Pairing by Kondo interaction and magnetic phases in the Anderson–Kondo lattice model: Statistically consistent renormalized mean‐field theory

Abstract

Phone: þ48 12 663 5685, Fax: þ48 12 633 4079We start from the Anderson-Kondo lattice model derived by us earlier, in which both the Kondo interaction and the residual hybridization processes have been included in a systematic manner. In the present work we discuss a fairly complete phase diagram including magnetic, pure superconducting (SC), and coexistent antiferromagnetic (AF)-SC phases. Both intra-and interatomic hybridization cases have been considered, separately. The Kondo insulating state with completely compensated magnetic moments has been obtained as a reference state, from which either AF or SC or mixed AF þ SC phases evolve when the metallic state becomes stable. The SC pairing is induced mainly by the Kondo interaction. The method of approach we use is the so-called statistically consistent renormalized mean-field theory (SC-RMFT), encompassing essential corrections to the standard Gutzwiller-ansatz approach.ß 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 1 Motivation: consistent single-particle description of strongly correlated state We have developed recently the so-called statistically consistent renormalized mean-field theory (SC-RMFT) for the description of phase diagrams in high-temperature (high-T c ) superconductors [1][2][3][4] and heavy-fermion systems [5]. The need for statistical consistency was motivated by the circumstance [6] that the so-called Gutzwiller-ansatz approach is inconsistent in the sense that, e.g., self-consistent equations for magnetization or the superconducting (SC) gap in the Hubbard or t À J models, provide solutions that differ from those obtained from the corresponding variational procedure! This is the principal defect of the Gutzwiller ansatz, rarely noted in the literature [7,8]. To achieve the statistical consistency in that sense we have introduced constraints with the help of a Lagrange-multiplier method, with the multipliers being interpreted as the self-consistent correlation fields. The constraints introduced to achieve the consistency correspond directly to those introduced within the slave-boson approach [1,6], except here we do not need to introduce the slave Bose fields. We will not discuss in detail the method here [1], but instead concentrate on the novel features emerging from the method implementation to the heavy-fermion physics.2 Anderson-Kondo lattice model: Its physical meaning Apart from implementing the SC-RMFT method of calculating the physical properties, we introduce the Anderson-Kondo model, as represented by the effective Hamiltonian in between the pure Kondo-lattice and full periodic-Anderson models. The Anderson-Kondo-lattice Hamiltonian is discussed formally in the Appendix; here we elaborate on its physical meaning. The situation is depicted schematically in Fig. 1. The need for introducing this form of modified Anderson-lattice Hamiltonian is motivated by the circumstance that the application of the full SchriefferWolff transformation, reducing the Anderson-lattice model to its Kondo-lattice counterpart, may not be correct from th...

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