Do Linear Dispersions of Classical Waves Mean Dirac Cones?

Details Do Linear Dispersions of Classical Waves Mean Dirac Cones? Do Linear Dispersions of Classical Waves Mean Dirac Cones?

2012-02-07

arxiv.org/abs/1202.1430v1

Physics

Condensed Matter

Materials Science

Scientific paper

By using the \vec{k}\cdot\vec{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 -\pi. Triply-degenerate states can also generate Dirac-like cone dispersions, but the wavefunctions transform like a spin-1 particle and the Berry phase is zero. Our theory is capable of predicting accurately the linear slopes of Dirac/Dirac-like cones at various symmetry points in a Brilliouin zone, independent of frequency and lattice structure.

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