Correlation energy of 2-D electrons

The correlation energy and the Fermi momentum of an electron gas in 2-D are evaluated explicitly as functions of density. The ring diagram and first- and second-order exchange contributions are treated. In comparison with the 3-D case, the kinetic energy for the same r_s is approximately one-half and the exchange and correlation energies are somewhat larger. The ground state energy plotted against r_s shows a minimum at around r_s = 1.65 with a minimum value of ?0.9858 Ryd. If the third-order ring contribution is added, the curve is shifted upward. The correlation energy is ?0.6258 to order e⁴. The third-order ringw contribution increases this value almost linearly with r_s. The Fermi momentum decreases with r_s due to the contribution. Different from the 3-D case, no ln r_s term appears in the correlation energy within the approximation.     

Rigorous evaluation of the ring diagram contribution to the ground state energy of an electron gas

The ground state energy and the correlation energy of an electron gas are evaluated rigorously without using the smallr _s expansion and the small momentum-transfer approximation in the ring diagram contribution and taking into consideration the first order and second order exchange graphs. The Fermi momentum is determined by solving the number density equation without using iteration and is compared with that obtained by iteration. The ground state energy is found to stay positive in contrast to the iterative solution which becomes negative beyond a certain value ofr _s .     

Electronic properties of metals at low temperatures

A many body theory of an electron gas is developed to find the internal and correlation energies at low but finite temperatures. The contribution from the first order exchange, second order (regular and anomalous) exchange, and ring diagrams are treated. The Fermi momentum and the correlation energy are determined as functions of the density by two different methods, one being based on iteration and the other a direct solution of the number density relation. It was found that the iterative solutions which are correct to ordere ² ore ⁴ become negative forr _s of order 5 while the direct solutions do not, indicating the invalidity of the former. Hence, the correlation energy evaluated to the same orders by iteration will not be satisfactory in the same range. The highest order iterative solution which includes terms of ordere ⁶ does not show such a breakdown. These terms which give the contribution of orderr _s to the correlation energy are therefore important and tend to reduce the magnitude of the correlation energy. The corresponding curve is indeed close to that determined by the direct method for smallr _s but a significant deviation takes place at largerr _s . The Coulomb interaction seems less effective at higher temperatures. The internal energy is also determined as a function of density and temperature.     

Spatial correlations in the electron gas: Path integral Monte Carlo simulation

Thermally excited states of the three-dimensional electron gas in a neutralizing background are computed by path integral Monte Carlo simulation for values of the Wigner-Seitz radius within the interval 5 < r _s < 15. Coulomb and exchange interactions, permutation symmetry, and spin state are treated explicitly. Variation of electron correlation functions with density and temperature is analyzed. Quantum effects suppress and enhance spatial correlation at low and high densities, respectively. Transition between the electron-gas states characterized by these opposite trends corresponds to a density of approximately 2.5 × 10²¹ cm^?3. A transition line between liquid-like and gaslike phases is determined in the temperature-density diagram. Weak anisotropy of many-body correlations in the liquid-like state stimulates excitation of spherically symmetric collective rotational modes. The effective short-range pseudopotential exhibits strong temperature dependence due to exchange effects. For strongly correlated systems, the characteristic screening length deviates from that predicted by the Thomas-Fermi screening model ( $ \sim \sqrt {r_s } $ ), approaching a linear function of r _s. The effective short-range interaction substantially differs from the Yukawa potential in mean field theory. Coulomb interaction shifts the Fermi level up by an order of magnitude or higher, and this effect becomes stronger with decreasing density.     

Multicomponent dense electron gas as a model of Si MOSFET

We solve a 2D model of N-component dense electron gas in the limit N→∞ and in the range of the Coulomb interaction parameter N ^?3/2?r _s ?1. The quasiparticle interaction on the Fermi circle vanishes as ?²/Nm. The ground-state energy and the effective mass are found as series in powers of r _s ^2/3 . In the quantum Hall state on the lowest Landau level at integer filling 1?ν<N, the charge-activation-energy gap and the exchange constant are Δ=log(r _s N^3/2)?ω_H/ν and J=0.66?ω_H/ν.     

Ground state properties of nuclear matter

The ground state properties of nuclear matter are calculated in theΛ ₁₁-approximation¹. A nucleon-nucleon interaction of the Yamaguchi-type and thes-wave part ofTabakin's potential have been considered. In both cases too large values for the density of nuclear matter and the binding energy per nucleon are found. The momentum distribution turns out to be very small for momenta larger than the Fermi momentum.     

On the ground state energy of a two-dimensional electron fluid

A new theory of the ground state energy of a two-dimensional electron fluid is presented. It is shown that the ring diagram contribution changes its analytical behavior atr _s =2^1/2, wherer _s is the usual density parameter defined by r_S = 1/a ₀(π n)^1/2,a ₀ being the Bohr radius andn is the electron density. For smallr _s , a high density series is obtained in agreement with the previous calculation. For larger _s , a hitherto unknown low density series is obtained. In the low density region, the first order exchange energy is completely cancelled out by a term from the ring contribution so that the ground state energy decreases in proportion tor _s ^?2/3 , followed byr _s ^/?4/3 and higher order terms. The energy is found to be minimum atr _s=1.4757, the minimum value being ?0.481915 Rydbergs.     

