Flat bands andPTsymmetry in quasi-one-dimensional lattices

Abstract

We examine the effect of adding PT -symmetric gain and loss terms to quasi 1D lattices (ribbons) that possess flatbands. We focus on three representative cases: (a) The Lieb ribbon, (b) The kagome ribbon, and (c) The stub Ribbon. In general we find that the effect on the flatband depends strongly on the geometrical details of the lattice being examined. One interesting and novel result that emerge from an analytical calculation of the band structure of the Lieb ribbon including gain and loss, is that its flatband survives the addition of PT-symmetry for any amount of gain and loss, while for the other two lattices, any presence of gain and loss destroys the flatbands. For all three ribbons, there are finite stability windows whose size decreases with the strength of the gain and loss parameter. For the Lieb and kagome cases, the size of this window converges to a finite value. The existence of finite stability windows, plus the constancy of the Lieb flatband are in marked contrast to the behavior of a pure one-dimensional lattice.

Artificial flat band systems: from lattice models to experiments

“…The first class considered effect of adding non-Hermiticity to existing Hermitian flat bands, e.g. by replacing each site in a flat band lattice by non-Hermitian dimers with balanced gain and loss [179][180][181][182][183]. In these examples, it was found that either the existing compact localized states become amplified or attenuated, or the compact localized states are destroyed by unflattening of the energy spectrum [184].…”

Localization of weakly disordered flat band states

“…Finally, while we have focused on the case of static disorder potentials, our detangling procedure may also be useful in characterizing the response of flat bands to other perturbations, such as nonlinearities [8,10,9] or balanced gain and loss [54,55,56].…”

Flat bands in lattices with non-Hermitian coupling

“…Recently, Ramezani has shown that a flat band with completely real eigenvalues can exist in a quasi-1D PT photonic lattice 36 . This PT symmetric flat band was realized by fine-tuning gain/loss levels, and it is not obvious what features of this model, compared to earlier models [33][34][35] , make it possible. Here, we show that PT symmetric flat bands generically occur in non-Hermitian lattices with a bipartite sublattice symmetry hosting a differing number of sites per sublattice 37,38 .…”