The transport properties of Kekul\'e-ordered graphene $p$-$n$ junctions

The transport properties of electrons in graphene $p$-$n$ junction with uniform Kekul\'e lattice distortion have been studied using the tight-binding model and the Landauer-B\"uttiker formalism combined with the nonequilibrium Green's function method. In the Kekul\'e-ordered graphene, the original $K$ and $K^{\prime}$ valleys of the pristine graphene are folded together due to the $\sqrt{3} \times \sqrt{3}$ enlargement of the primitive cell. When the valley coupling breaks the chiral symmetry, special transport properties of Dirac electrons exist in the Kekul\'e lattice. In the O-shaped Kekul\'e graphene $p$-$n$ junction, Klein tunneling is suppressed, and only resonance tunneling occurs. In the Y-shaped Kekul\'e graphene $p$-$n$ junction, the transport of electrons is dominated by Klein tunneling. When the on-site energy modification is introduced into the Y-shaped Kekul\'e structure, both Klein tunneling and resonance tunneling occur, and the electron tunneling is enhanced. In the presence of a strong magnetic field, the conductance of O-shaped and on-site energy-modified Y-shaped Kekul\'e graphene $p$-$n$ junctions is non-zero due to the occurrence of resonance tunneling. It is also found that the disorder can enhance conductance, with conductance plateaus forming in the appropriate range of disorder strength. The ideal plateau value is found only in the Kekul\'e-Y system.