The Influence of Lattice Defects on the Ground-State Properties of the Falicov-Kimball Model in Two Dimensions

Abstract

The influence of lattice defects (vacancies) on the ground-state properties of the spinless Falicov-Kimball model is studied by a well-controlled numerical method in two dimensions. It is shown that in the presence of vacancies (distributed randomly) the ground states of the Falicov-Kimball model are phase separated for small f -electron concentrations n f and exhibit the long-range order for n f near the half-filled band case n f = 1/2. In addition, the dependence of average f -orbital occupancy on the concentration of vacancies is calculated for a wide range of model parameters. The resultant behaviours are used to interpret the experimental data obtained for the mixed-valence system Sm1−xB6.

Investigation of Mixed Valence State of Sm_{1-x}B_{6} and Sm_{1-x}La_{x}B_{6} by XANES

“…2) shows that the IV state of Sm ions is maintained in Sm 1−x B 6 samples up to 20 % of concentration x of vacancies and the valence increases with increasing x. These results are in good qualitative agreement with susceptibility and Xray measurements [4,7] and exact numerical calculation of the spinless FKM in two dimensions [10]. This theoretical study of Sm 1−x B 6 has shown that the valence transition of Sm ions is maintained up to 25% of vacancy concentration x and that the average f -orbital occupancy, n f = 3 − v, decreases with x.…”