Application of the induction procedure and the Smith Decomposition in the calculation and topological classification of electronic band structures in the 230 space groups

Understand

The electronic properties in a solid depend on the specific form of the wave-functions that represent the electronic states in the Brillouin zone.

• Since the discovery of topological insulators, much attention has been paid to the restrictions that the symmetry imposes on the electronic band structures.
• In this work we apply two different approaches to characterize all types of bands in a solid by the analysis of the symmetry eigenvalues: the induction procedure and the Smith Decomposition method.
• The symmetry eigenvalues or irreps of any electronic band in a given space group can be expressed as the superposition of the eigenvalues of a relatively small number of building units (the \emph{basic} bands).