The Spectral Properties of the Falicov–kimball Model in the Weak-Coupling Limit

Abstract

The f and d electron density of states of the one-dimensional FalicovKimball model are studied in the weak-coupling limit by exact diagonalization calculations. The resultant behaviors are used to examine the d-electron gap (∆ d ), the f -electron gap (∆ f ), and the f d-electron gap (∆ f d ) as functions of the f -level energy E f and hybridization V . It is shown that the spinless Falicov-Kimball model behaves fully differently for zero and finite hybridization between f and d states. At zero hybridization the energy gaps do not coincide (∆ d = ∆ f = ∆ f d ), and the activation gap ∆ f d vanishes discontinuously at some critical value of the f -level energy E f c . On the other hand, at finite hybridization all energy gaps coincide and vanish continuously at the insulator-metal transition point E f = E f c . The importance of these results for a description of real materials is discussed.

Valence transition behavior of the doped Falicov–Kimball model at nonzero temperatures

“…For SmB 6 a very good agreement of experimental and theoretical results has been obtained also for nonzero temperatures for both the temperature dependence of the specific heat as well as magnetic susceptibility [10]. In addition, it was found that the spinless FKM can describe the anomalous temperature increase of electrical conductivity σ in SmB 6 (due to the valence transition) [11] as well as the low temperature behavior of σ (due to the appearance of the in-gap structure) in this material [9,12]. Recently, the FKM has been successfully used to describe the inelastic light scattering in the SmB 6 systems [13].…”

“…In particular, it has been found that the spinless FKM, can describe the discontinuous valence and insulator-metal transitions [4,5] (induced by external pressure) observed experimentally in some rare-earth sulfides, halides and borides [6]. A nice correspondence between theoretical and experimental results has been found, for example, for SmB 6 [5,7,8,9], where the alternative explanation of formation and disappearance of the energy gap in the electronic spectrum of SmB 6 has been presented. For SmB 6 a very good agreement of experimental and theoretical results has been obtained also for nonzero temperatures for both the temperature dependence of the specific heat as well as magnetic susceptibility [10].…”