Abstract
We study the interband wave tunnelling (Zener transitions) in two-dimensional hexagonal lattices with superimposed index gradient and derive simple analytical models capturing the essence of the tunnelling phenomenon. We find that the two-dimensional tunnelling in hexagonal lattices occurs at the high-symmetry points (e.g., the M and lceil points), and it involves either three or six Bloch bands being described by the corresponding multi-level Landau-Zener-Majorana (LZM) system. We derive several types of the generalized LZM systems and verify analytical predictions by direct numerical simulations of the full linear Schrodinger equation with tilted periodic potential.
Published Version
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