Hall effect and resistivity in high-Tcsuperconductors: The conserving approximation

The Hall coefficient $R_H$ in high-$T_c$ cuprates in the normal state shows the striking non-Fermi-liquid behavior: $R_H$ follows a Curie-Weiss type temperature dependence and $|R_H|\gg 1/|\mathrm{ne}|$ at low temperatures in the underdoped compounds. Moreover, $R_H$ is positive for hole-doped compounds and negative for electron-doped ones, although each of them has a similar holelike Fermi surface. In this paper, we give the explanation of this long-standing problem from the standpoint of the nearly antiferromagnetic (AF) Fermi liquid. We consider seriously the vertex corrections for the current which are indispensable to satisfy the conservation laws, which are violated within the conventional Boltzmann transport approximation. The obtained total current $J_{\mathbf{k}}$ takes an enhanced value and is no longer perpendicular to the Fermi surface due to the strong AF fluctuations. By virtue of this mechanism, the anomalous behaviors of $R_{\mathrm{H}}$ in high-${\mathrm{T}}_c$ cuprates are naturally explained. Both the temperature and the (electron, hole) doping dependences of $R_H$ in high-$T_c$ cuprates are reproduced well by numerical calculations based on the fluctuation-exchange approximation, applied to the single-band Hubbard model with a holelike Fermi surface. We also discuss the singular temperature dependence of $R_{\mathrm{H}}$ in other nearly AF metals, e.g., ${\mathrm{V}}_2{\mathrm{O}}_3,$ $\kappa$-BEDT-TTF organic superconductors, and heavy fermion systems close to the AF phase boundary.