Aharonov-Bohm Effect and Valley Polarization in Nanoscopic Graphene Rings

The conductance of an Aharonov-Bohm interferometer is studied in a tight-binding model of graphene. Two point contacts with zigzag edges, which function as valley filters, axe connected by a ring with an irregular boundary. We find that the narrowest rings show strong current suppression and nearly sinusoidal magnetoconductance oscillations, whereas for wide rings higher harmonics are equally represented. In the intermediate width range, oscillations with a basic periodicity are suppressed when two valley filters have opposite polarity, while higher harmonics are unaffected. The effect is interpreted in terms of a relatively weak intervalley scattering in the system.