Single hole dispersion relation for the real CuO$_2$ plane

TL;DR

This paper calculates the dispersion relation of a hole in the CuO$_2$ plane using a generalized $t$-$t^{\u2019}$-$J$ model, showing excellent agreement with experimental ARPES data, and discusses the physical justification of model parameters.

Contribution

It introduces a detailed calculation of the CuO$_2$ hole dispersion based on a generalized model derived from the three-band system, with parameter justification and comparison to experiments.

Findings

Calculated dispersion matches ARPES data.

Parameter ranges are physically justified.

Self-consistent Born approximation effectively models the system.

Abstract

Dispersion relation for the CuO$_2$ hole is calculated basing on the {\it generalized} $t$-$t^{\prime}$-$J$ model, recently derived from the three-band one. Numerical ranges for all model parameters, $t/J=2.4..2.7$, $t^{\prime}/t = 0..-0.25$, $t^{\prime\prime}/t=0.1..0.15$, and three-site terms $2t_N\sim t_S\sim J/4$, have been strongly justified previously. Physical reasons for their values are also discussed. Self-consistent Born approximation is used for the calculation of the hole dispersion. An excellent agreement between calculated $E_{\bf k}$ and one obtained from the angle-resolved photoemission experiments is found.