Abstract
A flat band is nondispersive and formed under destructive interference. Although flat bands are found in various Hermitian systems, to realize a flat band in non-Hermitian systems is an interesting task. Here, we propose a flat band in a parity-time symmetric non-Hermitian lattice. The proposed flat band has entirely real energy and is formed at an appropriate match between synthetic magnetic flux and non-Hermiticity. The flat band energy is tunable. At a weak intercell coupling, the flat band is isolated, whereas at a strong intercell coupling, it intersects with the dispersive band at the non-Hermitian phase transition point. The eigenstates of the flat band are compact localized states and are confined in one, two, or three unit cells at the edges or inside the non-Hermitian lattice.
Highlights
A flat band is entirely constituted by degenerate states, is nondispersive, and has a zero group velocity
The flat band energy is flexible at different appropriate matches instead of pinning to zero, and the flat band can intersect the dispersive bands or appear isolatedly inside or outside the dispersive band gap; the flat band states form bound states in the continuum when energy bands intersect
The synthetic magnetic flux is attributed to the AB-type nonreciprocal phase factor in the intracell coupling
Summary
A flat band is entirely constituted by degenerate states, is nondispersive, and has a zero group velocity. A flat band can be formed by non-Hermiticity at the PT symmetric phase transition point in a triangular lattice [67] and a cross-stitch lattice [69], and a polynomial increase of the intensity for a single site excitation has been revealed [68,69]. Another type of zero-energy flat band with net amplification and attenuation emerging from lattices under nonHermitian particle-hole symmetry has been investigated [70].
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