Hall effect of epitaxial ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathit{x}}$ and ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_{\mathit{y}}$ films: Interpretation of the Hall effect on the basis of a renormalized tight-binding model

The Hall effect of epitaxial ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathit{x}}$ (${\mathit{T}}_{\mathit{c}}$≊90 K) and ${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_2$ ${\mathrm{CaCu}}_2$ ${\mathrm{O}}_{\mathit{y}}$ (${\mathit{T}}_{\mathit{c}}$≊80 K) films has been investigated. In both compounds the Hall coefficient ${\mathit{R}}_{\mathit{H}}$ (${\mathit{B}}_{\mathit{c}}$ axis) in the normal phase is positive and exhibits a strong temperature dependence, which is more pronounced in ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_2$ ${\mathrm{O}}_{7\mathrm{-}\mathit{x}}$ than in ${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_2$ ${\mathrm{CaCu}}_2$ ${\mathrm{O}}_{\mathit{y}}$. On the basis of a renormalized two-dimensional tight-binding band structure the normal-state Hall coefficient ${\mathit{R}}_{\mathit{H}}$ has been calculated as a function of doping concentration and temperature using the relaxation-time approximation. Strong correlation effects are considered to some extent via doping-dependent nearest- and next-nearest-neighbor hopping terms leading to band-narrowing effects. The consideration of the latter term strongly influences the Hall coefficient. The Hall effect has been explored for two quite different models: (i) doping creates holes close to the top of an effective oxygen band, which is located between the lower and the upper Hubbard band; (ii) doping creates holes in a less than half-filled antibonding ${\mathrm{CuO}}_2$ subband.