▎ 摘　　要

It is currently a promising approach to experimentally realize the topological insulator phase transition of graphene by introducing the extrinsic spin-orbit coupling (SOC). Then, electronic total transmission through various topological nontrivial graphene nanojunctions (GNJs) is obtainable, if the electronic transport is supported by the helical edge states. Though the bulk graphene is a gapless semiconductor, the inter-valley scattering could introduce a topological trivial gap in semiconducting armchair-edged graphene nanoribbon (GNR). The SOC should be strong enough to reopen a topological nontrivial gap before close such a trivial gap. Therefore, our theoretical study indicates that a semiconducting armchair-edged graphene nanoribbon (GNR) can not develop the helical edge states when the SOC strength is lower than a threshold, though the bulk phase is topological nontrivial. This implies a competition between the SOC and the inter-valley scattering. However, for a metallic armchair-edged GNR, a small SOC can always open a nontrivial gap. Nevertheless, the helical edge state is much less localized than that in a zigzag-edged GNR of the same width. As a result, and by numerically calculating the electronic transmission spectrum of step-and L-shaped GNJs, we conclude that when an armchair-edged GNR is a part of a GNJ, it is the weak point to realize the electronic total transmission even though the bulk phase of graphene is topologically insulating.