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arXiv:cond-mat/0107453 · Physical review. B, Condensed matter

Two-particle pairing and phase separation in a two-dimensional Bose gas with one or two sorts of bosons

M. Yu. Kagan, Dmitri V. Efremov

Published Apr 18, 2002• 38 citations

Abstract

We present a phase diagram for a dilute two-dimensional Bose gas on a lattice. For one sort of boson we consider a realistic case of the van der Waals interaction between particles with a strong hard-core repulsion U and a van der Waals attractive tail V. For $V<2t,$ t being a hopping amplitude, the phase diagram of the system contains regions of usual one-particle Bose-Einstein condensation (BEC). However for $V>2t$ we have total phase separation on a Mott-Hubbard Bose solid and a dilute Bose gas. For two sorts of structureless bosons described by the two-band Hubbard model, an s-wave pairing of the two bosons of different sort $〈{b}_{1}{b}_{2}〉\ensuremath{\ne}0$ is possible. The results we obtained should be important for different Bose systems, including submonolayers of ${}^{4}\mathrm{He},$ excitons in semiconductors, Schwinger bosons in magnetic systems and holons in HTSC. In the HTSC case a possibility of two-holon pairing in the slave-boson theories of superconductivity can restore a required charge $2e$ of a Cooper pair.

DOI: 10.1103/physrevb.65.195103

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We present a phase diagram for a dilute two-dimensional Bose gas on a lattice. For one sort of boson we consider a realistic case of the van der Waals interaction between particles with a strong hard-core repulsion U and a van der Waals attractive tail V. For

V<2t,

t being a hopping amplitude, the phase diagram of the system contains regions of usual one-particle Bose-Einstein condensation (BEC). However for

V>2t

we have total phase separation on a Mott-Hubbard Bose solid and a dilute Bose gas. For two sorts of structureless bosons described by the two-band Hubbard model, an s-wave pairing of the two bosons of different sort

V>2t

is possible. The results we obtained should be important for different Bose systems, including submonolayers of

{}^{4}\mathrm{He},

excitons in semiconductors, Schwinger bosons in magnetic systems and holons in HTSC. In the HTSC case a possibility of two-holon pairing in the slave-boson theories of superconductivity can restore a required charge

2e

of a Cooper pair.

To analyze the ground-state phase diagram of Bose-Bose mixtures loaded into

d

-dimensional hypercubic optical lattices, we perform a strong-coupling power-series expansion in the kinetic energy term (plus a scaling analysis) for the two-species Bose-Hubbard model with onsite boson-boson interactions. We consider both repulsive and attractive interspecies interaction, and obtain an analytical expression for the phase boundary between the incompressible Mott insulator and the compressible superfluid phase up to third order in the hoppings. In particular, we find a re-entrant quantum phase transition from paired superfluid (superfluidity of composite bosons, i.e., Bose-Bose pairs) to Mott insulator and again to a paired superfluid in all one, two, and three dimensions, when the interspecies interaction is sufficiently large and attractive. We hope that some of our results could be tested with ultracold atomic systems.

The ground state phase diagram of the one-dimensional Bose-Fermi Hubbard model is studied in the canonical ensemble using a quantum Monte Carlo method. We focus on the case where both species have half filling in order to maximize the pairing correlations between the bosons and the fermions. In case of equal hopping we distinguish among phase separation, a Luttinger liquid phase, and a phase characterized by strong singlet pairing between the species. True long-range density waves exist with unequal hopping amplitudes.

We consider a model of a Fermi-Bose mixture with strong hard-core repulsion between particles of the same sort and attraction between particles of different sorts. In this case, besides the standard anomalous averages of the type

⟨b⟩

,

⟨bb⟩

, and

⟨cc⟩

, a pairing between fermions and bosons of the type

bc

is possible. This pairing corresponds to the creation of composite fermions in the system. At low temperatures and equal densities of fermions and bosons composite fermions are further paired in quartets. At higher temperatures trios, which consist of composite fermions and elementary bosons, are also present in the system. Our investigations are important in connection with the recent observation of weakly bound dimers in magnetic and optical dipole traps at ultralow temperatures and with the observation of the collapse of a Fermi gas in an attractive Fermi-Bose mixture of neutral particles.

We have obtained the quantum phase diagram of one dimensional extended Bose-Hubbard model using the density-matrix renormalization group and Abelian bosonization methods for different commensurabilities. We describe the nature of different quantum phases at the charge degeneracy point. We find a direct phase transition from Mott insulating phase to superconducting phase for integer band fillings of bosons. We predict explicitly the presence of two kinds of repulsive Luttinger liquid phases, apart from the charge density wave and superconducting phases for half-integer band fillings. Our study reveals that extended range interactions are necessary to get the correct phase boundary of an one-dimensional interacting bosons system.

Bose condensation of a dilute charged Bose gas in contact with a dense Fermi liquid is examined. The particles have hard cores and hop on a lattice. It is argued that a ``Bose metal phase,'' i.e., a phase with vanishing condensate fraction, is unlikely to exist in this problem at zero temperature. However very strong renormalizations of the properties of the Bose system occur when the boson band is narrower than the fermion band. We find that the condensate fraction at zero temperature is suppressed by a factor 4(W/

{\mathit{w}}_{\mathit{b}}

{)}^{2}

exp(-W/

{\mathit{w}}_{\mathit{b}}

) in two dimensions over Gutzwiller-type variational estimates. Here,

{\mathit{w}}_{\mathit{b}}

and W are the boson and fermion half-band-widths, respectively. There is a similar reduction in the transition temperature. Thus the possibility that high-

{\mathit{T}}_{\mathit{c}}

superconductors are Bose metals in their normal states cannot be excluded on the basis of present experimental or theoretical evidence.