3.9 Article

Complementary local-global approach for phonon mode connectivities

期刊

出版社

IOP PUBLISHING LTD
DOI: 10.1088/2399-6528/abd8ed

关键词

Phnon band connectivity; Phonon dispersions; Phonon mode symmetry; Similarity between phonon eigenmodes; Degenerate phonon modes; Perturbation theory; Least-squares fit

资金

  1. Science and Engineering Research Council [152-70-00017]
  2. Science and Engineering Research Council through RIE2020 Advanced Manufacturing and Engineering (AME) Programmatic Grant [A1898b0043]

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Sorting and assigning phonon branches is crucial for characterizing crystal phonon bands, and the proposed two-stage hybrid method efficiently solves this problem by combining perturbative approach and numerical fitting. This method can be easily extended to other condensed matter problems involving Hermitian matrix operators.
Sorting and assigning phonon branches (e.g., longitudinal acoustic) of phonon modes is important for characterizing the phonon bands of a crystal and the determination of phonon properties such as the Gruneisan parameter and group velocity. To do this, the phonon band indices (including the longitudinal and transverse acoustic) have to be assigned correctly to all phonon modes across a path or paths in the Brillouin zone. As our solution to this challenging problem, we propose a computationally efficient and robust two-stage hybrid method that combines two approaches with their own merits. The first is the perturbative approach in which we connect the modes using degenerate perturbation theory. In the second approach, we use numerical fitting based on least-squares fits to circumvent local connectivity errors at or near exact degenerate modes. The method can be easily generalized to other condensed matter problems involving Hermitian matrix operators such as electronic bands in tight-binding Hamiltonians or in a standard density-functional calculation, and photonic bands in photonic crystals.

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