Elementary Energy Bands Research Articles

Vibronic interaction in crystals with the Jahn-Teller centers in the elementary energy bands concept

The order-disorder type phase transition caused by the vibronic interaction (collective Jahn-Teller effect) in a monoclinic CuInP$_2$S$_6$ crystal is analyzed. For this purpose, a trigonal protostructure model of CuInP$_2$S$_6$ is created, through a slight change in the crystal lattice parameters of the CuInP$_2$S$_6$ paraelectric phase. In parallel to the group-theoretical analysis, the DFT-based {\it ab initio} band structure calculations of the CuInP$_2$S$_6$ protostructure, para-, and ferriphases are performed. Using the elementary energy bands concept, a part of the band structure from the vicinity of the forbidden energy gap, which is created by the $d$-electron states of copper, has been related with a certain Wyckoff position where the Jahn-Teller's centers are localized. A construction procedure of the vibronic potential energy matrix is generalized for the case of crystal using the elementary energy bands concept and the group theoretical method of invariants. The procedure is illustrated by the creation of the adiabatic potentials of the $\Gamma_5$-$\Gamma_5$ vibronic coupling for the protostructure and paraphase of the CuInP$_2$S$_6$ crystal. A structure of the obtained adiabatic potentials is analyzed, followed by conclusions on their transformation under a phase transition and the discussion on the possibility for the spontaneous polarization to arise in this crystal.

Peculiarities of Chemical Bonding in Crystals of the In-Se System

The investigation of the ab initio band structure and the resulting spatial electron density distribution of the In Se system in the framework of the density functional theory and the elementary energy bands concept is presented. It gives us reliable information about the valence band structure and peculiarities of the chemical bonding in these crystals. Some regularities in the evolution of the elementary energy bands topology is established, together with the choice of the actual Wycko position that is responsible for this topology and, at the same time, for the valence band formation in the InSe, In2Se3, In4Se3, and In6Se7 crystals. The calculated Mulliken charges and the degree of ionicity allow to estimate the character of chemical bonding in these crystals.

Non‐standard anisotropy of the energy spectrum of a layered TlGaSe2 crystal

AbstractThe ab initio band structure calculations of the TlGaSe2 crystal in the framework of DFT, within LDA were performed using the relevant Brillouin zone for the base‐centered monoclinic lattice. It was shown that the main features of this structure can be obtained in the framework of the elementary energy bands concept, taking into account the existence of the Davydov splitting that is the consequence of structural properties of TlGaSe2.The obtained results confirm that TlGaSe2 is an indirect band‐gap material, however, an additional local minimum of the conduction band in the Γ point is located both in a near energetic and near k‐space distance from the absolute minimum. It was shown that TlGaSe2 is the next example of a layered semiconductor for which an universal anisotropy of the energy spectrum branches that coincide with its mechanical anisotropy cannot be established.

Elementary energy bands concept, band structure, and peculiarities of bonding in β-InSe crystal

The elementary energy bands concept together with the analysis of the Davydov-like splitting were applied for the first time for investigation of energy band structure and spatial electron density distribution in hexagonal crystals. This approach was used for consideration of the valence band states and for determination of peculiarities of the spatial charge density distribution in the unit cell of the layered β-InSe crystal. It was established that the valence charge density can be located in the so-called Van-der-Waals space. Conclusions following from the elementary energy bands concept were confirmed by the ab initio calculations of the band structure of β-InSe.

Fundamental characteristics of a new Hg3TeCl4 crystal obtained by means of the elementary energy bands concept based on ab initio band structure calculations

Fundamental characteristics of a new Hg₃TeCl₄ crystal obtained by means of the elementary energy bands concept based on <i>ab initio</i> band structure calculations

Relation between the topology of the elementary energy bands in the valence band of the Hg3TeCl4 crystal and its anisotropy

AbstractA mechanism of the Davydov‐like splitting formation in the Brillouin zone of the Hg3TeCl4 crystal (Pbca, D2h15) with two double translationally nonequivalent layers in the unit cell was analyzed. The topology of the 8‐branch elementary energy bands creating the valence band of Hg3TeCl4 was explained. Energetic distances between states of the elementary energy bands at the Brillouin zone edges were estimated by means of the localized function method. The topology of the elementary energy bands was related with the ratio of the interaction strength between the double layers in the unit cell and the interaction strength between single layers creating the double layer. (© 2009 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

The band structure of a layered Hg3TeCl4 crystal formed by energy states of HgCl2 and HgTe crystals

AbstractThe ab‐initio calculated band structure of a not as yet investigated orthorhombic Hg3TeCl4 crystal (Pbca, D152h) was analyzed by means of the elementary energy‐bands concept. It was demonstrated that this band structure originates from that of a layered HgCl2 dielectric deformed by the presence of the HgTe structural elements. Further, it was revealed that the valence band of Hg3TeCl4 is composed of the 8‐branch elementary energy bands corresponding to the actual Wyckoff position c (x, y, z) of D152h group that indicates the presence of ionic and covalent contributions to the chemical bonding in the crystal. The existence of Davydov splitting in the 8‐branch elementary energy band situated in the low‐energy range of the valence band was observed, which is typical for layered crystals with a weak interlayer interaction between translationally nonequivalent structural units. It was shown that the anisotropy of the electron and hole effective masses does not correspond to the macroscopic anisotropy of the crystal and an explanation of this behaviour was proposed. The obtained parameters of the crystal (direct energy gap Eg = 2.49 eV as well as values of the estimated electron effective masses) indicate that it could find an application in optoelectronics. (© 2008 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Possibilities of the elementary energy bands concept to determine characteristics of crystals with phase transitions

It is demonstrated that the concept of the elementary energy bands can be used to predict a structural change of a crystal's primitive cell during a phase transition without investigating this mechanism itself. Three examples of the phase transitions have been chosen: deformational phase transition occuring in GeTe (O5h), pressure induced phase transition in ZnTe (T2d) and induced by phonon-phonon interaction in SbSI (D162h). The discussed approach demands a knowledge about the space symmetry group of a crystal after phase transition.

