Importance of interlayer pair tunneling: A variational perspective

We study the effect of interlayer pair tunneling in a bilayer superconductor where each layer is described by a two dimensional t-J model and the two layers are connected by the Josephson pair tunneling term. We study this model using a grand canonical variational Monte Carlo (GVMC) method, for which we develop a new algorithm to perform Monte Carlo simulation of a system with fluctuating particle number. The variational wavefunction is taken to be the product of two Gutzwiller projected d-wave BCS wavefunctions with variable particle densities, one for each layer. We calculate the energy of the above state as a function of the d-wave superconducting gap parameter, Δ. We find that the interlayer pair tunneling energy, E⊥ shows interesting variation with Δ. E⊥ tends to enhance the optimal value of Δ, thereby the superconducting pairing. However the magnitude of the tunneling energy is found to be too small to have any appreciable effect on the physical properties. While the result is supported by early experiments and hence may appear known to the community, the current work presents a new approach to the problem and confirms the diminished role of interlayer pair tunneling by directly calculating its contribution to superconducting condensation energy.