Anomalous transport phenomena in Fermi liquids with strong magnetic fluctuations

In this paper, we present recent developments in the theory of transport phenomena based on the Fermi liquid theory. In conventional metals, various transport coefficients are scaled according to the quasiparticles relaxation time, tau, which implies that the relaxation time approximation (RTA) holds well. However, such a simple scaling does not hold in many strongly correlated electron systems. The most famous example would be high-T-c superconductors (HTSCs), where almost all the transport coefficients exhibit a significant deviation from the RTA results. This issue has been one of the most significant unresolved problems in HTSCs for a long time. Similar anomalous transport phenomena have been observed in metals near their antiferromagnetic (AF) quantum critical point (QCP). The main goal of this study is to demonstrate whether the anomalous transport phenomena in HTSC is evidence of a non-Fermi liquid ground state, or just RTA violation in strongly correlated Fermi liquids. Another goal is to establish a unified theory of anomalous transport phenomena in metals with strong magnetic fluctuations. For these purposes, we develop a method for calculating various transport coefficients beyond the RTA by employing field theoretical techniques. In a Fermi liquid, an excited quasiparticle induces other excited quasiparticles by collision, and current due to these excitations is called a current vertex correction (CVC). Landau noticed the existence of CVC first, which is indispensable for calculating transport coefficients in accord with the conservation laws. Here, we develop a transport theory involving resistivity and the Hall coefficient on the basis of the microscopic Fermi liquid theory, by considering the CVC. In nearly AF Fermi liquids, we find that the strong backward scattering due to AF fluctuations induces the CVC with prominent momentum dependence. This feature of the CVC can account for the significant enhancement in the Hall coefficient, magnetoresistance, thermoelectric power, and Nernst coefficient in nearly AF metals. According to the present numerical study, aspects of anomalous transport phenomena in HTSC are explained in a unified way by considering the CVC, without introducing any fitting parameters; this strongly supports the idea that HTSCs are Fermi liquids with strong AF fluctuations. Further, the present theory also explains very similar anomalous transport phenomena occurring in CeMIn5 (M = Co or Rh), which is a heavy-fermion system near the AF-QCP, and in the organic superconductor kappa-(BEDT-TTF). In addition, the striking omega-dependence of the ac-Hall coefficient and the remarkable effects of impurities on the transport coefficients in HTSCs appear to fit naturally into the present theory. Many aspects of the present theory are in accord with the anomalous transport phenomena in HTSCs, organic superconductors and heavy-fermion systems near their AF-QCPs. We discuss some of the open questions for future work.