic density $n_U(\mathbf{r})$, a conditional probability density depending parametrically on the phonon normal mode amplitudes $U=\{U_{\mathbf{q}λ}\}$, is coupled to the nuclear Schrödinger equation of the exact factorization method. The phonon modes are defined from the harmonic expansion of the nuclear Schrödinger equation. A nonzero Berry curvature on nuclear configuration space affects the phonon modes, showing that the potential energy surface alone is generally not sufficient to define the phonons. An orbital-dependent functional approximation for the non\-adiabatic exchange-correlation energy reproduces the leading-order nonadiabatic electron-phonon-induced band structure renormalization in the Fröhlich model.

cond-mat.mtrl-sci↗

arXiv2018

Exact-exchange density functional theory of the integer quantum Hall effect: strict 2D limit

A strict bidimensional (strict-2D) exact-exchange (EE) formalism within the framework of density-functional theory (DFT) has been developed and applied to the case of an electron gas subjected to a strong perpendicular magnetic field, that drives the system to the regime of the integer quantum Hall effect (IQHE). As the filling of the emerging Landau levels proceeds, two main features results: i) the EE energy minimizes with a discontinuous derivative at every integer filling factor $ν$; and ii) the EE potential display sharp discontinuities at every integer $ν$. The present contribution provides a natural improvement as compared with the widely used local-spin-density approximation (LSDA), since the EE energy functional fully contains the effect of the magnetic field, and includes an inter-layer exchange coupling for multilayer systems. As a consistency test, the LSDA is derived as the leading term of a low-field expansion of the EE energy and potential.

cond-mat.mes-hall↗

arXiv2017

Exact Exchange: a pathway for a Density Functional Theory of the Integer Quantum Hall Effect

It is shown here that the Exact Exchange (EE) formalism provides a natural and rigorous approach for a Density Functional Theory (DFT) of the Integer Quantum Hall Effect (IQHE). Application of a novel EE method to a quasi two-dimensional electron gas (q2DEG) subjected to a perpendicular magnetic field leads to the following main findings. \textit{i)} the microscopic exchange energy functional of the IQHE has been obtained, whose main feature being that it minimizes with a discontinuous derivative at every integer filling factor $ν$; \textit{ii)} an analytical solution is found for the magnetic-field dependent EE potential, in the one-subband regime; \textit{iii)} as a consequence of \textit{i)}, the EE potential display sharp discontinuities at every integer $ν$; and \textit{iv)} the widely used Local Spin Density Approximation (LSDA) is strongly violated for filling factors close to integer values.

cond-mat.mes-hall↗

arXiv2016

Kohn-Sham potential for a strongly correlated finite system with fractional occupancy

Using a simplified one-dimensional model of a diatomic molecule, the associated interacting density and corresponding Kohn-Sham potential have been obtained analytically for all fractional molecule occupancies $N$ between 0 and 2. For the homonuclear case, and in the dissociation limit, the exact Kohn-Sham potential builds a barrier at the midpoint between the two atoms, whose strength increases linearly with $N$, with $1 < N \leq 2$. In the heteronuclear case, the disociating KS potential besides the barrier also exhibits a plateau around the atom with the higher ionization potential, whose size (but not its strength) depends on $N$. An anomalous zero-order scaling of the Kohn-Sham potential with regards to the strength of the electron-electron repulsion is clearly displayed by our model; without this property both the unusual barrier and plateau features will be absent.

physics.atom-ph↗

arXiv2016

Coulomb and tunneling coupled trilayer systems at zero magnetic field

The ground-state electronic configuration of three coupled bidimensional electron gases has been determined using a variational Hartree-Fock approach, at zero magnetic field. The layers are Coulomb coupled, and tunneling is present between neighboring layers. In the limit of small separation between layers, the tunneling becomes the dominant energy contribution, while for large distance between layers the physics is driven by the Hartree electrostatic energy. Transition from tunneling to hartree dominated physics is shifted towards larger layer separation values as the total bidimensional density of the trilayers decreases. The inter-layer exchange helps in stabilize a "balanced" configuration, where the three layers are approximately equally occupied; most of the experiments are performed in the vicinity of this balanced configuration. Several ground-state configurations are consequence of a delicate interplay between tunneling and inter-subband exchange.

