Engineering flat-bands using non-Hermiticity

The emergence of an entire flat band embedded in dispersive bands at the exceptional point of a Parity-Time (PT) symmetric lattice has been previously demonstrated as a route for controllable localization of light. Gain and loss parameters in such non-Hermitian lattices effectively alter the size of the partial flat band windows and the band gap of the lattice. We demonstrate that by engineering the lattice couplings and under certain conditions of non-Hermiticity, these induced flat bands experience a gradual energy shift away from the dispersive bands. This will allow us to design different types of flat bands that form bound states in or out of the continuum.