Interplay between effects of barrier tilting and scatterers within a barrier on tunneling transport of Dirac electrons in graphene

Abstract

Dirac-electronic tunneling and transport properties with both finite and zero energy band gap are investigated for graphene with an in-plane tilted potential barrier embedded with scatters. For a tilted barrier, by using Wentzel-Kramers-Brillouin approximation, an analytical solution is obtained first for transmission coefficient of Dirac electrons in gapped graphene in the absence of any scatters. In the presence of either a single or a continuous distribution of scatters embedded within a tilted barrier, however, a numerical scheme based on finite-difference approach is developed for accurately calculating both transmission coefficient and tunneling resistance of Dirac electrons. Here, the combination of a tilted barrier and a scatter potential can be viewed as an effective barrier-potential profile facilitated by a proper gate structure. Meanwhile, a full analysis and detailed comparisons are presented for the interplay between effects of both distributed scatters in a barrier and barrier tilting on tunneling transport of Dirac electrons in graphene. The barrier-tilting field and scatter position are found to play a key role in controlling a peak of tunneling resistance as well as in its switching to a cusp by a mid-barrier-embedded scatter as the incident energy reaches the Dirac point in a barrier. Different from a single scatter, a continuous distribution within a barrier can enhance the unimpeded incoherent tunneling for head-on collision while greatly suppressing skew ones with increasing barrier-tilting field. All these predicted attractive transport properties are expected to be extremely useful for designing both novel electronic and optical graphene-based devices and electronic lenses in ballistic-electron optics.