Revivification of the Concept of Coexisting CDDW and DSC Orders for Bi2212

The Chiral d-density wave (CDDW or d+id) order, corresponding to the anti-ferromagnetic wave vector Q= (± (1- ), ± ),(± , ± (1- )) with ~ 0.2258 located roughly on the boundary of the Fermi pockets in the momentum space. is assumed to represent the pseudo-gap (PG) state of a Bilayer Bi2212 system- a cuprate superconductor. This system involves quasi-particle interlayer tunnelling different from Cooper pair tunnelling in Josephson junctions. The dominant interaction coupling the quasiparticle pairs in the PG state, conjecturally, is none other than the same “super-exchange” spin coupling which causes the undoped cuprates to be antiferromagnetic Mott insulators The intra-layer d wave superconductivity (DSC) is assumed to be induced by appropriate assumed attractive interactions. The entire analysis is presented within the mean-field framework. The gap equations are solved self-consistently together with the equation to determine the chemical potential (applying Luttinger sum rule). The Hamiltonian, in the CDDW state involving the positive(negative) second-neighbor hopping (and the absence (presence) of the fourth neighbor hopping), displays Wyle/ Dirac semi-metal like (narrow-gap direct semiconductor like) scenario in the limited region of the momentum space in the absence of the momentum conserving inter-layer tunnelling (MCIT). There is pseudo spin- momentum locking (PSML) due to the pseudo-Zeeman field induced by the inter-layer tunnelling. The observed PSML seems to be a generic feature of the system where the sign of the second neighbour has no role to play. In the presence of Rashba coupling and MCIT, spin-bandlocking is found to be possible in the limited region of momentum space. Furthermore, the pseudo-Zeeman term appearing in the quasi-particle excitation spectrum leads to momentum space tunnelling. The CDDW and DSC are found to represent two competing orders as the former brings about a depletion of the spectral weight available for pairing in the anti-nodal region of momentum space. This is not in agreement with a preformed pairing scenario and justifies the different structures we have assumed for the pseudo-gap and the superconducting gap. Furthermore, the depletion of the spectral weight below Tc at energies larger than the gap energy occurs. This is an indication of the strong-coupling superconductivity in cuprates.