Photonics Research, 2018, 6 (4): 04000A10, Published Online: Aug. 1, 2018  

Non-Hermitian lattices with a flat band and polynomial power increase [Invited] Download: 520次

Li Ge 1,2,*
Author Affiliations
1 Department of Engineering Science and Physics, College of Staten Island, CUNY, Staten Island, New York 10314, USA
2 The Graduate Center, CUNY, New York, New York 10016, USA (li.ge@csi.cuny.edu)
Abstract
In this work, we first discuss systematically three general approaches to construct a non-Hermitian flat band, defined by its dispersionless real part. These approaches resort to, respectively, spontaneous restoration of non-Hermitian particle-hole symmetry, a persisting flat band from the underlying Hermitian system, and a compact Wannier function that is an eigenstate of the entire system. For the last approach in particular, we show the simplest lattice structure where it can be applied, and we further identify a special case of such a flat band where every point in the Brillouin zone is an exceptional point of order 3. A localized excitation in this “EP3 flat band” can display either a conserved power, quadratic power increase, or even quartic power increase, depending on whether the localized eigenstate or one of the two generalized eigenvectors is initially excited. Nevertheless, the asymptotic wave function in the long time limit is always given by the eigenstate, in this case, the compact Wannier function or its superposition in two or more unit cells.

Li Ge. Non-Hermitian lattices with a flat band and polynomial power increase [Invited][J]. Photonics Research, 2018, 6(4): 04000A10.

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