Hall effect of epitaxial YBa2Cu3O7-x and Bi2Sr2CaCu2Oy films: Interpretation of the Hall effect on the basis of a renormalized tight-binding model.

Abstract

The Hall effect of epitaxial ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathit{x}}$ (${\mathit{T}}_{\mathit{c}}$\ensuremath{\approxeq}90 K) and ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{2}$${\mathrm{CaCu}}_{2}$${\mathrm{O}}_{\mathit{y}}$ (${\mathit{T}}_{\mathit{c}}$\ensuremath{\approxeq}80 K) films has been investigated. In both compounds the Hall coefficient ${\mathit{R}}_{\mathit{H}}$ (${\mathit{B}}_{\mathit{c}}$ axis) in the normal phase is positive and exhibits a strong temperature dependence, which is more pronounced in ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{2}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathit{x}}$ than in ${\mathrm{Bi}}_{2}$${\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.The influence of the relaxation time \ensuremath{\tau}(k) on the Hall coefficient has been explored by considering two simple choices, namely a k-independent ${\mathrm{\ensuremath{\tau}}}_{0}$, and \ensuremath{\tau}(k)=l(T,\ensuremath{\delta})/\ensuremath{\Vert}v(k)\ensuremath{\Vert} (l is the mean free path and \ensuremath{\delta} the doping concentration). Depending on the relaxation time different results have been obtained for the Hall coefficient. Assuming that holes are doped in the oxygen band and \ensuremath{\tau}(k)\ensuremath{\propto}\ensuremath{\Vert}v(k)${\mathrm{\ensuremath{\Vert}}}^{\mathrm{\ensuremath{-}}1}$ a good agreement between theory and experimental data of ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{2}$${\mathrm{CaCu}}_{2}$${\mathrm{O}}_{\mathit{y}}$ has been achieved, whereas for ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathit{x}}$ the pronounced temperature dependence of ${\mathit{R}}_{\mathit{H}}$ is qualitatively reproduced. A comparison between the predictions of the Hall effect and the corresponding Fermi surfaces is made. We have also calculated some band parameters including the Drude plasma energy, the Fermi velocity, and the carrier effective mass.