Persistent current states in bilayer graphene

We argue that at finite carrier density and large displacement fields, bilayer graphene is prone to l=0 and l=1 Pomeranchuk Fermi-surface instabilities. The broken symmetries are driven by nonlocal exchange interactions which favor momentum-space condensation. We find that electron-electron interactions lead first to spontaneous valley polarization, which breaks time-reversal invariance and is associated with spontaneous orbital magnetism, and then under some circumstances to a nematic phase with reduced rotational symmetry. When present, nematic order is signaled by reduced symmetry in the dependence of optical absorption on light polarization.