Anomalous Minimum and Scaling Behavior of Localization Length Near an Isolated Flat Band. Issue 8 (29th June 2017) - Ge, L.
Abstract : Localization of waves occurs when a system does not support wave propagation (e.g., inside a band gap of a crystal) or due to modified wave interference introduced by disorder. How strong the localization is depends on the energy of the wave, and typically one finds the strongest localization near the middle of a band gap. This conventional wisdom is now challenged when one or more isolated flat bands are present. Abstract : Using one‐dimensional tight‐binding lattices and an analytical expression based on the Green's matrix, we show that anomalous minimum of the localization length near an isolated flat band, previously found for evanescent waves in a defect‐free photonic crystal waveguide, is a generic feature and exists in the Anderson regime as well, i.e., in the presence of disorder. Our finding reveals a scaling behavior of the localization length in terms of the disorder strength, as well as a summation rule of the inverse localization length in terms of the density of states in different bands. Most interestingly, the latter indicates the possibility of having two localization minima inside a band gap, if this band gap is formed by two flat bands such as in a double‐sided Lieb lattice.