Generalized $t$-$t^{\prime }$-$J$ model: parameters and single-particle spectrum for electrons and holes in copper oxides

Abstract

A microscopically based Hamiltonian of the generalized $t$-$t^{\prime }$-$J$ model is presented. Two types of the additional $t^{\prime }$-terms are discussed. The set of ranges of the additional $t^{\prime }$-terms for the real CuO${}_2$ planes is derived from the three-band model calculations. Using the variational spin-polaron approach the single-carrier dispersions in the generalized $t$-$t^{\prime }$-$J$ model are calculated both for the hole- and electron-doped systems. Hole and electron band minima are found to be at points $(0,\pm \pi )$, $(\pm \pi ,0)$, and $(\pm \pi /2,\pm \pi /2)$, respectively. The band minima shifts $|{\Delta }_{(0,\pi )-(\pi /2,\pi /2)}|$ are not small ($\sim J$). Bandwidths for both cases of doping are found to be $1.5-4.5$ times larger than the t-J model ones.

10 pages, RevTeX. 6 postscript figures are appended