Density of non-Bloch electron states in perfect cubic crystals

✍ Scribed by T. Bulski; S. Olszewski; A. Wierzbicki

• Book ID: 104579817
• Publisher: John Wiley and Sons
• Year: 1980
• Tongue: English
• Weight: 992 KB
• Volume: 17
• Category: Article
• ISSN: 0020-7608
• DOI: 10.1002/qua.560170411

✦ Synopsis

Abstract

This paper gives an abbreviated method for the calculation of the density of states of a crystal on the basis of that band theory in which the crystal electron states are represented by the standinglike wave functions classified according to the point‐group symmetry species. The crystal is a large but finite sphere filled regularly with atoms, and the wave functions are quantized at the boundary of the sphere. The Bloch theorem is not satisfied in this theory since the wave functions are not basis functions of the irreducible representations of the translation subgroup. On the other hand, a theorem is established that the density of states can be made up of contributions given by all irreducible representations of the crystal point group, any contribution being proportional to the square of the dimension of the irreducible representation. In distinction to a former approach, the band structure is calculated solely from the energy eigenvalues obtained with the aid of the diagonalization process of the Wannier–Slater differential operator. A simple cubic lattice with an s atomic orbital on each lattice site is taken as an example, and the results are compared with Bloch's theory.