Kondo lattice without Nozières exhaustion effect

Abstract

Abstract. -We discuss the properties of layered Anderson/Kondo lattices with metallic electrons confined in 2D xy planes and local spins in insulating layers forming chains in the z direction. Each spin in this model possesses its own 2D Kondo cloud, so that the Nozières' exhaustion problem does not occur. The high-temperature perturbational description is matched to exact low-T Bethe-ansatz solution. The excitation spectrum of the model is gapless both in charge and spin sectors. The disordered phases and possible experimental realizations of the model are briefly discussed.The famous exhaustion problem formulated by Nozières [1] states that the number of electrons eligible to participate in Kondo screening is not enough to screen magnetic moments localized in each site of periodic Anderson lattice (AL) or Kondo lattice (KL). In spite of his latest revision [2] based on mean-field 1/N expansion, this exhaustion is a stumbling stone on the way from exactly solvable Anderson or Kondo impurity model [3] to the 3D AL/KL models, which are believed to be the generic models for heavy-fermion materials [4]. The problem arises already for concentrated Kondo alloys, where the number or localized spins N i is comparable with the number of sites N = L n in the n-dimensional lattice. In this case the number of spin degrees of freedom provided by conduction electrons in a KL is not enough for screening N i localized spins. As an option a scenario of dynamical screening was proposed [5,6], where only part of spins screened by Kondo clouds form magnetically inert singlets. The lowtemperature state of such KL is a quantum liquid, where N s singlets are mixed with N − N s "bachelor" spins, which hop around and exchange with singlets thereby behaving as effective fermions. Nozières' exhaustion is measured by a parameter p N = N i /(ρ 0 T K ) (the number of spins per screening electron). Here] is the energy scale of Kondo effect, J is the exchange coupling constant in the single-impurity Kondo Hamiltonian, ρ 0 is the density of states on the Fermi level of metallic reservoir.Second obstacle, which does not allow the extrapolation of Kondo impurity scenario to KL is the indirect RKKY exchange I jj between the localized spins, which arises in the 2nd order in J or in the 4th order in V (hybridization parameter in the generic AL Hamiltonian). The corresponding energy scale isc EDP Sciences Article published by EDP Sciences and available at http://www.edpsciences.org/epl or http://dx