Mode decomposition based on crystallographic symmetry in the band-unfolding method

The band-unfolding method is widely used to calculate the effective band structures of a disordered system from its supercell model. The unfolded band structures show the crystallographic symmetry of the underlying structure, where the difference of chemical components and the local atomic relaxation are ignored. However, it has still been difficult to decompose the unfolded band structures into the modes based on the crystallographic symmetry of the underlying structure, and therefore detailed analyses of the unfolded band structures have been restricted. In this study, a procedure to decompose the unfolded band structures according to the small representations (SRs) of the little groups is developed. The decomposition is performed using the projection operators for SRs derived from the group representation theory. The current method is employed to investigate the phonon band structure of disordered face-centered-cubic Cu0.75Au0.25, which has large variations of atomic masses and force constants among the atomic sites due to the chemical disorder. In the unfolded phonon band structure, several peculiar behaviors such as discontinuous and split branches are found in the decomposed modes corresponding to specific SRs. They are found to occur because different combinations of the chemical elements contribute to different regions of frequency.