Symmetry classification of electron and phonon states in TiO2 -based nanowires and nanotubes.

Abstract

Procedure for deriving Wyckoff positions for nanowires (NWs) and nanotubes (NTs) from Wyckoff positions of ambient space group is described. It is proposed how to use SITESYM code available on Bilbao Crystallographic Server to calculate representations induced from orbit stabilizers for 1-periodic groups. This procedure is demonstrated on the example of TiO2 rutile-based NWs. General analytic expressions for Line group representations induced from irreps of their orbit stabilizers are obtained. This approach presupposes the use of the standard (crystallographic) factorization of Line groups. Computer construction of orbits and induced representations can be efficiently implemented and the corresponding computer code SITESYML, which can be considered as a certain elaboration of the existing code SITESYM is written. The application of the code is demonstrated on the example of TiO2 anatase-based NTs with the rectangular and hexagonal morphology.