Spin-polaron damping in the spin-fermion model for cuprate superconductors

Abstract

A self-consistent, spin-rotational invariant Green's-function procedure has been developed to calculate the spectral function of carrier excitations in the spin-fermion model for the ${\mathrm{CuO}}_{2}$ plane. We start from the mean-field description of a spin polaron in the Mori-Zwanzig projection method. In order to determine the spin polaron lifetime in the self-consistent Born approximation, the self-energy is expressed by an irreducible Green's function. Both spin polaron and bare hole spectral functions are calculated. The numerical results show a well pronounced quasiparticle peak near the bottom of the dispersion at $(\ensuremath{\pi}/2,\ensuremath{\pi}/2),$ the absence of the quasiparticle at the $\ensuremath{\Gamma}$ point, a rather large damping away from the minimum, and an asymmetry of the spectral function with respect to the antiferromagnetic Brillouin zone. These findings are in qualitative agreement with photoemission data for undoped cuprates. The direct oxygen-oxygen hopping is responsible for a more isotropic minimum at $(\ensuremath{\pi}/2,\ensuremath{\pi}/2).$