Nonlocal Signatures of Spin Interference and Incipient Edge-State Formation in Graphene-on-Chromia Heterostructures

We provide evidence of incipient edge-state formation in graphene-on-chromia heterostructures, resulting from the presence of substrate-induced spin-orbit coupling (SOC). Low-temperature spin-Hall measurements of the graphene exhibit large fluctuations of the nonlocal resistance (R_nl) as the Fermi level is swept through its bands. These features persist to much higher temperatures (>60 K) than is typical for mesoscopic effects in normal metals and semiconductors, suggesting that they are associated with a very different mechanism to normal charge-based transport. The fluctuations of the nonlocal resistance are moreover invariant to the application of large magnetic fields (as high as 7 T), a characteristic that speaks to a significant edge-like component to transport. To provide insight into these results, we have formulated a (Landauer-Büttiker) model of quantum transport in graphene in the presence of strong SOC. Our calculations capture the key features of experiments, connecting the large quantum fluctuations in R_nl to the impact of the substrate-induced SOC. More specifically, the spin-orbit interaction is found to imbue the spin diffusion with an edge-like character, displacing injected spins toward the edges of the graphene channel while retaining a coupling to disorder within its interior. It is this interplay of edge-like conduction, with more conventional transport within the interior of the two-dimensional channel, which gives rise to the observed fluctuations in R_nl as the Fermi level is varied.