“…The alternative geometry of transmission through potential barriers has also been a subject of extensive research, with the majority of studies utilizing "sharp but smooth potentials", i.e., potentials which are step-like or have kinks but are assumed to be smooth on the scale of the lattice constant, so that the effects of inter-valley scattering are neglected. Supercritical transmission [50][51][52][53][54][55][56][57][58] and tunneling through barriers has been studied for a variety of one-dimensional (1D) model potentials in both massless and massive 2D Dirac systems [25,27,49,[59][60][61][62][63][64][65][66][67][68][69][70][71][72][73][74][75] including square barrier structures such as the double barrier [76][77][78], inverted double well [79,80], asymmetric waveguides [34,43] and various other step-like structures [41,42,80]. A variety of approaches ranging from the transfer matrix method through to the WKB method have been used.…”