Competing Types of Order in Two-Dimensional Bose-Fermi Mixtures

Using a functional renormalization group approach we study the zero temperature phase diagram of two-dimensional Bose-Fermi mixtures of ultracold atoms in optical lattices, in the limit when the velocity of bosonic condensate fluctuations is much larger than the Fermi velocity. For spin-$1/2$ fermions we obtain a phase diagram, which shows a competition of pairing phases of various orbital symmetry ($s$, $p$, and $d$) and antiferromagnetic order. We determine the value of the gaps of various phases close to half filling, and identify subdominant orders as well as short-range fluctuations from the renormalization group flow. For spinless fermions we find that $p$-wave pairing dominates the phase diagram.

Figure 1

Phase diagram, interaction strength, $U_{ff}/t_f$, vs number of fermions per site, $n$, for a Fermi-Bose mixture in a square lattice in 2D ($\tilde{V}/t_f=2$, $\xi =1$).

Figure 2

RG flow for the different effective interactions (in units of $t_f$) as a function of the RG parameter $l$ ($\tilde{V}/t_f=3$ and $\xi =1$). (a) $U_{ff}/t_F=0.5$; (b) $U_{ff}/t_f=1.2$.

Figure 3

Energy gaps at half filling ($\mu =0$), as a function of $U_{ff}/t_f$, for $\tilde{V}/t_f=3$ and at $\xi =1$. Dashed line: $s$-wave gap; continuous line: $d$-wave gap; dot-dashed line: AF gap. The inset shows a magnified plot of the $d$-wave regime.