Probing of valley polarization in graphene via optical second-harmonic generation

Valley polarization in graphene breaks inversion symmetry and therefore leads to second-harmonic generation. We present a complete theory of this effect within a single-particle approximation. It is shown that this may be a sensitive tool to measure the valley polarization created, e.g., by polarized light and, thus, can be used for a development of ultrafast valleytronics in graphene.