Antiferromagnetism and pairing symmetries in two-dimensional t-J model

To elucidate systematically the interplay between antiferromagnetism (AF) and superconductivity (SC) in High-T_c cuprates, we study the effect of the long-range transfers, t′ and t″, by applying a variational Monte Carlo method to a t-J model. In the trial wave function, coexistence of SC and AF phases and contribution of long-range Cooper pairs, namely the higher harmonic components of the SC gap, are considered. Our result exhibits marked electron-hole asymmetry; for the hole-(electron-)doped case, the SC state is very stable (unstable), while the AF state is irrelevant (predominant). The coexisting phase always appears in the under-doped region, both in the hole-doped and electron-doped cases. Furthermore, the optimized long-range pairing components successfully yield the asymmetry of the gap form observed in the hole-doped and electron-doped cuprates.