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 (Rnl) 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 Rnl 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 Rnl as the Fermi level is varied.