Ground-state properties of jellium metals with low electron densities

The ground state of a three-dimensional electron gas is theoretically investigated within the framework of the local spin density approximation with the Perdew–Zunger exchange-correlation energy. The system has been found to be in a one- or two-dimensional crystal state, when the Wigner sphere radius r_s has an intermediate value. At r_s=60, a triangular lattice with the lattice spacing 96.10 is the lowest energy state among fluids, 1D, 2D, and 3D crystals.     

Single-particle spectrum of a dilute 2D electron gas

Single-particle spectra of a homogeneous 2D electron gas have been calculated in the microscopic functional approach. The effective mass in this system is found to diverge at r _s ? 7. It is shown that the inclusion of the local exchange and correlation corrections to the effective interaction modifies the instability picture from that obtained in the random phase approximation: in the latter, the instability arises away from the Fermi surface, whereas, with the introduction of the corrections, it manifests itself as the divergence of the effective mass.     

THE EFFECT OF LATTICE VIBRATION ON THE MAGNETISM IN METALLIC HYDROGEN

In this note, a new approach is adopted to the magnetism in metallic hydrogen, i.e., based on the Kim theory and Stoner model the electron-phonon interaction is introduced into the itinerant electron mag-netism theory. A calculation of spontaneous magnetization of metallic hydrogen at T=0 K shows that in spite of no change in the para- to ferro-magnetism value, r_sc of W-S radius r_s, the spontaneous magnetic moment of electron in ferromagnetic state, where r_s>>r_sc, is considerably reduced by lattice vibrations.     

Effect of a lattice upon an interacting system of electrons in two dimensions: Breakdown of scaling and decay of persistent currents

The ground state of an electron gas is characterized by the interparticle spacing to the effective Bohr radius ratio r _s = a/a _B ^*. For polarized electrons on a two dimensional square lattice with Coulomb repulsion, we study the threshold value r _s ^* below which the lattice spacing s becomes a relevant scale and r _s ceases to be the scaling parameter. For systems of small ratios s/a _B ^*, s becomes only relevant at small r _s (large densities) where one has a quantum fluid with a deformed Fermi surface. For systems of large s/a _B ^*, s plays also a role at large r _s (small densities) where one has a Wigner solid, the lattice limiting its harmonic vibrations. The thermodynamic limit of physical systems of different a _B ^* is qualitatively discussed, before quantitatively studying the lattice effects occurring at large r _s . Using a few particle system, we compare exact numerical results obtained with a lattice and analytical perturbative expansions obtained in the continuum limit. Three criteria giving similar values for the lattice threshold r _s ^* are proposed. The first one is a delocalization criterion in the Fock basis of lattice site orbitals. The second one uses the persistent current which can depend on the interaction in a lattice, while it becomes independent of the interaction in the continuum limit. The third one takes into account the limit imposed by the lattice to the harmonic vibrations of the electron solid.Received: 20 January 2004, Published online: 18 June 2004PACS: 71.10.-w Theories and models of many-electron systems - 71.10.Fd Lattice fermion models (Hubbard model, etc.) - 73.20.Qt Electron solids     

Effects of electron interaction on the change in sound velocity under de Haas-van Alphen conditions

Based on a temperature propagator technique in the grand ensemble of an interacting electron gas, the oscillatory sound velocity is examined under the de Haas-van Alphen conditions. In consideration of the oscillation of the Fermi energy (chemical potential) and the first order exchange effects, the dHvA oscillations of the sound velocity are shown to have the same one phase as in the case of an ideal electron gas, in agreement with experimental results. For large electron density, that is, for very small r_s, and by a proper renormalization of the Fermi energy, we have succeeded in eliminating one of the two oscillatory functions which have a phase difference of $\text{π}\text{2}$.     

Thermodynamics of an interacting Fermi system in the static fluctuation approximation

We suggest a new method of calculation of the equilibrium correlation functions of an arbitrary order for the interacting Fermi-gas model in the framework of the static fluctuation approximation method. This method based only on a single and controllable approximation allows obtaining the so-called far-distance equations. These equations connecting the quantum states of a Fermi particle with variables of the local field operator contain all necessary information related to the calculation of the desired correlation functions and basic thermodynamic parameters of the many-body system. The basic expressions for the mean energy and heat capacity for the electron gas at low temperatures in the high-density limit were obtained. All expressions are given in the units of r _s , where r _s determines the ratio of a mean distance between electrons to the Bohr radius a ₀. In these expressions, we calculate terms of the respective order r _s and r _s ². It is also shown that the static fluctuation approximation allows finding the terms related to higher orders of the decomposition with respect to the parameter r _s .     

