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arXiv:cond-mat/0204018

Condensate of a charged boson fluid at non-integer dimensions

Sang-Hoon Kim, Chul Koo Kim, Kyun Nahm

Published Apr 1, 2002• 0 citations
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Abstract

Condensate of a charged boson fluid at non-integer dimensions between 2 and 3 is studied. Interaction between particles is assumed to be Coulombic, and Bogoliubov approximation is applied for a weak coupling regime. The condensate and the superfluid fraction at finite temperatures and at non-integer dimensions are calculated. The theoretical results are compared with the superfluid densities of superconducting films, which show a universal splitting behavior. The qualitative similarity between the charged boson fluid and the superconducting films gives a strong clue for the origin of the universality.

DOI
10.48550/arxiv.cond-mat/0204018

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Condensate of a charged boson fluid at non-integer dimensions between 2 and 3 is studied. Interaction between particles is assumed to be Coulombic, and Bogoliubov approximation is applied for a weak coupling regime. The condensate and the superfluid fraction at finite temperatures and at non-integer dimensions are calculated. The theoretical results are compared with the superfluid densities of superconducting films, which show a universal splitting behavior. The qualitative similarity between the charged boson fluid and the superconducting films gives a strong clue for the origin of the universality.
The Bogoliubov--de Gennes equations are solved for the Coulomb Bose gas describing a fluid of charged bosons at finite temperature. The approach is applicable in the weak-coupling regime and the extent of its quantitative usefulness is tested in the three-dimensional fluid, for which diffusion Monte Carlo data are available on the condensate fraction at zero temperature. The one-body density matrix is then evaluated by the same approach for the two-dimensional fluid with e2/r{e}^{2}/re2/r interactions, to demonstrate the presence of a quasicondensate from its power-law decay with increasing distance and to evaluate the superfluid fraction as a function of temperature at weak coupling.
We study the condensate and superfluid fraction of a homogeneous gas of weakly interacting bosons in three spatial dimensions by adopting a self-consistent Popov approximation, comparing this approach with other theoretical schemes. Differently from the superfluid fraction, we find that at finite temperature the condensate fraction is a non-monotonic function of the interaction strength, presenting a global maximum at a characteristic value of the gas parameter, which grows as the temperature increases. This non-monotonic behavior has not yet been observed, but could be tested with the available experimental setups of ultracold bosonic atoms confined in a box potential. We clearly identify the region of parameter space that is of experimental interest to look for this behavior and provide explicit expressions for the relevant observables. Finite size effects are also discussed within a semiclassical approximation.
A new approach developed in Ref.1 for investigating the spatial boson correlations at low temperatures is considered in the particular case of the Coulomb interaction potential. This approach is based on integro–differential equations for the radial distribution function and can be used beyond the weak coupling regime. PACS: 05.30.Jp, 67.90.+z Description of the charged Bose liquid, or, in other words, of the strongly correlated many–boson system with the Coulomb interparticle potential, is a long–standing problem of the condensed matter physics. Recently, interest in this problem has been renewed in the connection with the noteworthy results of applying the Bose and Bose–Fermi liquid models [2] to the explanation of various phenomena inherent in the superconductors with high critical temperatures. These models are based on the Bogoliubov approach [3] implying the weak coupling regime. For the system of charged bosons the weak coupling approximation can be used at small values of the Brueckner parameter rS ∼ 0.1. However, questions requiring detailed investigations often concern the materials with relatively low densities of charge carriers which correspond to rS−values even larger than those of the electron gas at 1 the metallic densities. For example, there are the results [4] testifying to the possibility of forming the so–called large bipolaron (e.g. the two–electron cluster with a large radius of electron–electron separation, see papers in Ref. [5]) inside the polaron environment at the electron densities ∼ 10 19 cm −3 close to the carrier densities of the heavily doped degenerate polar semiconductors. To investigate the possible phase transition of the charge carrier system from the polaron state to the bipolaron phase at these densities, one should operate with the charged Bose liquid of large bipolarons for rS ≫ 1. Indeed, the ”large–bipolaron“ Bohr radius can be expressed [4] as abip =
We critically examine the Hartree-Fock-Bogoliubov (HFB) solution of the equations of motion for condensate fluctuations in a weakly coupled plasma of charged bosons at finite temperature. Analytic expressions are derived for the first two infrared-divergent terms in both the momentum distribution of the noncondensate and the anomalous Bose correlation function at low momenta. Incorporation into the theory of the appropriate form of the Hugenholtz-Pines relation for the chemical potential is needed to cancel an unphysical divergence. Exact cancellation of infrared-divergent terms is demonstrated in the HFB shift of the single-particle excitation energy away from the Bogoliubov value at long wavelengths, with the residual terms raising it towards the plasma frequency at low temperature. Numerical illustrations are presented for a number of properties of the boson plasma as functions of temperature and density in the weak-coupling regime: these are the chemical potential, the condensate fraction, the normal and anomalous momentum distribution functions and the corresponding one-body density matrices, and the dispersion relation of single-particle excitations.
Two unrelated problems can be reduced to a model of a Bose gas interacting with a gauge field: (i) the effect of thermal fluctuations on a system of vortices in bulk superconductors in fields Hc1{\mathit{H}}_{\mathit{c}1}Hc1​\ensuremath{\ll}H\ensuremath{\ll}Hc2{\mathit{H}}_{\mathit{c}2}Hc2​, and (ii) charged, spinless excitations in two-dimensional (2D) strongly correlated electron systems. Both problems are important for the theory of high-temperature superconductors. We study this model in three regimes: at finite temperatures, assuming that the gauge field is purely transverse; at T=0, for the purely static (2D Coulomb) interaction; and at T=0, for a weak Coulomb interaction and a strong transverse one. Transverse interactions suppress the temperature of the superfluid transition significantly. A sufficiently strong transvese interaction is shown to produce a phase separation as the temperature decreases (in the absence of Coulomb repulsion). If there is Coulomb repulsion, the ground state does not have off-diagonal long-range order but the superfluid density is not zero unless the Coulomb constant exceeds a critical value. Sufficiently strong coupling to the transverse field destroys superfluidity as well. In the normal state formed at large couplings, the translational invariance is intact. We propose a bosonic ground state that is not superfluid at T=0. We discuss the implications of these results both for vortex liquids and strongly correlated electron systems.
Abstract At zero temperature, homogeneous interacting Bose-condensed fluids are entirely superfluid, with remarkable transport properties. A non-superfluid, normal component is induced by finite temperatures and spatial inhomogeneity, the combined effects of which are rather intriguing, and difficult to describe quantitatively. By inhomogeneous Bogoliubov theory, applicable to weakly interacting condensed Bose gases in static external potentials with arbitrary spatial correlations, we calculate the normal fluid density via the transverse current–current correlation. We obtain finite-temperature disorder corrections to the normal fraction known since Laudau’s seminal two-fluid theory, using diagrammatic perturbation theory for systems of any dimensionality, with closed analytical expressions to leading, quadratic order in disorder strength.