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Pseudospin and nonlinear conical diffraction in Lieb lattices
Author(s) -
Daniel Leykam,
Omri Bahat-Treidel,
Anton S. Desyatnikov
Publication year - 2012
Publication title -
physical review a
Language(s) - English
Resource type - Journals
eISSN - 1094-1622
pISSN - 1050-2947
DOI - 10.1103/physreva.86.031805
Subject(s) - physics , conical surface , diffraction , nonlinear system , wave packet , dirac equation , lattice (music) , quantum mechanics , operator (biology) , condensed matter physics , mathematical physics , classical mechanics , geometry , mathematics , biochemistry , chemistry , repressor , acoustics , transcription factor , gene
We study linear and nonlinear wave dynamics in the Lieb lattice, in the vicinity of an intersection point between two conical bands and a flat band. We define a pseudospin operator and derive a nonlinear equation for spin-1 waves, analogous to the spin-1/2 nonlinear Dirac equation. We then study the dynamics of wave packets that are associated with different pseudospin states, and find that they are distinguished by their linear and nonlinear conical diffraction patterns.

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