d-wave Superfluid with Gapless Edges in a Cold Atom Trap

TL;DR

This paper explores a cold atom system in a 2D optical lattice, demonstrating how a d-wave superfluid with gapless edges can be stabilized and characterized using theoretical models, revealing insights into Mott insulator proximity.

Contribution

It introduces a method to realize and analyze a d-wave superfluid with gapless edges in a trapped fermionic gas using the $t-J$ model and Bogoliubov-de Gennes equations.

Findings

Identification of a d-wave superfluid region with gapless edges

Detection of Mott insulator proximity via Fermi liquid order parameter

Linear evolution of density profile with distance from trap center

Abstract

We consider a strongly repulsive fermionic gas in a two-dimensional optical lattice confined by a harmonic trapping potential. To address the strongly repulsive regime, we consider the $t-J$ Hamiltonian. The presence of the harmonic trapping potential enables the stabilization of coexisting and competing phases. In particular, at low temperatures, this allows the realization of a d-wave superfluid region surrounded by purely (gapless) normal edges. Solving the Bogoliubov-de Gennes equations and comparing with the local density approximation, we show that the proximity to the Mott insulator is revealed by a downturn of the Fermi liquid order parameter at the center of the trap where the d-wave gap has a maximum. The density profile evolves linearly with distance.