Electrons in graphene, in addition to their spin, have two pseudospin degrees of freedom: sublattice and valley pseudospin. Valleytronics uses the valley degree of freedom as a carrier of information similarly to the way spintronics uses electron spin. We show how a double-barrier structure consisting of electric and vector potentials can be used to filter massive Dirac electrons based on their valley index. We study the resonant transmission through a finite number of barriers and we obtain the energy spectrum of a superlattice consisting of electric and vector potentials. When a mass term is included, the energy bands and energy gaps at the $K$ and $K^{\prime }$ points are different and they can be tuned by changing the potential.

• Received 16 July 2012

DOI:https://doi.org/10.1103/PhysRevB.86.115431