Exotic Superconducting Phases of Ultracold Atom Mixtures on Triangular Lattices

TL;DR

This paper investigates the phase diagram of ultracold Bose-Fermi mixtures on triangular lattices, revealing exotic superconducting phases with various pairing symmetries due to lattice geometry and frustration effects.

Contribution

It demonstrates the emergence of exotic superconducting phases in Bose-Fermi mixtures on triangular lattices using functional renormalization group methods, highlighting the role of lattice geometry.

Findings

Presence of s-, p-, d-, and f-wave superconducting phases.

Competition between different pairing symmetries depending on lattice anisotropy.

Identification of antiferromagnetic order and extended p-wave phases.

Abstract

We study the phase diagram of two-dimensional Bose-Fermi mixtures of ultracold atoms on a triangular optical lattice, in the limit when the velocity of bosonic condensate fluctuations is much larger than the Fermi velocity. We contrast this work with our previous results for a square lattice system in Phys. Rev. Lett. {\bf 97}, 030601 (2006). Using functional renormalization group techniques we show that the phase diagrams for a triangular lattice contain exotic superconducting phases. For spin-1/2 fermions on an isotropic lattice we find a competition of $s$-, $p$-, extended $d$-, and $f$-wave symmetry, as well as antiferromagnetic order. For an anisotropic lattice, we further find an extended p-wave phase. A Bose-Fermi mixture with spinless fermions on an isotropic lattice shows a competition between $p$- and $f$-wave symmetry. These phases can be traced back to the geometric shapes of the Fermi surfaces in various regimes, as well as the intrinsic frustration of a triangular lattice.