Theory of (001) surface and bulk states in Y$_{1-y}$Ca$_y$Ba$_2$Cu$_3$O$_{7-δ}$}

Abstract

A self-consistent model is developed for the surface and bulk states of thin Y_{1-y}Ca_yBa_2Cu_3O_{7-δ} (YCBCO) films. The dispersions of the chain and plane layers are modelled by tight-binding bands, and the electronic structure is then calculated for a finite-thickness film. The dopant atoms are treated within a virtual crystal approximation. Because YCBCO is a polar material, self-consistent treatment of the long range Coulomb interaction leads to a transfer of charge between the film surfaces, and to the formation of surface states. The tight binding band parameters are constrained by the requirement that the calculated band structure of surface states at CuO$_2$-terminated surfaces be in agreement with photoemission experiments. The spectral function and density of states are calculated and compared with experiments. Unlike the case of Bi_2Sr_2CaCu_2O_8, where the surfaces are believed to be representative of the bulk, the densities of states at the YCBCO surfaces are shown to be qualitatively different from the bulk, and are sensitive to doping. The calculated spectral function agrees closely with both bulk-sensitive and surface-sensitive photoemission results, while the calculated density of states for optimally-doped YCBCO agrees closely with tunneling experiments. We find that some density of states features previously ascribed to competing order can be understood as band structure effects.