Staggered flux state of electron in two-dimensional t-J model

TL;DR

This paper investigates the competition between staggered flux and d-wave pairing states in the 2D t-J model using U(1) slave boson mean-field theory, revealing phase transitions and consistency with ARPES data.

Contribution

It introduces a detailed analysis of staggered flux states considering both spinon and holon fluxes, and clarifies the phase transition mechanism in the electron's flux state.

Findings

Phase transition between $$-flux and staggered flux phases is second order.

No coexistence of staggered flux and d-wave pairing states.

Results align with ARPES experimental observations.

Abstract

The competition between the staggered flux state, or the d-density wave state, and the d-wave pairing state is analyzed in two-dimensional t-J model based on the U(1) slave boson mean-field theory. Not only staggered flux of spinon but also staggered flux of holon are considered. In this formalism, the hopping order parameter of $physical$ electron is described by the product of hopping order parameters of spinon and holon. The staggered flux amplitude of electron is the difference of staggered flux amplitude of spinon and that of holon. In $\pi$-flux phase of spinon, staggered fluxes of spinon and holon cancel completely and staggered flux order of electron does not exist. However, in staggered flux phase of spinon whose staggered flux amplitude is not $\pi$, fluxes does not cancel completely and staggered flux amplitude of electron remains. Thus, the phase transition between these two phases, $\pi$-flux phase and staggered flux phase of spinon, becomes a second order transition in $physical$ electron picture. The order parameter which characterizes this transition is staggered flux order parameter of electron. A mean-field phase diagram is shown. It is proved analytically that there is no coexisistence of staggered flux and d-wave pairing. The temperature dependences of Fermi surface and excitation gap at $(0,\pi)$ are shown. These behaviors are consistent with angle-resolved photoemission spectroscopy (ARPES) experiments.