Theory of the nonmetal-metal transition in rare-earth compounds. I. Electronic density of states

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Abstract
A theory of the nonmetal-metal transition in rare-earth compounds which occurs with increasing temperature is presented. An essential feature of the transition is that a hybridization gap (an energy gap due to the hybridization between localized and conduction electrons) decreases continuously and vanishes at the transition temperature by virtue of the spin-field fluctuation that arises from the Coulomb repulsion between localized electrons. The transition is examined by the calculation of the electronic density of states for conduction and localized electrons in the periodic Anderson model. Its calculation is done by the functional-integral method using the static and single-site coherent-potential approximations. The one-particle Green's function at O K coincides with that obtained by the Hartree-Fock approximation, and there appears the hybridization gap. In the case of two electrons per site including spin degeneracy, the electronic state becomes insulating (or semiconducting). Temperature dependence of the electronic density of states is calculated in the paramagnetic state. With increasing temperature, the spin-field fluctuation grows in proportion to the square root of temperature at very low temperature compared with the width of the uncorrelated conduction band. The spin-field fluctuation makes the hybridization gap decrease continuously and vanish at the transition temperature. The insulating electronic state changes to a paramagnetic metal state.

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