Transport signatures of topological commensurate off-diagonal Aubry-Andr\'e-Harper chain

Abstract

We study the interplay between quantum transport and topology in a one-dimensional off-diagonal commensurate Aubry-Andr\'e-Harper (AAH) chain. The model, formulated within AAH framework, effectively represents a one-dimensional lattice with two competing commensurate modulations, supporting two distinct types of topological edge modes: zero-energy states in the central gapless region and quantum Hall (QH) edge states bridging the gapped bulk bands. These edge modes govern the transport behavior and give rise to sharp variations in transmission across the corresponding gap-closing transitions. A pronounced even-odd effect further emerges, where chains with an odd number of sites exhibit nearly perfect zero-energy transmission at the Dirac points, independent of system-lead coupling, system size, or modulation strength; a robust signature of ballistic transport. To capture the influence of environmental decoherence, we also incorporate B\"uttiker dephasing probes, which enable a phenomenological description of inelastic scattering and reveal how dephasing modifies, and in some regimes enhances, coherent transport.