Cooper problem in a cuprate lattice

TL;DR

This paper investigates the formation of d-wave Cooper pairs in a cuprate lattice using a three-band model, highlighting the role of next-nearest-neighbor tunneling and proposing experimental detection methods.

Contribution

It provides a detailed solution to the Cooper problem in a cuprate lattice, emphasizing the importance of next-nearest-neighbor tunneling for d-wave pairing in hole-doped systems.

Findings

Wave function exhibits d_{x^2-y^2} symmetry.

Next-nearest-neighbor tunneling is crucial for d-wave pairing.

Proposes experimental signatures in cold-atom systems.

Abstract

We solve the Cooper problem in a cuprate lattice by utilizing a three-band model. We determine the ground state of a Cooper pair for repulsive on-site interactions, and demonstrate that the corresponding wave function has an orbital $d_{x^2-y^2}$ symmetry. We discuss the influence of next-nearest-neighbor tunneling on the Cooper pair solution, in particular the necessity of next-nearest-neighbor tunneling for having $d$-wave pairs for hole-doped systems. We also propose experimental signatures of the $d$-wave Cooper pairs for a cold-atom system in a cuprate lattice.