Anomalous Valley Magnetic Moment of Graphene

Carrier interactions on graphene are studied. The study shows that besides the well known Coulomb repulsion between carriers, there also exist four-fermion interactions associated with U-process, one of which attracts carriers in different valleys. We then calculate the contributions to valley magnetic moment from vertex correction and from four-fermion corrections explicitly. The relative contributions are -18% and 3% respectively. At last we point out that we can mimic heavy quarkonium system by carrier interactions in graphene.