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The competition between the staggered flux state, or the d-density wavestate, and the d-wave pairing state is analyzed in two-dimensional t-J modelbased on the U(1) slave boson mean-field theory. Not only staggered flux ofspinon but also staggered flux of holon are considered. In this formalism, thehopping order parameter of $physical$ electron is described by the product ofhopping order parameters of spinon and holon. The staggered flux amplitude ofelectron is the difference of staggered flux amplitude of spinon and that ofholon. In $\pi$-flux phase of spinon, staggered fluxes of spinon and holoncancel 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 electronremains. Thus, the phase transition between these two phases, $\pi$-flux phaseand staggered flux phase of spinon, becomes a second order transition in$physical$ electron picture. The order parameter which characterizes thistransition is staggered flux order parameter of electron. A mean-field phasediagram is shown. It is proved analytically that there is no coexisistence ofstaggered flux and d-wave pairing. The temperature dependences of Fermi surfaceand excitation gap at $(0,\pi)$ are shown. These behaviors are consistent withangle-resolved photoemission spectroscopy (ARPES) experiments.Comment: 10 pages, 8 figure

physical review. b, condensed matter

Staggered flux state of electrons in a two-dimensional<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>t</mml:mi><mml:mo>−</mml:mo><mml:mi>J</mml:mi></mml:math>model

Staggered flux state of electrons in a two-dimensionalt−Jmodel