Charge Density Wave-Soliton Model for Se and Te

Abstract

A new microscopic theory is proposed for the electronic and lattice structures of crystal and defects of Se and Te. Consideration of the valence bond picture shows that electron correlation in valence P electrons produces a charge density wave (CDW) of vector nature, the vector CDW (VCDW), which has the period of three and keeps every atom neutral. Defects including valence alternation pairs and recombinations of helical chains may be generated as' low energy solitonic excitations of the VCDW. Amorphous Se and Te may be regarded as an assembly of solitonic excitations in the VCDW. A formulation of the VCDW and its soli tonic excitations is given in the HF approximation. Valence P electrons are described by an INDO type Hamiltonian with the nearest neighbour transfer and exchange interactions, intraatomic Coulomb repulsion and exchange and interatomic Coulomb repulsion. The remaining closed shell part of each atom is represented as a core with a repulsive potential. The lattice geometry is determined by the balance of the cohesive force of P electrons and the repulsion of cores. The effective intraatomic Coulomb interaction in a neutral atom has the form of a negative on-site interaction which stabilizes the VCDW. An equation is obtained which determines self-consistently the electronic and lattice structures of the VCDW and its solitonic defects. The VCDW and its defects always accompany not only an electron density modulation but also a bond order modulation so that they have lattice structures distorted from a standard cubic lattice. The trigonal lattice of the crystalline Se and Te can be explained as due to the presence of the VCDW. § 1. Introduction 1 In a current model of chalcogenideglasses, 1)_5) defects intrinsic in them are considered to be a pair of atoms with unusual valences, one atom overcoordinated and another undercoordinated_ Such defects are called valence alternation pairs 4),5) (V AP). Among the two possible YAP species, the ionic non-magnetic species is considered to be lower in energy than the neutral paramagnetic one owing to a stabilization by a lattice distortion. This model is able to explain many unusual properties of chalcogenide glasses in terms of intrinsic defects of a few kinds. Several attempts 6),7) have been made to justify the model by microscopic calculations. However, we have not yet had a satisfactory microscopic formulation of the model.7} The fact revealed by the model that characteristic properties of chalcogenide glasses appear to originate from intrinsic defects of a few kinds suggests a new approach to the microscopic theory of chalcogenide glasses. The approach stands on a possible analogy of chalcogenides to polyacetylene. It has been shown that many outstanding electrical, magnetic and optical properties of polyacetylene arise from intrinsic defects of a few kinds which are solitons generated by an electron-lattice coupling. S) In this paper, we shall attempt to make a new microscopic model of chalcogenides in which V AP defects are generated as low energy solitonic excitations. We shall formulate such a model for pure Se and Te. To get low energy solitonic excitations, the ground state of regular lattice is necessary to have a degeneracy; In the case of polyacetylene the degeneracy in the dimeriza-tion phase is the basis for soliton generation. S) In the case of Se and Te, electron correlation provides a degeneracy in the ground state. We shall show, with qualitative A new microscopic theory is proposed for the electronic and lattice structures of crystal and defects of Se and Te. Consideration of the valence bond picture shows that electron correlation in valence P electrons produces a charge density wave (CDW) of vector nature, the vector CDW (VCDW), which has the period of three and keeps every atom neutral. Defects including valence alternation pairs and recombinations of helical chains may be generated as' low energy solitonic excitations of the VCDW. Amorphous Se and Te may be regarded as an assembly of solitonic excitations in the VCDW. A formulation of the VCDW and its soli tonic excitations is given in the HF approximation. Valence P electrons are described by an INDO type Hamiltonian with the nearest neighbour transfer and exchange interactions, intraatomic Coulomb repulsion and exchange and interatomic Coulomb repulsion. The remaining closed shell part of each atom is represented as a core with a repulsive potential. The lattice geometry is determined by the balance of the cohesive force of P electrons and the repulsion of cores. The effective intraatomic Coulomb interaction in a neutral atom has the form of a negative on-site interaction which stabilizes the VCDW. An equation is obtained which determines self-consistently the electronic and lattice structures of the VCDW and its solitonic defects. The VCDW and its defects always accompany not only an electron density modulation but also a bond order modulation so that they have lattice structures distorted from a standard cubic lattice. The trigonal lattice of the crystalline Se and Te can be explained as due to the presence of the VCDW. § 1. Introduction 1 In a current model of chalcogenideglasses, 1)_5) defects intrinsic in them are considered to be a pair of atoms with unusual valences, one atom overcoordinated and another undercoordinated_ Such defects are called valence alternation pairs 4),5) (V AP). Among the two possible YAP species, the ionic non-magnetic species is considered to be lower in energy than the neutral paramagnetic one owing to a stabilization by a lattice distortion. This model is able to explain many unusual properties of chalcogenide glasses in terms of intrinsic defects of a few kinds. Several attempts 6),7) have been made to justify the model by microscopic calculations. However, we have not yet had a satisfactory microscopic formulation of the model.7} The fact revealed by the model that characteristic properties of chalcogenide glasses appear to originate from intrinsic defects of a few kinds suggests a new approach to the microscopic theory of chalcogenide glasses. The approach stands on a possible analogy of chalcogenides to polyacetylene. It has been shown that many outstanding electrical, magnetic and optical properties of polyacetylene arise from intrinsic defects of a few kinds which are solitons generated by an electron-lattice coupling. S) In this paper, we shall attempt to make a new microscopic model of chalcogenides in which V AP defects are generated as low energy solitonic excitations. We shall formulate such a model for pure Se and Te. To get low energy solitonic excitations, the ground state of regular lattice is necessary to have a degeneracy; In the case of polyacetylene the degeneracy in the dimeriza-tion phase is the basis for soliton generation. S) In the case of Se and Te, electron correlation provides a degeneracy in the ground state. We shall show, with qualitative