Flatbands feature the distortion-free storage of compact localized states of tailorable shape. Their reliable storage sojourn is, however, limited by disorder potentials, which generically cause uncontrolled coupling into dispersive bands. We find that, while detuning flatband states from band intersections suppresses their direct decay into dispersive bands, disorder-induced state distortion causes a delayed, dephasing-mediated decay, lifting the static nature of flatband states and setting a finite lifetime for the reliable storage sojourn. We exemplify this generic, disorder-induced decay mechanism at the cross-stitch lattice. Our analysis, which applies platform independently, relies on the time-resolved treatment of disorder-averaged quantum systems with quantum master equations.

• Received 9 March 2018
• Revised 23 August 2018

DOI:https://doi.org/10.1103/PhysRevB.98.134203