Transport phenomena in a three-dimensional system close to the magnetic quantum critical point: The conserving approximation with current vertex corrections

It is known that various transport coefficients strongly deviate from conventional Fermi-liquid behaviors in many electron systems which are close to antiferromagnetic (AF) quantum critical points (QCP). For example, Hall coefficients and Nernst coefficients in three-dimensional heavy fermion CeCo In5 and Ce Cu6-x Aux increase strikingly at low temperatures, whose overall behaviors are similar to those in high- Tc cuprates. These temperature dependencies are too strong to explain in terms of the relaxation time approximation. To elucidate the origin of these anomalous transport phenomena in three-dimensional systems, we study the current vertex corrections (CVC) based on the fluctuation exchange approximation, and find out the decisive role of the CVC. The main finding of the present paper is that the Hall coefficient and the Nernst coefficient strongly increase thanks to the CVC in the vicinity of the AF QCP, irrespective of dimensionality. We also study the relaxation time of quasiparticles, and find that "hot points" and "cold lines" are formed in general three-dimensional systems due to strong AF fluctuations.