# $d_{x^2-y^2}$-wave density wave and $d_{x^2-y^2}$-wave superconducting gap on the extended Hubbard model on a square lattice

## TL;DR

This study investigates the extended Hubbard model on a square lattice, proposing that the pseudogap phase in cuprate superconductors can be explained by a $d_{x^2-y^2}$-wave density wave, with superconductivity emerging from this order.

## Contribution

The paper introduces a mean-field theory for the extended Hubbard model, linking the pseudogap to a $d_{x^2-y^2}$-wave density wave and explaining the emergence of superconductivity.

## Key findings

- Qualitative agreement with experimental phase diagrams of HTS
- Pseudogap interpreted as $d_{x^2-y^2}$-wave density wave order
- Van Hove singularity at the Fermi level near optimal doping

## Abstract

The extended Hubbard model with a nearest-neighbor Coulomb repulsion on the square lattice is studied to obtain insight into the phase diagram of cuprate high $T_c$ superconductors (HTS). To pursue the hidden-order scenario proposed in [S. Chakravarty et al., Phys. Rev. B 63, 094503 (2001)], we derive an effective Hamiltonian by using the canonical transformation and develop a mean-field theory. The calculated phase diagrams are qualitatively consistent with the experimental phase diagrams of HTS, and we thus conclude that the pseudogap can be interpreted as the order parameter of the $d_{x^2-y^2}$-wave density wave (DDW) state, and the $d_{x^2-y^2}$-wave superconducting (DSC) rises based on the DDW order. Furthermore, the analytical representation of the density of states is obtained and, near the optimal doping of the DSC, the van Hove singular point of the density of states is located at the Fermi level.