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arXiv:0708.3241 · Physical Review Letters

Supersolid Bose-Fermi Mixtures in Optical Lattices

Irakli Titvinidze, Michiel Snoek, Walter Hofstetter

Published Mar 10, 2008• 99 citations
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Abstract

We study a mixture of strongly interacting bosons and spinless fermions with on-site repulsion in a three-dimensional optical lattice. For this purpose we develop and apply a generalized dynamical mean-field theory, which is exact in infinite dimensions and reliably describes the full range from weak to strong coupling. We restrict ourselves to half filling. For weak Bose-Fermi repulsion a supersolid forms, in which bosonic superfluidity coexists with charge-density wave order. For stronger interspecies repulsion the bosons become localized while the charge-density wave order persists. The system is unstable against phase separation for weak repulsion among the bosons.

DOI
10.1103/physrevlett.100.100401

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We study a mixture of strongly interacting bosons and spinless fermions with on-site repulsion in a three-dimensional optical lattice. For this purpose we develop and apply a generalized dynamical mean-field theory, which is exact in infinite dimensions and reliably describes the full range from weak to strong coupling. We restrict ourselves to half filling. For weak Bose-Fermi repulsion a supersolid forms, in which bosonic superfluidity coexists with charge-density wave order. For stronger interspecies repulsion the bosons become localized while the charge-density wave order persists. The system is unstable against phase separation for weak repulsion among the bosons.
We give a detailed discussion of the recently developed generalized dynamical mean-field theory (GDMFT) for a mixture of bosonic and fermionic particles. We show that this method is nonperturbative and exact in infinite dimensions, and reliably describes the full range from weak to strong coupling. Like in conventional dynamical mean-field theory, the small parameter is 1/z1/z1/z, where zzz is the lattice coordination number. We apply the GDMFT scheme to a mixture of spinless fermions and bosons in an optical lattice. We investigate the possibility of a supersolid phase, focusing on the case of 1/2 filling for the fermions and 3/2 filling for the bosons.
We obtain the phase diagram of a Bose-Fermi mixture of hardcore spinless bosons and spin-polarized fermions with nearest-neighbor intraspecies interaction and on-site interspecies repulsion in an optical lattice at half filling using a slave-boson mean-field theory. We show that such a system can have four possible phases which are (a) supersolid bosons coexisting with fermions in the Mott state, (b) Mott state of bosons coexisting with fermions in a metallic or charge-density wave state, (c) a metallic fermionic state coexisting with superfluid phase of bosons, and (d) Mott insulating state of fermions and bosons. We chart out the phase diagram of the system and provide analytical expressions for the phase boundaries within mean-field theory. We demonstrate that the transitions between these phases are generically first order with the exception of that between the supersolid and the Mott states which, within mean-field theory, is a continuous quantum phase transition. We also obtain the low-energy collective excitations of the system in these phases. Finally, we study the particle-hole excitations in the Mott insulating phase and use it to determine the dynamical critical exponent zzz for the supersolid-Mott insulator transition. We discuss experiments which can test our theory.
We investigate a cold-atom mixture of spinless bosons and fermions in two-dimensional optical lattices. In the presence of a nested Fermi surface, the bosons may develop a fascinating supersolid behavior characterized by a finite superfluid density as well as a spatial density wave order. Focusing on the triangular lattice geometry and combining a general Landau-Ginzburg-Wilson approach with microscopically derived mean-field theory, we find an exotic supersolid phase at a fermionic band filling of nf=3∕4{n}_{f}=3∕4nf​=3∕4 with a kagome-type crystalline order. We also address the case of anisotropic hopping amplitudes and show that striped supersolid phases emerge on the square and triangular lattices. For weak interactions, the supersolid competes with phase separation. For strong intraspecies and interspecies interactions, with the total number of fermions and bosons corresponding to one particle per site, the bosons form an alternating Mott insulator ground state. Finally, for a mixture of 87Rb40K^{87}\mathrm{Rb}^{40}\mathrm{K}87Rb40K and 23Na6Li^{23}\mathrm{Na}^{6}\mathrm{Li}23Na6Li, we show that supersolidity can be observed in the range of accessible temperatures in the square lattice geometry.
Using quantum Monte Carlo simulations, we study a mixture of bosons and fermions loaded on an optical lattice. With simple on-site repulsive interactions, this system can be driven into a solid phase. We dope this phase and, in analogy with pure bosonic systems, identify the conditions under which the bosons enter a supersolid phase, i.e., exhibit at the same time charge density-wave and superfluid order. We perform finite-size scaling analysis to confirm the presence of a supersolid phase and discuss its properties, showing that it is a collective phase that also involve phase coherence of the fermions.
We calculate the phase diagram of the Bose-Fermi Hubbard model on the 3d cubic lattice at fermionic half filling and bosonic unit filling by means of single-site dynamical mean-field theory. For fast bosons, this is equivalent to the Cooper problem in which the bosons can induce s-wave pairing between the fermions. We also find miscible superfluid and canted supersolid phases depending on the interspecies coupling strength. In contrast, slow bosons favor fermionic charge density wave structures for attractive fermionic interactions. These competing instabilities lead to a rich phase diagram within reach of cold gas experiments.
We study the phase structure of mixtures of strongly interacting bosonic atoms in a combined potential of a parabolic trap and an optical lattice. We apply a mean-field approximation and a local density approximation to the Bose-Hubbard model for the Bose-Bose mixture, and calculate the superfluid order parameter and the number of particles per site for both species. We find that the mixture is phase-separated due to the strong onsite inter-species repulsion. Considering a zero-hopping limit, we find that the coexisting phase can appear when onsite inter-species repulsion interaction is weak.