Slave-boson approach to the $t$-$t'$-$t''$-$U$ model applied to electron-doped cuprates

By applying Hartree-Fock (HF) mean-field theory to the $t$-$t'$-$t''$-$U$ model, Kusko {\it et al.} have studied the Fermi surface evolution with doping in the antiferromagnetic (AF) phase for electron-doped cuprates. Although they reached consistent results with ARPES data, a doping-dependent effective $U$ was adopted, specifically, $U$ drops from $6t$ at $x=0$ to $3t$ at $x=0.15$. The strong doping dependence of $U$ and its small value at $x=0.15$ are both in disagreement with the analysis on the optical conductivity [A. J. Millis {\it et al.}, cond-mat/0411172]. In view that the HF theory often overestimates the AF order, we re-study the model analytically by Kotliar-Ruckenstein slave-boson approach which improves the consideration of fluctuations. A quicker decreasing of the staggered magnetization (and AF gap) with increasing doping than in HF theory is obtained, thus the ARPES results are possibly reproduced even under a doping-independent constant $U$. We have further considered superconductivity and its interplay with antiferromagnetism by introducing an attractive intersite $V$.