Interplay between superconductivity and flux phase in the t-J model

TL;DR

This paper investigates the phase diagram of the t-J model, revealing the interplay between superconductivity and flux phases, including coexistence, competition, and the effects of incommensurate charge-density waves.

Contribution

It introduces a mean field approach to analyze the t-J model, highlighting the coexistence and competition between d-wave superconductivity and flux phases near optimal doping.

Findings

Superconducting transition temperature increases with doping in the overdoped region.

Flux and superconducting phases coexist in the underdoped region below Tc.

Incommensurate charge-density waves do not significantly alter the phase diagram.

Abstract

We study the phase diagram of the t-J model using a mean field type approximation within the Baym-Kadanoff perturbation expansion for Hubbard $X$-operators. The line separating the normal state from a d-wave flux or bond-order state starts near optimal doping at T=0 and rises quickly with decreasing doping. The transition temperature $T_c$ for d-wave superconductivity increases monotonically in the overdoped region towards optimal doping. Near optimaldoping a strong competition between the two d-wave order parameters sets in leading to a strong suppression of $T_c$ in the underdoped region. Treating for simplicity the flux phase as commensurate the superconducting and flux phases coexist in the underdoped region below $T_c$, whereas a pure flux phase exists above $T_c$ with a pseudo-gap of d-wave symmetry in the excitation spectrum. We also find that incommensurate charge-density-wave ground states due to Coulomb interactions do not modify strongly the above phase diagram near the superconducting phase, at least, as long as the latter exists at all.