cond-mat.mes-hall↗

arXiv2016

Pseudospin anisotropy of trilayer semiconductor quantum Hall ferromagnets

When two Landau levels are brought to a close coincidence between them and with the chemical potential in the Integer Quantum Hall regime, the two Landau levels can just cross or collapse while the external or pseudospin field that induces the alignment changes. In this work, all possible crossings are analyzed theoretically for the particular case of semiconductor trilayer systems, using a variational Hartree-Fock approximation. The model includes tunneling between neighboring layers, bias, intra-layer and inter-layer Coulomb interaction among the electrons. We have found that the general pseudospin anisotropy classification scheme used in bilayers applies also to the trilayer situation, with the simple crossing corresponding to an easy-axis ferromagnetic anisotropy analogy, and the collapse case corresponding to an easy-plane ferromagnetic analogy. An isotropic case is also possible, with the levels just crossing or collapsing depending on the filling factor and the quantum numbers of the two nearby levels. While our results are valid for any integer filling factor $ν$ (=1,2,3,...), we have analyzed in detail the crossings at $ν=3$ and $4$, and we have given clear predictions that will help in their experimental search. In particular, the present calculations suggest that by increasing the bias, the trilayer system at these two filling factors can be driven from an easy-plane anisotropy regime to an easy-axis regime, and then can be driven back to the easy-plane regime. This kind of reentrant behavior is an unique feature of the trilayers, compared with the bilayers.

cond-mat.mes-hall↗

arXiv2014

The virial theorem and exact properties of density functionals for periodic systems

In the framework of density functional theory, scaling and the virial theorem are essential tools for deriving exact properties of density functionals. Preexisting mathematical difficulties in deriving the virial theorem via scaling for periodic systems are resolved via a particular scaling technique. This methodology is employed to derive universal properties of the exchange-correlation energy functional for periodic systems.

cond-mat.other↗

arXiv2011

Exact conditions and scaling relations in finite temperature density functional theory

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.

cond-mat.stat-mech↗

arXiv2010

Parameter-free density functional for the correlation energy in two dimensions

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.

cond-mat.str-el↗

arXiv2010

Localized versus extended systems in density-functional theory: some lessons from the Kohn-Sham exact exchange potential

A long-standing puzzle in density-functional theory is the issue of the long-range behavior of the Kohn-Sham exchange-correlation potential at metal surfaces. As an important step towards its solution, it is proved here, through a rigurouos asymptotic analysis and accurate numerical solution of the Optimized-Effective-Potential integral equation, that the Kohn-Sham exact exchange potential decays as $\ln(z)/z$ far into the vacuum side of an {\it extended} semi-infinite jellium. In contrast to the situation in {\it localized} systems, like atoms, molecules, and slabs, this dominant contribution does not arise from the so-called Slater potential. This exact-exchange result provides a strong constraint on the suitability of approximate correlation-energy functionals.

cond-mat.mtrl-sci↗

arXiv2009

Position-dependent exact-exchange energy for slabs and semi-infinite jellium

The position-dependent exact-exchange energy per particle $\varepsilon_x(z)$ (defined as the interaction between a given electron at $z$ and its exact-exchange hole) at metal surfaces is investigated, by using either jellium slabs or the semi-infinite (SI) jellium model. For jellium slabs, we prove analytically and numerically that in the vacuum region far away from the surface $\varepsilon_{x}^{\text{Slab}}(z \to \infty) \to - e^{2}/2z$, {\it independent} of the bulk electron density, which is exactly half the corresponding exact-exchange potential $V_{x}(z \to \infty) \to - e^2/z$ [Phys. Rev. Lett. {\bf 97}, 026802 (2006)] of density-functional theory, as occurs in the case of finite systems. The fitting of $\varepsilon_{x}^{\text{Slab}}(z)$ to a physically motivated image-like expression is feasible, but the resulting location of the image plane shows strong finite-size oscillations every time a slab discrete energy level becomes occupied. For a semi-infinite jellium, the asymptotic behavior of $\varepsilon_{x}^{\text{SI}}(z)$ is somehow different. As in the case of jellium slabs $\varepsilon_{x}^{\text{SI}}(z \to \infty)$ has an image-like behavior of the form $\propto - e^2/z$, but now with a density-dependent coefficient that in general differs from the slab universal coefficient 1/2. Our numerical estimates for this coefficient agree with two previous analytical estimates for the same. For an arbitrary finite thickness of a jellium slab, we find that the asymptotic limits of $\varepsilon_{x}^{\text{Slab}}(z)$ and $\varepsilon_{x}^{\text{SI}}(z)$ only coincide in the low-density limit ($r_s \to \infty$), where the density-dependent coefficient of the semi-infinite jellium approaches the slab {\it universal} coefficient 1/2.

cond-mat.other↗

arXiv2009

On the lower bound on the exchange-correlation energy in two dimensions

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.

cond-mat.str-el↗

arXiv2009

Non-collinear spin-spiral phase for the uniform electron gas within Reduced-Density-Matrix-Functional Theory

The non-collinear spin-spiral density wave of the uniform electron gas is studied in the framework of Reduced-Density-Matrix-Functional Theory. For the Hartree-Fock approximation, which can be obtained as a limiting case of Reduced-Density-Matrix-Functional Theory, Overhauser showed a long time ago that the paramagnetic state of the electron gas is unstable with respect to the formation of charge or spin density waves. Here we not only present a detailed numerical investigation of the spin-spiral density wave in the Hartree-Fock approximation but also investigate the effects of correlations on the spin-spiral density wave instability by means of a recently proposed density-matrix functional.

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

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

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↗