Transition from band insulator to Bose-Einstein-condensate superfluid and Mott state of cold Fermi gases with multiband effects in optical lattices

Abstract

We study two models realized by two-component Fermi gases loaded in optical lattices. We clarify that multi-band effects inevitably caused by the optical lattices generate a rich structure, when the systems crossover from the region of weakly bound molecular bosons to the region of strongly bound atomic bosons. Here the crossover can be controlled by attractive fermion interaction. One of the present models is a case with attractive fermion interaction, where an insulator-superfluid transition takes place. The transition is characterized as the transition between a band insulator and a Bose-Einstein condensate (BEC) superfluid state. Differing from the conventional BCS superfluid transition, this transition shows unconventional properties. In contrast to the one-particle excitation gap scaled by the superfluid order parameter in the conventional BCS transition, because of the multi-band effects, a large gap of one-particle density of states is retained all through the transition although the superfluid order grows continuously from zero. A reentrant transition with lowering temperature is another unconventionality. The other model is the case with coexisting attractive and repulsive interactions. Within a mean field treatment, we find a new insulating state, an orbital ordered insulator. This insulator is one candidate for the Mott insulator of molecular bosons and is the first example that the orbital internal degrees of freedom of molecular bosons appears explicitly. Besides the emergence of a new phase, a coexisting phase also appears where superfluidity and an orbital order coexist just by doping holes or particles. The insulating and superfluid particles show differentiation in momentum space as in the high-Tc cuprate superconductors.

Unitarity in periodic potentials: A renormalization group analysis

“…The present interest in this subject is driven in parallel by a variety of unconventional superconductors in condensed matter physics, and ultra-cold atoms with nearly resonant scattering. The recent theoretical studies of scattering resonances in lattice potentials [18][19][20][21][22][23][24] often rely on twochannel tight-binding models, featuring fermionic atoms resonantly coupled to closed channel bosonic particles. It has been argued that models of this kind provide a good effective description of the microscopic lattice systems of interest [25][26][27] .…”

Fate of the Bose insulator in the limit of strong localization and low Cooper-pair density in ultrathin films

“…Thus, pair unbinding turns on in the strong localization regime so that the thinnest films appear to support a mixture of fermions and remanent localized bosons. We anticipate these findings will inform attempts to describe the transport observed in many thin film Bose insulator systems [19,21] while encouraging analogies to experiments on cold fermion atoms with attractive interactions in optical lattices [8,[33][34][35][36].…”

Resonant superfluidity in an optical lattice

“…As described below, we find a first order transition between the BEC/BCS state and the Mott insulator. For a total filling of two fermions per site the BCS state competes against a band insulating state [24,25,26].…”