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arXiv · 1704.00896

Flat bands in lattices with non-Hermitian coupling

Daniel Leykam·Sergej Flach·Y. D. Chong
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Abstract

We study non-Hermitian photonic lattices that exhibit competition between conservative and non-Hermitian (gain/loss) couplings. A bipartite sublattice symmetry enforces the existence of non-Hermitian flat bands, which are typically embedded in an auxiliary dispersive band and give rise to non-diffracting "compact localized states". Band crossings take the form of non-Hermitian degeneracies known as exceptional points. Excitations of the lattice can produce either diffracting or amplifying behaviors. If the non-Hermitian coupling is fine-tuned to generate an effective $\pi$ flux, the lattice spectrum becomes completely flat, a non-Hermitian analogue of Aharonov-Bohm caging in which the magnetic field is replaced by balanced gain and loss. When the effective flux is zero, the non-Hermitian band crossing points give rise to asymmetric diffraction and anomalous linear amplification.

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Daniel Leykam, Sergej Flach, Y. D. Chong. 2017-04-04. Flat bands in lattices with non-Hermitian coupling. https://doi.org/10.1103/physrevb.96.064305

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