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 $(0,\pmπ)$, $(\pmπ,0)$, and $(\pmπ/2,\pmπ/2)$, respectively. The band minima shifts $|Δ_{(0,π)-(π/2,π/2)}|$ 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.