Many-body band structure and Fermi surface of the Kondo lattice

We present a theory for the single-particle excitations and Fermi surface of the Kondo lattice. Thereby we construct an effective Hamiltonian describing the creation and propagation of single-particle-like charge fluctuations on a “resonating-valence-bond background” of local singlets. The theory may be viewed as a Fermionic version of linear spin-wave theory and is of comparable simplicity so that the calculations for the strong-coupling limit can be performed analytically. We calculate the single-particle spectral function for the “pure” Kondo lattice as well as for several extended versions: with a Coulomb repulsion between conduction and $f$ electrons, Coulomb repulsion between conduction electrons, and a “breathing” $f$ orbital. In all cases we study the evolution of the spectrum in going from the Kondo insulator to the heavy electron metal. We compare our results to exact diagonalization of small clusters and find remarkable agreement in nearly all cases studied. In the metallic case the $f$ electrons participate in the Fermi surface volume even when they are replaced by localized Kondo spins and the number of bands, their dispersion and spectral character, and the nontrivial (i.e., nonrigid bandlike) doping dependence including a pronounced transfer of spectral weight are reproduced at least semiquantitatively by the theory.