Aharonov-Bohm oscillations of four-probe resistance in clean systems with topologicaly protected channels in silicene and bilayer graphene
We consider observation of Aharonov-Bohm oscillations in system without disorder based on flow of topologically protected currents in silicene and bilayer graphene gated nanodevices. The chiral channels in these materials are defined by flips of the vertical electric field. The flip confines states at the junction with the direction of the current flow that is determined by the valley. We present an electric field profile that forms a crossed ring channels with four terminals and find that the conductance matrix elements oscillate in the perpendicular magnetic field in spite of the absence of backscattering of the valley protected channels in the system. 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 valley current between the current probes is forbidden.