Nuclear matter approach to the heavy-ion optical potential: (II). Imaginary part

The heavy-ion optical potentials are constructed in a nuclear matter approach, for the ¹⁶O + ¹⁶O, ⁴⁰Ca + ¹⁶O and ⁴⁰Ca + ⁴⁰Ca elastic scattering at the incident energies per nucleon E^lab/A ? 45 MeV. The energy density formalism is employed assuming that the complex energy density of colliding heavy ions is a functional of the nucleon density ?(r), the intrinsic kinetic energy density τ⁽²⁾(r) and the average momentum of relative motion per nucleon K_r(≦ 1.5 fm^?1). The complex energy density is numerically evaluated for the two units of colliding nuclear matter with the same values of ρ, τ⁽²⁾ and K_r. The Bethe-Goldstone equation is solved for the corresponding Fermi distribution in momentum space using the Reid soft-core interaction. The “self-consistent” single-particle potential for unoccupied states which is continuous at the Fermi surface plays a crucial role to produce the imaginary part. It is found that the calculated optical potentials become more attractive and absorptive with increasing incident energy. The elastic scattering and the reaction cross sections are in fair agreement with the experimental data.     

Cluster studies of CO adsorption: II. CO on small Al clusters

Results for the free-electron-like metal Al (r_s = 2.07 bohr) are compared with previous Li (r_s = 3.25 bohr) results. From an analysis of the various contributions to the total adsorption energy (steric interaction, σ-bonding, π-backbonding) as a function of the CO height above the surface, and the adsorption site, it appears that high conduction electron density leads to strong exchange repulsion. At the top site this effect is partly cancelled by the favourable interaction possibilities with Al 3p functions. The most striking differences with Li are thus the very weak adsorption at the hollow site, and stronger adsorption at the top site.     

Grundzustand eines Fermi-Gases mit hard-sphere-Wechselwirkung

The decomposition of the ground state wave function of a Fermi gas interacting via hard core potentials into cluster functionsS _n leads to a systematic expansion of wave function and energy in powers of the parameterc=P _F r _c (r _c =hard core radius,P _F =Fermi momentum). For instance,S _n has the order of magnitudec ^n-λ-1, if λ=number of Fermion coordinates with distances smaller thanr _c . The first three energy terms agree with the ones given by other authors. Any occurrence of singular terms in the intermediate steps of the derivation can be avoided     

The specific heat of a degenerate electron gas

The internal energy of a degenerate electron gas is evaluated for finite temperature to first order ine ² by applying the Sommerfeld method to the grand partition function. The specific heat is obtained correctly by temperature differentiation in which the shift of the Fermi momentum from the ideal gas value is taken into consideration. Thus, this theory differs from those given previously by Pines, Gell-Mann and others. In fact, there appears no divergence such as encountered by Gell-Mann in his approximate approach. The specific heat thus evaluated increases slightly withr _s in agreement with recent experimental data on alkali metals. This work was supported by the National Science Foundation.     

On the solid-like phase transition in crystals of polystyrene spheres in aqueous suspensions

We present results of calculations for the fractional energy difference between the bcc and fcc phases present in ordered systems of polystyrene spheres in aqueous suspensions. The theoretical model developed for those systems is an extension of the concept of a Wigner lattice. The interaction between the particles is assumed to be a screened coulomb potential. We conclude that the phase transition occurs when λr₅ = 1.05 where λ^-1 is the Debye screening length and r_s is the radius of the spherical volume of the unitary cell.     

Electronic properties of iron arsenic high temperature superconductors revealed by angle resolved photoemission spectroscopy (ARPES)

We present an overview of the electronic properties of iron arsenic high temperature superconductors with emphasis on low energy band dispersion, Fermi surface and superconducting gap. ARPES data is compared with full-potential linearized plane wave (FLAPW) calculations. We focus on single layer NdFeAsO_0.9F_0.1 (R1111) and two layer Ba_1?xK_xFe₂As₂ (B122) compounds. We find general similarities between experimental data and calculations in terms of character of Fermi surface pockets, and overall band dispersion. We also find a number of differences in details of the shape and size of the Fermi surfaces as well as the exact energy location of the bands, which indicate that magnetic interaction and ordering significantly affects the electronic properties of these materials. The Fermi surface consists of several hole pockets centered at Γ and electron pockets located in zone corners. The size and shape of the Fermi surface changes significantly with doping. Emergence of a coherent peak below the critical temperature T_c and diminished spectral weight at the chemical potential above T_c closely resembles the spectral characteristics of the cuprates, however the nodeless superconducting gap clearly excludes the possibility of d-wave order parameter. Instead it points to s-wave or extended s-wave symmetry of the order parameter.     

Resonant scattering of light in a near-black-hole metric

We show that low-energy photon scattering from a body with radius R slightly larger than its Schwarzschild radius r _s resembles black-hole absorption. This absorption occurs via capture resulting in one of the many long-lived, densely packed resonances that populate the continuum. The lifetimes and density of these meta-stable states tend to infinity in the limit r _s →R. We determine the energy-averaged cross section for particle capture into these resonances and show that it is equal to the absorption cross section for a Schwarzschild black hole. Thus a non-singular static metric may trap photons for arbitrarily long times, making it appear completely ‘black’ before the actual formation of a black hole.