Non local transport in Graphene/Chromia

Robust non-local spin voltage signals have been demonstrated experimentally in monolayer Graphene deposited on the (0001) surface of the antiferromagnetic Chromium Oxide (Cr2O3). The measured non-local voltage shows fluctuations at a wide range of energies reminiscent of universal conductance fluctuations but with larger amplitudes. We take a toy model Hamiltonian to explain the main non-local signatures observed in the experiments. Tuning the strength of spin-orbit coupling, interfacial Zeeman exchange, sublattice asymmetries, and orbital effects of the magnetic field cause the Graphene to demonstrate different behaviors as it switches between the quantum spin Hall effect (QSH), quantum anomalous Hall effect (QAHE), and quantum Hall effect (QHE). We use the Landauer-Büttiker formalism to calculate the non-local resistance in the simulations and use self-consistent Born approximation to calculate the dephasing self energy. By including the dephasing effect in the Landauer-Büttiker formalism, we are able to distinguish the non local conductance fluctuation from the main non local signature. The presence of different types of disorder further introduces scattering and quantum effects associated with it in the presence of phase coherence.