Elementary energy bands in the band structure of A^IV, A^IIIB^V crystals and superlattices built upon them

Abstract

A concept of the elementary energy bands was applied to interpret the electronic energy spectra of crystals from the cubic system and the superlattices (GaAs) /(AlAs)(Si) /(Ge) built upon them. Based upon this example, it was shown that the elementary energy bands concept elaborated in the emptylattice 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 T d 2 symmetry crystals into a physical complex that is related to the elementary energy band of the O h 7 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.

Electronic Structure and Phase Transition in Ferroelectic Sn2P2S6 Crystal

“…By comparing these complexes with the representations induced by the irreps of site symmetry groups for all Wyckoff positions of the Sn 2 P 2 S 6 crystal elementary cell, one can find the so-called actual Wyckoff positions [45]. In our case two first complexes originate from Wyckoff position $d(\frac{1}{2},0,0)$, which is the point in the middle of the P–P bond and the last one corresponds to general position e ( x, y, z ).…”

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

“…Hence, the presented results show that the irreducible band representations of EEBs for the valence band of TlGaSe 2 were correctly predicted in the empty‐lattice approximation, and that the Wyckoff positions $e(p({\bf a}_{3} {-} {\bf a}_{2} ))$ and $f(x,y,z)$ are the actual ones. Our earlier investigations 10–12, 24 show that the highest valence electron density distribution is focussed in these positions in the unit cell. The valence electron density distribution in the unit cell of TlGaSe 2 is presented in Fig.…”

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

“…in the Γ-point as took place in the case of 4 3 In Se crystal [26] and 5 5 (GaAs) (AlAs) / superlattice [23]. This new kind of EEB originates from overlapping of the former ones and corresponds to another, the general Wyckoff position ( ) c x y z , , of the…”

“…the maximum of the spatial valence electron density distribution can be focused in this position in the unit cell. The last fact has been verified by the ab-initio bandstructure calculations of semiconductors as well as superlattices based on them [23]. Hence, the EEBs concept will be, in this paper, a tool to explain the topology of the valence band of the 3 4 Hg TeCl being a result of the evolution of the valence band of 2 HgCl crystal possessing structural elements of HgTe.…”

“…Since a few Wyckoff positions can be assigned to the given space group, there appears the problem of the choice of such a position that is responsible for the symmetry and topology of the real valence band of a crystal. Our investigations showed that among all Wyckoff positions there exist the so-called "actual" Wyckoff positions [23]. Irreducible representations induced from the site-symmetry group of the actual Wyckoff position describe the symmetry of the EEBs that create the valence band of a given crystal.…”