Bond-order modulated staggered flux phase for the $t-J$ model on the square lattice

Abstract

Motivated by the observation of inhomogeneous patterns in some high-T${}_c$ cuprate compounds, several variational Gutzwiller-projected wave-functions with built-in charge and bond order parameters are proposed for the extended $t-J-V$ model on the square lattice at low doping. First, following a recent Gutzwiller-projected mean-field approach by one of us (Phys. Rev. B. {\bf 72}, 060508(R) (2005)), we investigate, as a function of doping and Coulomb repulsion, the stability of the staggered flux phase with respect to small spontaneous modulations of squared unit cells ranging from $2\times 2$ to $\sqrt{32}\times \sqrt{32}$. It is found that a $4\times 4$ bond-order (BO) modulation appears spontaneously on top of the staggered flux pattern for hole doping around 1/8. A related wave-function is then constructed and optimized accurately and its properties studied extensively using an approximation-free variational Monte Carlo scheme. Finally, the competition of the BO-modulated staggered flux wave-function w.r.t. the d-wave RVB wave-function or the commensurate flux state is investigated. It is found that a short range Coulomb repulsion penalizes the d-wave superconductor and that a moderate Coulomb repulsion brings them very close in energy. Our results are discussed in connection to the STM observations in the under-doped regime of some cuprates.

arXiv comment10 pages, 9 figures

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• Unidirectional d-wave superconducting domains in the two-dimensional t-J model
• Stability of RVB hole stripes in high-temperature superconductors
• Checkerboard order in vortex cores from pair-density-wave superconductivity
• Finite compressibility in the low-doping region of the two-dimensional $t-J$ model
• Anticollinear magnetic order induced by impurities in the frustrated Heisenberg model of pnictides
• Strong particle-hole asymmetry of charge instabilities in doped Mott insulators
• Spin-rotationally symmetric domain flux phases in underdoped cuprates
• Plaquette bond order wave in the quarter-filled extended Hubbard model on the checkerboard lattice
• Spontaneous Currents in Spinless Fermion Lattice Models at the Strong-Coupling Limit