Correlated BCS wavefunction approach to unconventional superconductors

We propose a modified BCS wavefunction as the ground state of a correlated superconductor with the correlation specified between $k$ and $-k$ electrons in the reciprocal space. Owing to this correlation, low-energy excitations are not conventional BCS Bogoliubov quasiparticles. They display at least four poles in the Green's function and their particle-hole weights in the tunneling and photon-emission spectrum become asymmetric. The superfluid density or superfluid stiffness also deviates from the BCS predictions with finite paramagnetic terms inside the total diamagnetic response. Moreover, a $d$-wave correlated pairing state becomes robust against weak disorders. Hence, this state can explain many mysterious features observed in unconventional superconductors like cuprates.