# Unfrustrating the t-J Model: d-wave BCS Superconductivity in the $t'$-$J_z$-$V$ Model

## TL;DR

This paper introduces a modified t-J model with specific interactions that allows for an exact analytical understanding of d-wave superconductivity mechanisms in cuprates, revealing conditions for nodeless pairing.

## Contribution

It presents a modified $t'$-$J_z$-$V$ model enabling exact analysis of d-wave superconductivity in a strongly interacting limit, advancing understanding of cuprate superconductors.

## Key findings

- Exact ground state as an antiferromagnetic superconductor.
- Application of BCS theory yields nodeless d-wave or s-wave superconductivity.
- Model provides analytical control over superconducting mechanisms.

## Abstract

The t-J model is believed to be a minimal model that may be capable of describing the low-energy physics of the cuprate superconductors. However, although the t-J model is simple in appearance, obtaining a detailed understanding of its phase diagram has proved to be challenging. We are therefore motivated to study modifications to the t-J model such that its phase diagram and mechanism for d-wave superconductivity can be understood analytically without making uncontrolled approximations. The modified model we consider is a $t'$-$J_z$-$V$ model on a square lattice, which has a second-nearest-neighbor hopping $t'$ (instead of a nearest-neighbor hopping $t$), an Ising (instead of Heisenberg) antiferromagnetic coupling $J_z$, and a nearest-neighbor repulsion $V$. In a certain strongly interacting limit, the ground state is an antiferromagnetic superconductor that can be described exactly by a Hamiltonian where the only interaction is a nearest-neighbor attraction. BCS theory can then be applied with arbitrary analytical control, from which nodeless d-wave or s-wave superconductivity can result.