Regulation of Electronic Structure of Graphene Nanoribbon by Tuning Long-Range Dopant–Dopant Coupling at Distance of Tens of Nanometers

Long-range dopant–dopant coupling in graphene nanoribbon (GNR) has been under intensive study for a very long time. Using a newly developed dopant central insertion scheme (DCIS), we performed first-principles study on multiple H, O, OH, and FeN 4 dopants in long (up to 1000 nm) GNRs and found that, although potential energy of the dopant decays exponentially as a function of distance to the dopant, GNR’s electronic density of states (DOS) exhibits wave-like oscillation modulated by dopants separated at a distance up to 100 nm. Such an oscillation strongly infers the purely quantum mechanical resonance states constrained between double quantum wells. This has been unambiguously confirmed by our DCIS study together with a one-dimensional quantum well model study, leading to a proof-of-principle protocol prescribing on-demand GNR-DOS regulation. All these not only reveal the underlining mechanism and importance of long-range dopant–dopant coupling specifically reported in GNR, but also open a novel highway for rationally optimizing and designing two-dimensional materials.