One-Electron States in a Layered Crystal with Covalent Bridges

Abstract

One-electron states in a layered crystal with chaotically placed covalent bridges have been calculated using the group decomposition of the Green's function with respect to the concentration of interacting dopants. The calculations have been based on the Fivaz's dispersion law for conduction electrons. It has been shown that a rearrangement of the conduction band takes place at a certain concentration of the covalent bridges (c ) c 0 ; c ( 1, where c 0 is the characteristic concentration larger than that of an isotropic crystal). After this rearrangement an anisotropic dopant band is formed. All parameters of this rearrangement have been found as well as the effective mass tensor components for the rearranged conduction band and for the created dopant band. It has been demonstrated that the interaction process leading to the formation of the covalent bridges can be a reason of the change of the anisotropy of the electric conductivity in a layered crystal. The density and the number of the quasi-Bloch states have been calculated in the created energy band. The number of these states increases with the increase of the dopant concentration. The possibility of dielectric-metal transition in intercalated layered crystals was analyzed.

Covalent bridges – an induced modification of the conduction band in layered crystals

“…Numerous papers devoted to the investigation of intercalated materials [1]- [11] confirm variety of new phenomena that are conditioned by dopants. Recently we have shown in [12,13] that the electronic energy spectrum is a subject of essential changes near the energy gap at considerable concentration of dopants (c ) c 0 , c ( 1 where c 0 is the characteristic concentration) which create the "covalent bridges" with host atoms of a perfect crystal. When the initial dopant level e 0 is located in the forbidden energy gap (e 0 < 0) a rearrangement of the conduction band takes place.…”

“…In this paper we continue discussing one-electron states in a layered crystal with covalent bridges in the case when a dopant level is located in the conduction band (e 0 > 0). We apply the Fivaz's dispersion law [14]: eðc; xÞ ¼ h 2 c 2 =ð2m k Þ þ 2Jð1 À cos xdÞ and the model of a crystal which has been al-ready described in [12]. An analysis of the cross-rearrangement of the energy spectrum near a resonant level is conducted in a similar way to that of [12] i.e.…”

“…We apply the Fivaz's dispersion law [14]: eðc; xÞ ¼ h 2 c 2 =ð2m k Þ þ 2Jð1 À cos xdÞ and the model of a crystal which has been al-ready described in [12]. An analysis of the cross-rearrangement of the energy spectrum near a resonant level is conducted in a similar way to that of [12] i.e. using the group decomposition of the Green's function with respect to the concentration of interacting dopants [15][16][17].…”

“…In the first Section of our paper the self-consistent equation system for the diagonal Green's function obtained in [12] is refered. Afterwards, calculation results of the non-renormalized Green's function for different energy ranges: 0 < E < 4J, E > 4J and for chosen parameters of the model (Joverlap integral, lhybridization parameter) are presented.…”

“…Dopants are placed in the interlayer space and they create the covalent bridges with atoms of neighbouring layers. The model used in this paper is described in more detail in [12] where, in Appendix A, a derivation of the equation system (1)-(6) placed below is presented. This is the self-consistent system of equations for the Green's function from which a rearranged energy spectrum of a crystal with covalent bridges can be obtained.…”