Spectral function of small spin polaron in two-dimensional spherically symmetric antiferromagnetic state

Abstract

The spectral density ${\mathrm{A}}_{\mathrm{p}}$(k,\ensuremath{\omega}) of a small spin polaron in the ${\mathrm{CuO}}_{2}$ plane is calculated in the self-consistent Born approximation within the framework of the three-band model. It is shown that the spin polaron is a good quasiparticle excitation for this model. ${\mathrm{A}}_{\mathrm{p}}$(k,\ensuremath{\omega}) demonstrates small damping in contrast to ${\mathrm{A}}_{\mathrm{h}}$(k,\ensuremath{\omega}) for a bare hole, and the lowest boundary ${\mathrm{\ensuremath{\omega}}}_{\mathrm{p},\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{}}$ of ${\mathrm{A}}_{\mathrm{p}}$(k,\ensuremath{\omega}) lies much lower than ${\mathrm{\ensuremath{\omega}}}_{\mathrm{h},\mathrm{m}\mathrm{i}\mathrm{n}}$ for ${\mathrm{A}}_{\mathrm{h}}$(k,\ensuremath{\omega}). The quasiparticle peak dispersion reproduces the flat region near the band bottom that is characteristic of the bare polaron spectrum ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{k}}$. The spherically symmetric approach is used for description of spin excitations. It makes it possible to consider the quantum antiferromagnetic background without the spontaneous symmetry breaking and the unit cell doubling.