Study of gossamer superconductivity and antiferromagnetism in the t-J-U model

TL;DR

This paper analytically investigates the coexistence and competition of d-wave superconductivity and antiferromagnetism in a two-dimensional t-J-U model using renormalized mean field theory, revealing phase diagrams and order parameter behaviors.

Contribution

It introduces a combined t-J-U model with Gutzwiller approximation to study the phase diagram and coexistence of superconductivity and antiferromagnetism.

Findings

Antiferromagnetic order coexists with d-wave superconductivity in underdoped regions.

Superconductivity peaks near optimal doping at δ≈0.15.

Ground state energy favors coexistence over pure superconductivity.

Abstract

The d-wave superconductivity (dSC) and antiferromagnetism are analytically studied in a renormalized mean field theory for a two dimensional t-J model plus an on-site repulsive Hubbard interaction $U$. The purpose of introducing the $U$ term is to partially impose the no double occupancy constraint by employing the Gutzwiller approximation. The phase diagrams as functions of doping $\delta$ and $U$ are studied. Using the standard value of $t/J=3.0$ and in the large $U$ limit, we show that the antiferromagnetic (AF) order emerges and coexists with the dSC in the underdoped region below the doping $\delta\sim0.1$. The dSC order parameter increases from zero as the doping increases and reaches a maximum near the optimal doping $\delta\sim0.15$. In the small $U$ limit, only the dSC order survives while the AF order disappears. As $U$ increased to a critical value, the AF order shows up and coexists with the dSC in the underdoped regime. At half filing, the system is in the dSC state for small $U$ and becomes an AF insulator for large $U$. Within the present mean field approach, We show that the ground state energy of the coexistent state is always lower than that of the pure dSC state.