Nanoscale imaging of equilibrium quantum Hall edge currents and of the magnetic monopole response in graphene

The recently predicted topological magnetoelectric effect and the response to an electric charge that mimics an induced mirror magnetic monopole are fundamental attributes of topological states of matter with broken time reversal symmetry. Using a SQUID-on-tip, acting simultaneously as a tunable scanning electric charge and as ultrasensitive nanoscale magnetometer, we induce and directly image the microscopic currents generating the magnetic monopole response in a graphene quantum Hall electron system. We find a rich and complex nonlinear behavior governed by coexistence of topological and nontopological equilibrium currents that is not captured by the monopole models. Furthermore, by utilizing a tuning fork that induces nanoscale vibrations of the SQUID-on-tip, we directly image the equilibrium currents of individual quantum Hall edge states for the first time. We reveal that the edge states that are commonly assumed to carry only a chiral downstream current, in fact carry a pair of counterpropagating currents, in which the topological downstream current in the incompressible region is always counterbalanced by heretofore unobserved nontopological upstream current flowing in the adjacent compressible region. The intricate patterns of the counterpropagating equilibrium-state orbital currents provide new insights into the microscopic origins of the topological and nontopological charge and energy flow in quantum Hall systems

Spin–orbit-driven band inversion in bilayer graphene by the van der Waals proximity effect

© 2019, The Author(s), under exclusive licence to Springer Nature Limited. Spin–orbit coupling (SOC) is the key to realizing time-reversal-invariant topological phases of matter1,2. SOC was predicted by Kane and Mele3 to stabilize a quantum spin Hall insulator; however, the weak intrinsic SOC in monolayer graphene4–7 has precluded experimental observation in this material. Here we exploit a layer-selective proximity effect—achieved via a van der Waals contact with a semiconducting transition-metal dichalcogenide8–21—to engineer Kane–Mele SOC in ultra clean bilayer graphene. Using high-resolution capacitance measurements to probe the bulk electronic compressibility, we find that SOC leads to the formation of a distinct, incompressible, gapped phase at charge neutrality. The experimental data agree quantitatively with a simple theoretical model in which the new phase results from SOC-driven band inversion. In contrast to Kane–Mele SOC in monolayer graphene, the inverted phase is not expected to be a time-reversal-invariant topological insulator, despite being separated from conventional band insulators by electric-field-tuned phase transitions where crystal symmetry mandates that the bulk gap must close22. Our electrical transport measurements reveal that the inverted phase has a conductivity of approximately e2/h (where e is the electron charge and h Planck’s constant), which is suppressed by exceptionally small in-plane magnetic fields. The high conductivity and anomalous magnetoresistance are consistent with theoretical models that predict helical edge states within the inverted phase that are protected from backscattering by an emergent spin symmetry that remains robust even for large Rashba SOC. Our results pave the way for proximity engineering of strong topological insulators as well as correlated quantum phases in the strong spin–orbit regime in graphene heterostructures