  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.
