Spectral and spatial coexistence of localized and extended states in disordered systems

Yi-Xin Xiao, Zhao-Qing Zhang, C. T. Chan

Published 2016-12-30Version 1

Conventional wisdom tells us that the Anderson localized states and extended states do not coexist at the same energy. Here we propose a simple mechanism to achieve the coexistence of localized and extended states in a class of systems in which the Hilbert space can be partitioned in a way that the disorder affects only certain subspaces causing localization, while the states in the other subspaces remain extended. The coexistence of localized and extended states is achieved when the states in both types of subspaces overlap spatially and spectrally. We demonstrate such coexistence in quasi-1D and -2D disordered systems consisting of coupled diatomic chains and coupled honeycomb lattice sheets, respectively. A possible experimental realization based on coupled acoustic resonators is proposed. We show the method is very general and valid in different dimensions.