Deformable Jellium Research Articles

Collapse of the electron gas from three to two dimensions in Kohn-Sham density functional theory

Under pressure, a quasi-two-dimensional electron gas can collapse toward the true two-dimensional (2D) limit. In this limit, the exact exchange-correlation energy per electron has a known finite limit, but general-purpose semilocal approximate density functionals, such as the local density approximation (LDA) and the Perdew-Burke-Ernzerhof generalized gradient approximation (PBE GGA), are known to diverge to minus infinity. Here we consider a model density for a noninteracting electron gas confined to a thickness $L$ by infinite-barrier walls, with a fixed 2D density $1/[\ensuremath{\pi}{({r}_{s}^{\text{2D}})}^{2}]$ and ${r}_{s}^{\text{2D}}=4$ Bohr. We estimate that LDA, PBE, and the strongly constrained and appropriately normed (SCAN) meta-GGA are accurate for the exchange-correlation energy over a wide quasi-2D range, $1.5lL/{r}_{s}^{\text{2D}}l3.85$, but not for smaller $L$. Of these functionals, only SCAN tends to a finite limit when $L$ tends to 0. Since the noninteracting kinetic energy, treated exactly in Kohn-Sham theory, dominates in this limit within a deformable jellium model, all of the general-purpose functionals can estimate the pressure required to achieve any thickness (with SCAN and LDA better than PBE). This pressure vanishes around $L/{r}_{s}^{\text{2D}}=3.85$, where the 3D electron density is roughly that of the valence electrons in metallic potassium, and it reaches about 20 GPa at $L/{r}_{s}^{\text{2D}}=1.5$ and 400 GPa at $L/{r}_{s}^{\text{2D}}=0.6$.

How metals bind: The deformable-jellium model with correlated electrons

Atoms cohere to form solids largely due to exchange and correlation. The volume is set by a balance between the expansive electronic kinetic energy and the compressive exchange-correlation energy. These effects are simply illustrated by the jellium model, in which the valence electrons neutralize a positive background charge that is rigidly uniform. But the formation of free atoms under extreme expansion is found only in the deformable-jellium model. Deformable jellium is condensed matter in miniature, displaying not only bulk cohesion with a realistic equation of state and surface effects, but also phonons and plasmons and their soft mode instabilities. By drawing an analogy with the motion of shoppers in a mall, we also discuss an intuitive picture of exchange and correlation (the tendency of electrons not to bump into other electrons or into themselves).

Compressibility of a two-dimensional electron gas

The ground-state compressibility of the two-dimensional electron gas is determined for the density region which includes the fluid to localized phase transition. The behavior of the chemical potential $\ensuremath{\mu}(\ensuremath{\rho})$ across the transition agrees qualitatively with the experimental behavior near the $B=0$ metal-insulator transition reported in the literature. The calculations are made with the self-consistent Hartree-Fock approximation and the deformable jellium model.

Three-dimensional electron gas with localization along one, two, and three directions

A powerful non-perturbative technique, which allows a direct evaluation of the ground state properties of an interacting electron gas in three dimensions, has been developed. In a unified approach, the low-, intermediate-, and high-density regions are considered. This technique is applied to three-dimensional (3D) systems with periodic electron density along one and two directions. The electronic and magnetic states of these systems are theoretically studied on the basis of the deformable jellium model, within a self-consistent Hartree–Fock approach. To determine the magnetic character of the 3D electron gas ground state, the paramagnetic and ferromagnetic energies are calculated and compared at low, intermediate, and high densities. As r s increases, several symmetry and/or magnetic transitions occur, in each system. The electronic and magnetic states obtained are compared with other theoretical results reported in the literature with different models. In addition to planar and linear periodic electron densities, cubic electron densities are considered in order to look for symmetry transitions among these systems.

Magnetic character of the two-dimensional electron gas

The energies of the paramagnetic and ferromagnetic states of the two-dimensional electron gas are evaluated and compared in order to determine the magnetic character of the ground state. The calculations are made with the self-consistent Hartree–Fock approximation and the deformable jellium model. Several transition points between different magnetic phases are obtained. At very high densities of r s≈2 a first transition is obtained from a paramagnetic fluid to a ferromagnetic one. At r st1≈4.8 a symmetry and magnetic transition is obtained from a ferromagnetic fluid to a paramagnetic localized state with a periodic density centered on a hexagonal lattice. A ferromagnetic localized state is predicted at lower densities. The results are compared with those reported for the system with square symmetry.

Thomas–Fermi approximation for the quasi‐two‐dimensional electron gas

AbstractTo take into account static correlation effects in the quasi‐two‐dimensional electron gas a screened Coulombic interaction between particles is studied. The Thomas–Fermi approximation is used and the potential screening appears as a function of the Wigner–Seitz density parameter rs and the effective width t of the system. With the self‐consistent field theory applied to the modified deformable jellium, the ground‐state energy per particle and the conditions for electron localization are obtained in terms of the interparticle distance and the screening parameter μ. A critical minimum characteristic width tc is obtained; below tc no long‐range order is obtained. For larger widths a stable localized state is predicted at finite densities. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 82: 269–276, 2001

Properties of the two-dimensional electron gas

Ground state properties of the two-dimensional electron gas are studied in the deformable jellium model. The calculations are made within the self-consistent Hartree–Fock approximation. The phase transition from plane wave solutions to the corrugated state (Wigner like transition) is analysed for two different crystallographic symmetries. A comparison of the results in the cases studied is presented. The behaviour of the energy curve is studied for a wide range of densities. Our calculations of the melting point are within an order of magnitude of experimental data.

