  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.