Elementary energy bands in the band structure of AIV, AIIIBV crystals and superlattices built upon them

AbstractA concept of the elementary energy bands was applied to interpret the electronic energy spectra of crystals from the cubic system and the superlattices (GaAs)M /AlAsM (M = 5, 10), (Si)10/(Ge)10 built upon them. Based upon this example, it was shown that the elementary energy bands concept elaborated in the empty‐lattice approximation allows one to predict the symmetry and topology of the valence band of artificial periodic systems as well as the spatial valence‐electron density distribution in a unit cell of those systems. A verification of this conclusion was confirmed by the ab‐initio band‐structure calculations of the superlattices mentioned above. An energy‐structural factor was found that joins two elementary energy bands characteristic for Td2 symmetry crystals into a physical complex that is related to the elementary energy band of the Oh7 symmetry crystals. This relationship between the elementary energy bands was utilized to find the actual Wyckoff position in the superlattice's unit cell responsible for the spatial electron density distribution. (© 2007 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Elementary energy bands in isovalent IV–VI orthorhombic and cubic crystals and their solid solutions

AbstractIt is shown that elementary energy bands concept can be applied to complex systems like solid solutions. As in the case of single crystals, the symmetry of elementary energy bands in the valence band of such systems is related to the actual Wyckoff positions in their unit cells, where accumulation of valence electrons is observed. These results are predicted in the empty‐lattice approximation and confirmed by ab initio calculations of electronic properties of SnS, PbS and Pb0.5Sn0.5S systems. It is suggested that the presented application of the elementary energy bands concept together with the empty‐lattice approximation can be used as a simple method for obtaining charge localization centers in the crystalline lattice and thus for the construction of the well‐localized Wannier functions. (© 2007 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Elementary energy bands concept for IV–VI crystals with phase transitions

The possibility to describe the phase transformation in narrow-gap IV–VI-type semiconducting ferroelectrics, based upon the information about the symmetry of the elementary energy bands in the band structure of a given phase and the site symmetry of the related actual Wyckoff positions, is discussed. It is shown that the phase transition is accompanied by an increase of the degrees of freedom of the actual Wyckoff position as a result of the symmetry lowering. Such transformation in r-space is equivalent to the intervalley redistribution of free carriers due to electron–phonon coupling.

Universality of the Empty-Lattice Approximation to Predict the Topology of Energy Spectra of High-Symmetry Crystals and Superlattices Based upon Them

symmetry crystals were discussed to demonstrate univer-sality of the empty-lattice approximation to obtain the topology and sym-metry of the elementary energy bands creating the valence band of thosecrystals and to predict a localization of the maximum of valence electrondensity distribution in the unit cell. The elaborated concept of the ele-mentary energy bands was applied to the (GaAs)

Similarities of the band structure of In4Se3 and InSe under pressure and peculiarities of the creation of the band gap

AbstractThe existence of the physical elementary energy bands describing the Davydov splitting was demonstrated in the energy spectra of the layered orthorhombic In4Se3 crystal. It was confirmed that the physical elementary energy bands are related to the exactly determined Wyckoff position in the unit cell, where the maximum of the valence electron density is localized. By means of ab initio calculations, the dispersion laws with the low‐energy non‐parabolicity were obtained for electrons and holes of the In4Se3 crystal. The reasons for such a dispersion law to occur in In4Se3 are discussed as well as its similarity to the dispersion law for holes in the β ‐InSe crystal under pressure. (© 2006 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Elementary energy bands in the band structure of the narrow-band-gap semiconductor CdSb

Based upon the example of a narrow band gap covalent CdSb crystal $({D}_{2h}^{16})$, it is shown that a spatial electron density distribution in the unit cell is related to the Zak's elementary energy bands creating the valence band and to the corresponding Wyckoff positions. A role of particular electronic states in the creation of the elementary energy bands was analyzed by conducting ab initio band structure calculations of CdSb. The investigations of the topology of the elementrary energy bands allows one to predict the nature of chemical bondings in rhombic crystals.

Elementary energy bands in band structure calculations of some wide-bandgap crystals

Semiconducting Tl 3 AsS 4 crystal was chosen as an example to show that its valence band is composed of the elementary energy bands. Their topology and symmetry obtained in the empty-lattice approximation is confirmed by ab initio band structure calculations. It was shown that these elementary energy bands correspond to the Wyckoff position c in a unit cell. Earlier predictions that the largest electron density distribution is focused in the vicinity of this position, similarly to the case of YAlO 3 and SbSI crystals, is confirmed. A conclusion on the common topology and symmetry of the elementary energy bands in electronic and phonon spectra is presented.

Elementary energy bands inab initiocalculations of theYAlO3and SbSI crystal band structure

The local density approximation has been implemented to determine the band structure of orthorhombic crystals ${\mathrm{YAlO}}_{3}$ (YAP) and SbSI. The topology of the valence band structures was analyzed. It has been demonstrated that Zak's elementary energy bands in the band structure are distinguishable on the basis of the empty-lattice approximation. The calculated electron density distribution of YAP and SbSI crystals is related to particular Wyckoff positions. Moreover, there is a direct correspondence between the obtained elementary energy bands and the aforementioned Wyckoff positions characterized by electron density distribution.