Valley-coupled transport in graphene with Y-shaped Kekule structure

We investigate the valley-coupled transport of Dirac electrons in graphene with a uniform Y-shaped Kekule lattice distortion, in which the original K and K' valleys of the pristine graphene are folded together due to the root 3 x root 3 enlargement of the primitive cell. We show that the Klein tunneling effect of Dirac electrons tunneling through a rectangle potential barrier is significantly enhanced: The perfect transmission is not limited to normal incidence but occurs in a range of oblique incidence angle when the inversion symmetry of the system is broken to form a single Dirac-cone phase. It is also found that the C-C bond-length modulation of the Kekule lattice that keeps the inversion symmetry of the system can be used to manipulate the valley degree of freedom in a similar way to the exchange field precessing spin, and such valley manipulation can be implemented conveniently by a gate voltage controlling the local potential of the device. The disorder and temperature effects are also discussed.