Phonon dispersion unfolding in the presence of heavy breaking of spatial translational symmetry

Abstract

The phonon dispersion unfolding method is useful for obtaining hidden Bloch symmetries and comparing theoretical results with experiment spectrums (e.g. inelastic neutron scattering, inelastic X-ray scattering, Raman ). In this paper, we propose a method to unfold phonon dispersions. The main advantage of this method is the ability to handle systems with heavy breaking of spatial translational symmetry. Its validity is tested by pure diamond, diamond with Si substitution, and diamond with C vacancies.Since the discovery of effective energy bands in semiconductors [1,2] and alloys [3], unfolding methods for treating the electronic band structures of the weakly periodic solid systems have been rapidly developed [4][5][6][7][8][9][10][11][12][13][14]. Moreover, it has also stimulated the study of phonon dispersion unfolding method [14][15][16][17]. Like electronic energy bands, the phonon dispersions are also affected by translational symmetry (TS) breaking. Most usually, one has to artificially use a supercell to calculate the phonon dispersions of a TS-broken system. However, the theoretically calculated phonon dispersions of a supercell is much denser than that of the primitive cell. As a result, it can not be directly compared with the phonon dispersions detected in inelastic neutron (or X-ray) scattering experiments. Thus, as a further step, one needs to unfold the phonon dispersions into the Brillouin zone (BZ) of the primitive cell.

Unfolding phonon spectra by smearing of vibrational eigenmodes

“…This is similar to that presented in Ref. as an example when the translational symmetry is heavily broken by carbon vacancy that required the special treatment, that is, method two of Ref. .…”

“… as an example when the translational symmetry is heavily broken by carbon vacancy that required the special treatment, that is, method two of Ref. . The result of present calculations is shown in Fig.…”

“…[21] as an example when the translational symmetry is heavily broken by carbon vacancy that required the special treatment, that is, method two of Ref. [21]. The result of present calculations The vibrational spectra of CaF 2 (top left: triangles are experimental data of [28], dashed lines are first-principle calculations [29], continuous lines present the results of this work) and CsCl (top right: triangles -experiment [30]), crystal structure of CaF 2 (bottom left) and its spectrum unfolded into a Brillouin zone of simple cubic lattice (bottom right).…”

“…Unfolding methods, have become very popular and useful to analyze the results of calculations for complicated systems via mapping them on more simple underlying structures. The examples include both electronic structure and lattice dynamics calculations for crystals with local defects of the structure (vacancies, impurities, etc.)…”

“…This similarity becomes the most pronounced in case of tight‐binding method when, as noted in , p ‐orbitals play the same role as atomic degrees of freedom that in turn allowed to utilize the basic features of the unfolding scheme of tight‐binding method, for phonon band structures . On the other hand, the electronic and phonon unfolding approaches cannot be completely equivalent because, as noted in example, , the electronic and vibrational states are of different character being described by functions of continuous or discrete variable. This particular feature may require additional care for cases when the translational symmetry of PC‐lattice is heavily broken, so in Ref.…”