Accueil du site > Publications > Publications 2006 > Bond-order-modulated flux-phase of the t-J model on a square lattice

Cédric Weber, Didier Poilblanc, Sylvain Capponi, Frédéric Mila, Cyril Jaudet

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- 19 novembre 2004

Motivated by the observation of inhomogeneous patterns in some high-T cuprate compounds, several variational Gutzwiller-projected wave-functions with built-in charge and bond order parameters are proposed for the extended model on the square lattice at low doping. First, following a recent Gutzwiller-projected mean-field approach by one of us (Phys. Rev. B. **72**, 060508(R) (2005)), we investigate, as a function of doping and Coulomb repulsion, the relative stability of a wide variety of modulated structures with square unit cells of size , , and . It is found that the bond-order wave-function with staggered flux pattern (and small charge and spin current density wave) is a remarkable competitive candidate for hole doping around 1/8 in agreement with STM observations in the under-doped regime of some cuprates. This wave-function is then optimized accurately and its properties studied extensively using an approximation-free variational Monte Carlo scheme. Moreover, we find that under increasing the Coulomb repulsion, the d-wave superconducting RVB wave-function is rapidly destabilized with respect to the the bond-order wave-function. The stability of the bond-modulated wave-function is connected to a gain of Coulomb and exchange energies. We suggest that such ordering patterns could be dynamical or could spontaneously appear in the vicinity of an impurity or a vortex in the mixed phase of the cuprates. Finally, we consider also a commensurate flux phase, but this wave-function turns out *not* to be competitive because of its rather poor kinetic energy. However, we find it has very competitive exchange and Coulomb energies.