Interplay between staggered flux and d-wave superconducting orders in t-t′-J model

With cuprate superconductors in mind, we check whether the d-wave superconducting (dSC) state coexists with or excludes the staggered flux (SF) state, which was revealed to be a strong candidate for the pseudogap state. To this end, we use a variational Monte Carlo method for the square-lattice t-J model with diagonal transfer t′. We construct a trial wave function which can simultaneously represent dSC and SF orders for a continuous description of their interplay. Furthermore, a band renormalization effect is introduced into both orders independently. It is found that the SF state does not coexist with dSC and is unstable for a wide area in the parameter space. However, a strange state having both SF and antiferromagnetic orders is found to be stable for very low doping rate.