Spin-momentum locking and quantum anomalous Hall effect in d+id-density wave ordered pseudo gap phase of Bi2212

We model Bi2Sr2CaCu2O8+δ(Bi2212) bilayer system by a time reversal symmetry (TRS) and inversion symmetry (IS) broken Bloch Hamiltonian H. The pseudo-gap phase of the bilayer is assumed to be chiral d-density wave ordered. One of the focal points of the paper is the theoretical study of the spin-momentum locking (SML), due to the presence of a strong spin–orbit coupling in Bi2212, reported earlier in this phase in a spin-and angle-resolved photoemission spectroscopic measurement. The non-trivial spin texture in k-space, which is an outcome of the broken IS for the bilayer system, is found tuneable by electric field (and also by intercalation). We also show that this system exhibits anomalous quantum Hall effect due to the broken TRS and the presence of a strong spin–orbit coupling.