Transport Properties through Double Barrier Structure in Graphene
  The mode-dependent transmission of relativistic ballistic massless Dirac fermion through a graphene based double barrier structure is being investigated for various barrier parameters. We compare our results with already published work and point out the relevance of these findings to a systematic study of the transport properties in double barrier structures. An interesting situation arises when we set the potential in the leads to zero, then our 2D problem reduces effectively to a 1D massive Dirac equation with an effective mass proportional to the quantized wave number along the transverse direction. Furthermore we have shown that the minimal conductivity and maximal Fano factor remain insensitive to the ratio between the two potentials V_2/V_1=\alpha. 
Ahmed Jellal, El Bouazzaoui Choubabi, Hocine Bahlouli, Abdullah   Aljaafari
cond-mat.mes-hall hep-th math-ph math.MP quant-ph