Stability of the Gutzwiller projected BCS wavefunction in t–J bilayers: A variational Monte Carlo study

In this paper we investigate the stability of the Gutwiller projected BCS wavefunction on bilayered systems using the t–J model with a small but finite hopping amplitude and exchange coupling between the layers. Three possible pairing symmetries are proposed, viz.   (a) a planar dx2-y2dx2-y2-wave, (b) a dx2-y2dx2-y2-wave plus an antisymmetric piece corresponding to the z  -direction and (c) a dx2-y2dx2-y2-wave plus a partially antisymmetric piece corresponding to the z-direction. The energy minimization yields the pure d-wave to be the most suited wavefunction away from half filling. Further we have carried out a thorough study, elaborating the behaviour of optimal value of the variational parameter with hole doping and its dependence on the lattice size for different values of the interplanar parameters. The plots of optimal variational parameter versus hole concentration for the most stable wavefunction bear some interesting features, such as, a hump at small value of hole doping and a surprising dependence of critical doping (δc) on lattice size as the interplanar hopping parameter (t⊥) is increased. The latter feature which is a rather interesting one, results from the changes in the energy band structure with lattice size and the interplanar hopping.