Anomalous transport phenomena in Fermi liquids with strong magnetic fluctuations

Abstract

In this paper, we present a 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, τ , 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 the evidence of non-Fermi liquid ground state, or it is just the 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 had noticed the existence of CVC first, which is indispensable for calculating transport coefficient in accord with the conservation laws. Here, we develop a transport theory involving resistivity and 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 enhancements 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 CeM In 5 (M =Co or Rh), which is a heavy-fermion system near the AF QCP, and in the organic superconductor κ-(BEDT-TTF).In addition, the striking ω-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 heavyfermion systems near their AF QCPs. We discuss some of the open questions for future work.

Saturation of resistivity and Kohler's rule in Ni-dopedLa1.85Sr0.15CuO4cuprate

“…At lower T , the transport in La 1.85 Sr 0.15 Cu 1−y Ni y O 4 has a coherent description in the framework of Fermi-liquid theory, where Kohler's rule is derived under single-relaxation-time approximation with the assumption of small τ -anisotropy over Fermi surface [63,64]. Fulfillment of the rule when ρ 0 is changed by changing temperature indicates nearly T -independent frequency distribution of the phonons involved [65] and is consistent with Fermi-arc length in cuprates being constant [66,67] rather than decreasing with decreasing temperature [68].…”

“…Ni doping can restore antiferromagnetic fluctuations [30,69] that give additional T -dependence in nearly-antiferromagnetic-metals magnetoresistance via correlation length ξ AF (T ), OMR∝ξ 4 AF (T )ρ −2 0 (Ref. [64]). Thus fulfillment of conventional Kohler's rule suggests Tindependent ξ AF within the framework of this theory.…”

In-plane anisotropy of transport coefficients in electronic nematic states: Universal origin of nematicity in Fe-based superconductors

“…In this study, we neglect the VC for the current, since its effect is small for ρ and the TEP [35][36][37][38]. The detailed study of the current VC is important for future research.…”

A theoretical evaluation of magnetoresitance (magneto transport property) of some heavy-fermion superconductors

“…It has also been observed that magnetoresistance strongly violates the Kohler's rule in the case of CeCoIn5 and CeRhIn5 33 . It has also been observed that the transport properties are modified by the backflow accompanied with anisotropic inelastic scattering 34,35 .…”