Imaginary gauge-steerable edge mode in the non-Hermitian Aubry-André-Harper model
Phys. Rev. A 113, 053509 – Published 7 May, 2026
DOI: https://doi.org/10.1103/yq8q-9nkx
Abstract
We identify the steerable exponentially localized in-gap mode in a quasiperiodic non-Hermitian Aubry-André-Harper chain with a spatially fluctuating, zero-mean imaginary gauge field. Under open boundary conditions, the system is exactly related to the Hermitian Aubry-André-Harper model by a nonunitary gauge transformation: the open boundary conditions 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.
