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Aharonov-Bohm oscillations of four-probe resistance in topological quantum rings in silicene and bilayer graphene

We consider observation of Aharonov-Bohm oscillations in clean systems based on the flow of topologically protected currents in silicene and bilayer graphene. The chiral channels in these materials are defined by the flips of the vertical electric field. The line of the flip confines chiral currents flowing along it in the direction determined by the valley. We present an electric field profile that forms a crossed ring to which four terminals can be attached, and find that the conductance matrix elements oscillate in the perpendicular magnetic field in spite of the absence of backscattering. We propose a four-probe resistance measurement setup, and demonstrate that the resistance oscillations have large visibility provided that the system is prepared in such a way that a direct transfer of the chiral carriers between the current probes is forbidden.