Proximity-induced flat bands and topological properties in a decorated diamond chain

In the present study, we propose a unique scheme to generate and control multiple flat bands in a decorated diamond chain by using a strain-induced proximity effect between the diagonal sites of each diamond plaquette. This is in complete contrast to the conventional diamond chain, in which the interplay between the lattice topology and an external magnetic flux leads to an extreme localization of the single-particle states, producing the flat bands in the energy spectrum. Such a strain-induced proximity effect will enable us to systematically control one of the diagonal hoppings in the decorated diamond chain, which will lead to the formation of both gapless and gapped flat bands in the energy spectrum. These gapless or gapped flat bands have been corroborated by the computation of the compact localized states amplitude distribution as well as the density of states of the system using a real space calculation. We have also shown that these flat bands are robust against the introduction of small amounts of random onsite disorder in the system. In addition to this, we have also classified the nontrivial topological properties of the system by calculating the winding numbers and edge states for the gapped energy spectrum. These findings could be easily realized experimentally using the laser-induced photonic lattice platforms.