Topological and flat-band states induced by hybridized linear interactions in one-dimensional photonic lattices

We report on a study of a one-dimensional linear photonic lattice hosting, simultaneously, fundamental and dipolar modes at every site. We show how, thanks to the coupling between different orbital modes, this minimal model exhibits rich transport and topological properties. By varying the detuning coefficient we find a regime where bands become flatter (with reduced transport) and a second regime, where both bands connect at a gap-closing transition (with enhanced transport). We detect an asymmetric transport due to the asymmetric intermode coupling and a linear energy exchange mechanism between modes. Further analysis shows that the bands have a topological transition with a nontrivial Zak phase which leads to the appearance of edge states in a finite system. Finally, for zero detuning, we found a symmetric condition for coupling constants, where the linear spectrum becomes completely flat, with states fully localized in space occupying only two lattice sites.