First-principles study of Dirac and Dirac-like cones in phononic and photonic crystals

By using the k•p method, we propose a first-principles theory to study the linear dispersions in phononic and photonic crystals. The theory reveals that only those linear dispersions created by doubly degenerate states can be described by a reduced Hamiltonian that can be mapped into the Dirac Hamiltonian and possess a Berry phase of -π. Linear dispersions created by triply degenerate states cannot be mapped into the Dirac Hamiltonian and carry no Berry phase, and, therefore should be called Dirac-like cones. Our theory is capable of predicting accurately the linear slopes of Dirac and Dirac-like cones at various symmetry points in a Brillouin zone, independent of frequency and lattice structure. © 2012 American Physical Society.

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First-principles study of Dirac and Dirac-like cones in phononic and photonic crystals 2012, 86 (3) Physical Review B

First-principles study of Dirac and Dirac-like cones in phononic and photonic crystals

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arXiv

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