Abstract
We propose a method to generate a real-energy flat band in a two-dimensional (2D) non-Hermitian Lieb lattice. The coincidence of the flat band eigenstate in both real and momentum spaces is essential for the proposed flat band, which is flexible at the appropriate match between the synthetic magnetic flux and non-Hermiticity. The proposed method is not limited to the 2D non-Hermitian Lieb lattice, and is applied to the 2D non-Hermitian Tasaki's decorated square lattice, dice lattice, and kagome lattice. Our findings make a step forward for the flat band engineering in 2D non-Hermitian optical lattices.
Highlights
The flat band is a dispersionless energy band with fixed energy [1]
We have proposed a method to realize a flat band in a 2D non-Hermitian Lieb lattice, whose energy is flexible by the interplay of the non-Hermiticity and synthetic magnetic flux
We proposed two steps to achieve a 2D non-Hermitian lattice that supports a flat band
Summary
The flat band is a dispersionless energy band with fixed energy [1]. It is independent of the system momentum and leads to unconventional Anderson localization [2,3] and AharonovBohm cages [4,5,6,7,8]. The Lieb lattice has a three-site unit cell; the chiral symmetry ensures energy spectra corresponding to the flat band with a zeroenergy and two symmetric dispersive bands, with the three energy spectra sharing a common Dirac point [40]. Been realized in experiments [73,74,75,76,77,78,79,80] These provide an optical platform for the study of flat bands in non-Hermitian systems. With the precondition of non-Hermitian particle-hole symmetry, photonic zero modes in a flat band can appear in the gain and loss modulated lattices [24]. In the non-Hermitian generalization, a flat band in the Lieb lattice is maintained due to the destructive interference.
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