Compact modes in quasi one dimensional coupled magnetic oscillators

In this work we study analytically and numerically the spectrum and localization properties of three quasi-one-dimensional (ribbons) split-ring resonator arrays which possess magnetic flatbands, namely, the stub, Lieb and kagome lattices, and how their spectra is affected by the presence of perturbations that break the delicate geometrical interference needed for a magnetic flatband to exist. We find that the Stub and Lieb ribbons are stable against the three types of perturbations considered here, while the kagome ribbon is, in general, unstable. When losses are incorporated, all flatbands remain dispersionless but become complex, with the kagome ribbon exhibiting the highest loss rate.