Anderson localization induced by complex potential

Abstract

In the Hermitian regime, uncorrelated disorder potential in one-dimensional lattice induces Anderson localization, whereas quasiperiodic potential can lead to both localized and extended phases, depending on the potential strength. In this study, we investigate the non-Hermitian regime. We analytically and numerically study Anderson localization in a one-dimensional lattice with the non-Hermitian complex disorder and quasiperiodic potential. We present a non-Hermitian Su-Schrieffer-Heeger (SSH) chain and demonstrate that the Hermitian counterpart with full real spectrum is a standard Anderson chain, which indicates that a nonzero imaginary disorder on-site potential can induce standard Anderson localization. We further demonstrate that the non-Hermitian Aubry-André -Harper (AAH) model exhibits a transition in parameter space, which separates the localization and delocalization phases and is determined by the self-duality of the model. This indicates that a pure imaginary quasiperiodic potential plays the same role as a real quasiperiodic potential in the transition point between localization and delocalization. Notably, a system with complex quasiperiodic potential exhibits an interference-like pattern on the transition points, which arises from the interplay between the real and imaginary components.