▎ 摘　　要

In graphene, a Kekule-Y bond texture modifies the electronic band structure, generating two concentric Dirac cones with different Fermi velocities lying in the I' point in reciprocal space. The energy dispersion results in different group velocities for each isospin component at a given energy. This energy spectrum combined with the negative refraction index in p - n junctions allows the emergence of an electronic analog of optical birefringence in graphene. We characterize the valley birefringence produced by a circularly symmetric Kekule patterned and gated region using the scattering approach. We found caustics with two cusps separated in space by a distance dependent on the Kekule interaction and that provides a measure of its strength. Then at low carrier concentration, we find a nonvanishing skew cross-section, showing the asymmetry in the scattering of electrons around the axis of the incoming flux. This effect is associated with the appearance of the valley Hall effect as electrons with opposite valley polarization are deflected toward opposite directions.