One-band tight-binding model parametrization of the high-$T_c$ cuprates, including the effect of $k_z$-dispersion

Abstract

We discuss the effects of interlayer hopping and the resulting $k_z$-dispersion in the cuprates within the framework of the one-band tight binding (TB) model Hamiltonian. Specific forms of the dispersion relations in terms of the in-plane hopping parameters $t$, $t'$, $t''$ and $t'''$ and the effective interlayer hopping $t_z$ in La$_{2-x}$Sr$_x$CuO$_4$ (LSCO) and Nd$_{2-x}$Ce$_x$CuO$_4$ (NCCO) and the added intracell hopping $t_{bi}$ between the CuO$_2$ bilayers in Bi$_2$Sr$_2$CaCu$_2$O$_{8}$ (Bi2212) are presented. The values of the `bare' parameters are obtained via fits with the first principles LDA-based band structures in LSCO, NCCO and Bi2212. The corresponding `dressed' parameter sets which account for correlation effects beyond the LDA are derived by fitting experimental FS maps and dispersions near the Fermi energy in optimally doped and overdoped systems. The interlayer couplings $t_z$ and $t_{bi}$ are found generally to be a substantial fraction of the in-plane hopping $t$, although the value of $t_z$ in NCCO is anomalously small, reflecting absence of apical O atoms in the crystal structure. Our results provide some insight into the issues of the determination of doping from experimental FS maps in Bi2212, the role of intercell coupling in c-axis transport, and the possible correlations between the doping dependencies of the binding energies of the Van Hove singularities (VHSs) and various prominent features observed in the angle-resolved photoemission (ARPES) and tunneling spectra of the cuprates.