Molecular Dynamics in Shape Space and Femtosecond Vibrational Spectroscopy of Metal Clusters

We introduce a method of molecular dynamics in shape space aimed at metal clusters. The ionic degrees of freedom are described via a dynamically deformable jellium with inertia parameters derived from an incompressible, irrotational flow. The shell correction method is used to calculate the electronic potential energy surface underlying the dynamics. Our finite temperature simulations of Ag_14 and its ions, following the negative to neutral to positive scheme, demonstrate the potential of pump and probe ultrashort laser pulses as a spectroscopy of cluster shape vibrations.

The self-consistent ground state of the two-dimensional electron gas

The self-consistent Hartree-Fock approximation and the deformable jellium model are used to describe the ground state of the two-dimensional electron gas. Improved precision in the calculations allows us to confirm the existence of a stable corrugated state at finite densities. This is strongly corroborated by an extrapolation of our results to the low-density region. A positive bulk modulus is obtained in this region. A comparison with experimental data for the melting point and our model calculation is made and agreement is found within a factor of 2.

Magnetic character of the deformable jellium.

Ground-state properties for the electron gas, in the deformable jellium, are obtained. Periodic expansions for the state function, with fermion density centered around a cubic lattice, are introduced. The paramagnetic and ferromagnetic ground-state energies are calculated and compared at each density to determine the magnetic character of the deformable jellium. More than one transition point between different magnetic phases are obtained and compared with those reported in the literature with different models. A paramagnetic region at intermediate densities, in the self-consistent Hartree-Fock approach, is recovered. At these densities a symmetry transitions from homogeneous to localized solutions is obtained for both magnetic phases, and at lower densities the electrons are localized into a paramagnetic or ferromagnetic Wigner-like crystal, respectively. \textcopyright{} 1996 The American Physical Society.

Tetragonal symmetry in the electron gas.

Two transitions to localized charge density at intermediate and low densities are obtained for the three-dimensional (3D) electron gas in the deformable jellium. At very low densities, where the second transition occurs, the tetragonal structure is obtained. A discontinuity in the coupling parameter \ensuremath{\Gamma} appears at both transition points. The evolution of the charge density is obtained and it shows translational symmetry breaking. The function \ensuremath{\Gamma} and the ground-state energy obtained in this work are compared to values reported for 3D systems with linear and planar symmetries.

Stable corrugated state of the two-dimensional electron gas.

A corrugated and stable ground state is found for the two-dimensional electron gas in both the normal paramagnetic and the fully polarized phases. The self-consistent Hartree-Fock method is used with a modulated set of trial wave functions within the deformable jellium model. The results for high metallic densities reproduce the usual noncorrugated ferromagnetic electron-gas behavior. A transition to a paramagnetic corrugated state for values of {ital r}{sub {ital s}}{approx}6.5 is predicted. At lower densities {ital r}{sub {ital s}}{approx}30, a second transition to a corrugated ferromagnetic phase is suggested.

Excited states of the deformable jellium.

Excited states of the deformable jellium.

Ground-state properties of a strongly coupled one-component plasma.

The ground state of a quantum strongly coupled one-component plasma, with planar symmetry, is analyzed. The analysis was done working with the deformable jellium model and the particle-particle interaction as a screened Coulombic potential. For the single-particle state functions, two different periodic expansions were used. We obtained the behavior of the ground-state energy per particle, the coupling parameter \ensuremath{\Gamma}, the particle localization, and the density of states as functions of the interparticle distance ${\mathit{r}}_{\mathit{s}}$.

A variational approach to the ground state of the two-dimensional electron gas

Abstract In this work we calculate a variational upper bound for the ground-state energy of the two-dimensional electron gas. The calculation sheds light on the validity of approximate calculations and indicates that the “deformable jellium” model of an ideal two-dimensional electron gas may exhibit a CDW instability for rs greater than about 2. The original feature of the calculation is that some correlation effects are included in the variational bound by means of a “geminal” expansion of the many-body wave function.

Long-range order HF states in the deformable jellium model

The authors display three different kinds of HF-type orbitals with spatial long-range order which, at low densities and/or strong coupling, are stabler than the well-known HF self-consistent plane-wave homogeneous density solutions in the deformable jellium model of the electron gas.

Self-consistent long-range order in a deformable-jellium model

A system of $N$ fermions in a box interacting via repulsive delta forces and submersed in a deformable jellium background is analyzed in terms of several non-plane-wave Hartree-Fock states which are more stable than the classic Overhauser ones for charge-density waves, and which also show long-range order.