Chaos in the Honeycomb Optical Lattice Unit Cell

Abstract

Natural and artificial honeycomb lattices are of great interest because the band structure of these lattices, if properly constructed, contains a Dirac point. Such lattices occur naturally in the form of graphene and carbon nanotubes. They have been created in the lab in the form of semiconductor 2DEGs, optical lattices, and photonic crystals. We show that, over a wide energy range, gases (of electrons, atoms, or photons) that propagate through these lattices are Lorentz gases and the corresponding classical dynamics is chaotic. Thus, honeycomb lattices are also of interest for understanding eigenstate thermalization and the conductor-insulator transition due to dynamic Anderson localization.

12 pages plus 8 figures

References in corpus (10)

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• Transport Through an Electrostatically Defined Quantum Dot Lattice in a Two-Dimensional Electron Gas
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Cited by in corpus (3)

• Diffusion transitions in a 2D periodic lattice
• Fourth-order leapfrog algorithms for numerical time evolution of classical and quantum systems
• Escaping from a degenerate version of the four hill potential