Valence and Metal-Insulator Transitions in the Spinless Falicov–kimball Model Induced by Doping

Abstract

The influence of doping on valence and metal-insulator transitions in the spinless Falicov–Kimball model is studied by the well-controlled numerical method. Two types of doping are examined, and namely, the substitution of rare-earth ions by non-magnetic ions that introduce (i) one or (ii) no additional electron (per non-magnetic ion) into the conduction band. It is found that the first type of substitution increases the average f-state occupancy of rare-earth ions, whereas the second type of substitution has the opposite effect. In both cases valence changes are accompanied by a doping induced insulator-metal transition. The results obtained are used to describe valence and metal-insulator transitions in the samarium hexaboride solid solutions.

Formation of charge and spin ordering in strongly correlated electron systems

“…In addition, optimizing the n f (x) behaviour with respect to τ and E f one can obtain a nice quantitative correspondence between the theoretical and experimental results (see figure 57). Since no significant effects of the increasing dimension D (D = 2, 3) on the behaviour of n f (x) has been observed for both zero and non-zero temperatures [118,119], our results can be satisfactorily used to describe the behaviour of real three dimensional materials.…”

“…In our previous papers [118,119] we have examined theoretically both cases: (i) the substitution of rare-earth Sm ions by non-magnetic trivalent ions (e.g. Y 3+ ) which introduce conduction electrons into the d-conduction band (one electron per dopant) and (ii) the substitution of rare-earth ions by non-magnetic divalent ions (e.g.…”

“…The average occupancy of f orbitals as a function of x for divalent and trivalent dopants. The one-dimensional case [118]. total number of electrons N = N f + N d is equal to the total number of lattice sites L (the case of one electron per rare-earth atom is considered) and does not depend on the number of dopants X. Consequently, the ground-state energy E g (N f ) = L−N f k=1 λ k is also independent of X and can be calculated directly using our AM for arbitrary N f from the interval [0, L − X].…”

“…(b)The ground-state energy Eg as a function of N f /L calculated for two finite clusters of L = 120 and L=240 sites at n = 1/6, 1/3, 1/2, 2/3, 5/6. In both cases E f = 0 and U = 0.5[118].…”

“…The average occupancy of f orbitals as a function of x for divalent and trivalent dopants. The one-dimensional case[118].…”