Signatures of Fermion Pairing with Unconventional Symmetry around BCS-BEC Crossover in a Quasi-2D Lattice

TL;DR

This paper investigates signatures of unconventional fermion pairing symmetries, specifically $d_{x^2-y^2}$ and extended-s, across the BCS-BEC crossover in a 2D lattice, proposing experimental tests with cold atoms.

Contribution

It identifies distinctive signatures of unconventional pairing symmetries in the BCS-BEC crossover region on a 2D lattice, linking theoretical predictions to cold atom experiments.

Findings

Distinct differences in $v_k^2$, $v_k/u_k$, and Fourier transforms for $d$- and $s^*$-wave symmetries.

Features in chemical potential and gap functions vary with interaction strength.

Potential for experimental verification using current cold atom setups.

Abstract

We consider fermions on a 2D square lattice with a finite-range pairing interaction, and obtain signatures for unconventional pair-symmetry states, $d_{x^2-y^2}$ and extended-s ($s^*$), in the BCS-BEC crossover region. We find that the fermion momentum distribution function, $v_k^2$, the ratio of the Bogoliubov coefficients, $v_k/u_k$, and the Fourier transform of $v_k^2$ are strikingly different for $d$- and $s^*$ symmetries in the crossover region. The chemical potential and the gaps functions for both pairing symmetries show several interesting features as a function of interaction. Fermionic atoms in 2D optical lattices may provide a way to test these signatures. We discuss current generation cold atom experiments that may be utilized.