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

Abstract

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. It has been, however, still 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, we develop a procedure to decompose the unfolded band structures according to the small representations (SRs) of the little groups. For this purpose, we derive the projection operators for SRs based on the group representation theory. We also introduce another type of projection operators for chemical elements, which enables us to decompose the unfolded band structures into the contributions of different combinations of chemical elements. Using the current method, we investigate the phonon band structure of disordered face-centered cubic Cu 0.75 Au 0.25 , which has large variations of atomic masses and force constants among the atomic sites due to the chemical disorder. We find several peculiar behaviors such as discontinuous and split branches in the unfolded phonon band structure. They are found to occur because different combinations of the chemical elements contribute to different regions of frequency.

Universal disorder-induced broadening of phonon bands: from disordered lattices to glasses

“…Several recent efforts, e.g. [8][9][10][11][12], are devoted to resolving disorder-induced variations in the statistics of phonons of a prescribed wavevector. These studies exclusively focus on frequencies ω?ω † , and show that the major effect of disorder is observed at intermediate to high frequencies.…”

Phonon broadening in high entropy alloys

“…Similar negative contributions to the spectral function of the mutual interactions have been found and discussed for Cu-Au recently. 37 The mass fluctuation induced broadening and splitting of the spectral functions can be rather straightforwardly analyzed and understood in terms of the atomic masses, as illustrated above for the MoTaNbWV series (Fig. 2, lower panel).…”

“…[51][52][53][54] In this method, phonon spectra of random alloys are obtained by decomposing the phonon modes of SQS models onto the Brillouin zone of their underlying crystal structures according to their translational symmetry. Pair-projected contributions of the spectral functions are derived by the recently developed mode decomposition technique 37 and by the proposed modified projection scheme. A detailed description is given in the Supplementary Information.…”

“…Subsequently, we applied a recently introduced projection procedure 37 that resolves the contribution into the different pair interactions (Mo-Mo, Mo-Ta, etc.). The results for the MoTaNbWV series at the H-point are shown in the lower panel of Fig.…”

“…An important tool in the above analysis of the phonon spectral function was the decomposition into the contributions of the various element-element interactions. For the VW binary the projection procedure 37 resulted in partial spectral functions for V-V, V-W, and W-W interactions. The virtue of such a decomposition is the close correspondence to force constants between the elements as exploited above.…”