Imaginary Gauge-steerable Edge Modes In Non-Hermitian Aubry-Andr\'e-Harper Model

Abstract

We identify steerable exponentially localized in-gap mode in a quasiperiodic non-Hermitian Aubry-Andr\'e-Harper chain with a spatially fluctuating, zero-mean imaginary gauge field. Under open boundary conditions, the system is exactly related to the Hermitian AAH model by a nonunitary gauge transformation: the OBC spectrum and Lyapunov exponents are unchanged, while eigenstates acquire a gauge-dependent envelope. In a parameter region with spectrally isolated in-gap boundary modes, we find two exponentially localized in-gap modes with sharply different responses to the imaginary gauge field. One remains boundary pinned, but the other is gauge-steerable: it stays exponentially localized while its probability maximum shifts as the gauge field is changed, with its eigenenergy unchanged. We further show that weak on-site gain, applied at a single site chosen once and then kept fixed, can dynamically prepare this steerable mode from a generic bulk wave packet. Changing the gauge field then yields exponentially localized states at different locations.