Spin-polaron nature of fermion quasiparticles and their $d$-wave pairing in cuprate superconductors

In the framework of the spin-fermion model, to which the Emery model is reduced in the limit of strong electron correlations, it is shown that the fermion quasiparticles in cuprate high-$T_c$ superconductors (HTSCs) arise under a strong effect of exchange coupling between oxygen holes and spins of copper ions. This underlies the spin-polaron nature of fermion quasiparticles in cuprate HTSCs. The Cooper instability with respect to the $d$-wave symmetry of the order parameter is revealed for an ensemble of such quasiparticles. For the normal phase, the spin-polaron concept allows us to reproduce the fine details in the evolution of the Fermi surface with the changes in the doping level $x$ observed in experiment for La$_{2-x}$Sr$_x$CuO$_4$. The calculated $T-x$ phase diagram correlates well with the available experimental data for cuprate HTSCs.