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

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 $V<\mathrm{}2t,$ t being a hopping amplitude, the phase diagram of the system contains regions of usual one-particle Bose-Einstein condensation (BEC). However for $V>\mathrm{}2t$ 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 $〈b_1{b}_2〉\ne 0$ 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.