The Kondo effect has been playing an important role in strongly correlated electon systems. The important point is that the magnetic impurity in metals is a typical example of the Fermi liquid. In the system the local spin is conserved in the ground state and continuity with respect to Coulomb repulsion U is satisfied. This nature is satisfied also in the periodic systems as far as the systems remain as the Fermi liquid. This property of the Fermi liquid is essential to understand the cuprate high-Tc superconductors (HTSC). On the basis of the Fermi liquid theory we develop the transport theory such as the resistivity and the Hall coefficient in strongly correlated electron systems, such as HTSC, organic metals and heavy Fermion systems. The significant role of the vertex corrections for total charge-and heat-currents on the transport phenomena is explained. By taking the effect of the current vertex corrections into account, various typical non-Fermi-liquid-like transport phenomena in systems with strong magnetic and/or superconducting flucutations are explained within the Fermi liquid theory.
1.IntroductionSince the discovery of Kondo Effect, the theory of electron correlation has been developed remarkably. In particular, the study of the strongly correlated electron systems such as cuprates and heavy fermions is actively performed. In this article we discuss the contribution of Kondo theory to the theory of strongly correlated electron systems. The key word is the singlet: The ground state of the single impurity in metals is the singlet where a localized spin is coupled antiferromagnetically with conduction electron spin. The resonating-valence-bond (RVB) state is a spin singlet state and is considered to be the basis of the cuprate high-T c superconductivity (HTSC). By using Anderson's orthogonality theorem, we show that the Fermi liquid state is nothing but the RVB state in metal. As a result, we can reasonably arrive at the pairing theory of superconductivity.
Anderson HamiltonianIn 1961 Anderson presented the following Hamiltonian and explained the appearance of a localized moment in metals by using the Hartree-Fock approximation.[1]The first term is the energy of conduction electrons and the third term is the d-electron part. The last term is the Coulomb repulsion between two d-electrons and is the only many-body interaction. The symmetric Anderson Hamiltonian possesses the electron-hole symmetry and is easy to understand the physical meaning because of the suppressed charge fluctuations. By assuming the average number of d-electrons is unity and taking the nonmagnetic case (< n dσ >=< n d−σ >= 1/2) ,where E Here ρ is the density of states of conduction electrons at the Fermi energy. Hereafter, we assume the band-width of conduction band is infinite and ρ is constant.
2-1. Kondo effectAnderson explained the existence of magnetic moment as the effect of electron correlation. However, there existed a long standing mystery for these 30 years.[2] As shown in Fig.1, when we decrease the temperature, the resid...