Abstract
We study the Bloch-Zener oscillation, which is a superposition of Bloch oscillation and Landau-Zener tunneling between Bloch bands, for a quantum particle in a frustrated sawtooth lattice with and without uniform magnetic field. Under the single-band tight-binding approximation, the sawtooth lattice is a two-miniband system and may have a flat band structure. The presence of magnetic field can make the gap between two minibands close, and around the touch point the dispersion is an asymmetric Dirac cone. We analyze in detail the Landau-Zener tunneling and Bragg scattering in the Bloch-Zener oscillation and the effect of magnetic field. Our results also give a clear picture of the dynamical localization in real space induced by the flat band structure of the lattice.
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