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

TL;DR

This paper introduces a generalized $t$-$t^\prime$-$J$ model for copper oxides, deriving parameters from three-band calculations and analyzing single-particle spectra for electrons and holes, revealing significant shifts and bandwidths.

Contribution

The paper develops a microscopically based generalized $t$-$t^\prime$-$J$ model with derived parameters and calculates single-particle dispersions for both electron- and hole-doped systems.

Findings

Hole and electron band minima are at specific momentum points.

Band minima shifts are comparable to the exchange interaction J.

Bandwidths are significantly larger than in the traditional t-J model.

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.