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Modern Physics Letters B

DIELECTRIC SCREENING IN CHARGED BOSE VERSUS FERMI LIQUIDS

M. L. Chiofalo, Sergio Conti, M. P. Tosi

Published Aug 30, 1994• 10 citations
Publisher

Abstract

We briefly review the available theoretical results on dielectric screening properties of a fluid of charged bosons at zero temperature in comparison with those of a fluid of charged fermions. The paper is intended to highlight for the nonspecialists the differences in behavior that arise from the difference in statistics. After a general introduction to the dielectric screening function and to the local field factor accounting for exchange and correlation in dielectric screening, we focus on (i) the dependence of the static dielectric function on wave number and the screening of a charged impurity, (ii) the structure factor, the pair distribution function, and the ground state energy, and (iii) the spectrum of collective excitations. The review is concluded with some remarks on open questions and possible further developments.

DOI
10.1142/s0217984994001205

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We briefly review the available theoretical results on dielectric screening properties of a fluid of charged bosons at zero temperature in comparison with those of a fluid of charged fermions. The paper is intended to highlight for the nonspecialists the differences in behavior that arise from the difference in statistics. After a general introduction to the dielectric screening function and to the local field factor accounting for exchange and correlation in dielectric screening, we focus on (i) the dependence of the static dielectric function on wave number and the screening of a charged impurity, (ii) the structure factor, the pair distribution function, and the ground state energy, and (iii) the spectrum of collective excitations. The review is concluded with some remarks on open questions and possible further developments.
The dielectric screening function epsilon (k, omega ) of the fluid of charged bosom at zero temperature is evaluated in a range of low-to-intermediate coupling strength, in view of recent data on static screening and fluid structure from quantum Monte Carlo methods. Correlations beyond the random phase approximation are included within a class of approximations which are well known for the electron fluid, i.e. by introducing a frequency-independent local field factor to be determined through self-consistency requirements connecting various aspects of the physics contained in the dielectric function. The static dielectric function epsilon (k,0) is negative over a range of wavenumbers at all values of the density, leading to oscillatory screening of a foreign charge and to an effective long-range attraction between equi-charged impurities. Quantitative agreement with the Monte Carlo data on static screening is achieved by imposing self-consistency on the compressibility of the fluid in addition to self-consistency on the pair distribution function. Good agreement is also obtained on the pair distribution function and the correlation energy. Within the present class of approximations, the dispersion relation of longitudinal excitations takes the Feynman form, starting at the plasma frequency with a negative dispersion coefficient and going through a minimum before ending at the single-particle recoil frequency.
The dielectric function of a charged Bose gas is determined from the response to an imposed static sinusoidal electric field. Variational and diffusion quantum Monte Carlo simulations are used to calculate the ground-state properties of the system with trial wave functions containing a parameter dependent on the amplitude and wavelength of the perturbation. The induced charge is most efficiently extracted from the difference in ground-state energies at different magnitudes of the external field, rather than directly from the expectation value of the density fluctuation operator. Results are compared to the random-phase approximation for the weakly coupled fluid and to classical lattice values at low densities where the system forms a Wigner crystal. The dielectric function is also calculated at intermediate fluid densities and the transition from positive to negative response is found to occur in the metallic regime.
Some properties of a two-dimensional charged Bose gas interacting with a ln(r) potential are investigated on the basis of a self-consistent-field formalism which includes the short-range correlations between bosons through a local-field correction depending on the pair correlation function. Numerical results for the static structure factor, pair correlation function, spectrum of elementary excitations, and the response of the system to a static impurity charge are presented. Our results show the same qualitative behavior as those of the three-dimensional analog but the correlation effects are somewhat more pronounced in two dimensions.
The ground state of a double-layer charged Bose system is investigated beyond the random-phase approximation by including the many-body correlation effects. The correlations within the layer are accounted for within the self-consistent theory of Singwi, Tosi, Land, and Sj\"olander, while we have neglected the effect of interlayer correlations. The static susceptibility, the elementary excitation spectrum, and the static screened potentials are calculated and their dependence on the boson number density and the layer spacing is examined. Results are compared with the recent work of Tanatar and Das where correlations are not included. It is found that the inclusion of correlation effects combined with the interlayer interactions can significantly alter the nature of the ground state and, in particular, can favor an inhomogeneous charge-density-wave ground state. A comparison is also made in terms of screened potentials with the double-layer electron system that enables one to have a deeper insight into the role played by the exchange and Coulomb correlations separately.
We study the two-dimensional gas of charged bosons interacting via a logarithmic potential within the quantal hypernetted-chain approximation. The pair correlation function, the static structure factor, the ground-state energy, and the spectrum of collective excitations are calculated over a range of the density parameter rs.{r}_{s}.rs​. We find that the static and dynamical properties are described rather well in this approach in comparison to previous theories. Our results are in good agreement with the available quantum Monte Carlo simulations.
The ground state of a charged Bose gas is studied throughout a large range of densities in a self-consistent-field approximation formalism which includes the short-range correlations between bosons through a local-field correction. Numerical self-consistent calculations have been carried out in order to determine the static structure factor $S(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}})$. Hence, from $S(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}})$ we have obtained the pair-correlation functions, the ground-state energy which essentially is the correlation energy, the pressure of the gas, and, from Feynman's relation, the energy spectrum of elementary excitations. The response of the system to a static impurity charge has also been investigated. In the high-density limit our calculations show the same results as those given by Bogoliubov's perturbation theory. In the intermediate-density region, corresponding to the strongly coupled system, our results are in very good agreement with recent calculations based on the hypernetted-chain integral equation as well as Monte Carlo computations.