Fermion pairing in mixed-dimensional atomic mixtures

Abstract

We investigate the quantum phases of mixed-dimensional cold atom mixtures. In particular, we consider a mixture of a Fermi gas in a two-dimensional lattice, interacting with a bulk Fermi gas or a Bose-Einstein condensate in a three-dimensional lattice. The effective interaction of the two-dimensional system mediated by the bulk system is determined. We perform a functional renormalization group analysis, and demonstrate that by tuning the properties of the bulk system, a subtle competition of several superconducting orders can be controlled among $s$-wave, $p$-wave, $d_{x^2-y^2}$-wave, and $g_{xy(x^2-y^2)}$-wave pairing symmetries. Other instabilities such as a charge-density wave order are also demonstrated to occur. In particular, we find that the critical temperature of the $d$-wave pairing induced by the next-nearest-neighbor interactions can be an order of magnitude larger than that of the same pairing induced by doping in the simple Hubbard model. We expect that by combining the nearest-neighbor interaction with the next-nearest-neighbor hopping (known to enhance $d$-wave pairing), an even higher critical temperature may be achieved.Comment: 10 pages, 10 figure

Induced p -Wave Pairing in Bose-Fermi Mixtures

“…Cooper pairing in atomic Bose-Fermi mixtures was originally predicted using weak coupling BCS theory [21], and since then several authors have considered the problem using theories with varying degree of sophistication [22][23][24][25][26]. It has furthermore been predicted that topological p-wave superfluids can be realised in mixed dimensional Bose-Fermi mixtures [27,28]. However, a strong coupling theory for the critical temperature of a three-dimensional p-wave superfluid including the full energy and momentum dependent self-energy and retardation effects in a consistent way, is still lacking.…”

Effect of mediated interactions on a Hubbard chain in mixed-dimensional fermionic cold atoms

“…We also note that a 3 He - 4 He solution provides effectively mixed-dimensional Fermi gases [28]. Theoretical works on mixed-dimensional systems predict phenomena such as Efimov effects [29,30], mediated pairing [31][32][33][34][35], or a topological superfluid [36,37].…”

Weak three-dimensional mediators of two-dimensional triplet pairing

“…1) are the Friedel oscillations, where the sign of the interaction changes at different distances, and the nearest-neighbor interaction is exponentially smaller than the on-site interaction. This means that, if the on-site (non-mediated) contact interaction U 2 is strong enough to cancel the on-site mediated interaction, an integration of the effective 2D fermionic action done during the renormalization-group analysis (next section) will still be perturbative when g/2 This calculation was done for a finite-sized lattice in [21] and a similar calculation was done by [18] where the lattice potential is not included. Without the lattice, there is no natural ultraviolet cutoff and regularization is needed to deal with an ultraviolet divergence.…”

“…In this paper we address this question and find that, in fact, this system can be used to produce a robust pwave pairing phase for 2D fermions, and that relatively large transition temperatures, of the order of 10% of the bandwidth of the 2D fermions, can be achieved. This is done by appropriately exploiting the long-range mediated interaction in a parameter space not considered in previous works [21]. We consider a 2D-3D mixture where the 3D particles mediate a long-range interaction between the 2D particles, which we take to be SU(2) symmetric fermions.…”