Quantum transport through a commensurate off-diagonal Aubry-André-Harper chain with dephasing.

We investigate quantum transport in a commensurate off-diagonal Aubry-André-Harper (AAH) chain with modulation parameter b =1/6, the smallest even-denominator supercell that supports band gap reconstruction at both zero and non-zero energies. Using a tight-binding framework combined with the Landauer-Büttiker formalism, we analyze coherent electron transport through finite lattices coupled to external electrodes. The phase-dependent energy spectrum exhibits a hierarchy of bulk-gap reconstructions associated with the six-site supercell modulation, giving rise to distinct transmission windows and resonant transport channels. Finite-size classes characterized by N=6m+r (0 ≤ r ≤ 5) modify the boundary-state configuration and shift the corresponding transmission win- dows. In particular, lattices with odd number of sites exhibit robust zero-energy transmission channels arising from sublattice imbalance in the bipartite hopping network. To evaluate the stability of these features under realistic conditions, environmental decoherence is incorporated through Büttiker dephasing probes. While increasing dephasing progressively suppresses interference-assisted transport, the underlying finite-size transport classification remains clearly identifiable over a broad parameter range. Our results establish clear transport signatures of commensurate off-diagonal modulation beyond the dimer limit and highlight the crucial role of supercell termination and decoherence in determining electron transport through finite AAH chains.