  We investigate physical properties that can be used to distinguish the valley
degree of freedom in systems where inversion symmetry is broken, using graphene
systems as examples. We show that the pseudospin associated with the valley
index of carriers has an intrinsic magnetic moment, in close analogy with the
Bohr magneton for the electron spin. There is also a valley dependent Berry
phase effect that can result in a valley contrasting Hall transport, with
carriers in different valleys turning into opposite directions transverse to an
in-plane electric field. These effects can be used to generate and detect
valley polarization by magnetic and electric means, forming the basis for the
so-called valley-tronics applications.
