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(a) Sectional and (b) top schematic diagrams for a particle quantum tunneling through a graphene DBS, with the two barriers of width , height , and distance d between them. is the total width of the structure. In (a), the dashed lines show smooth electric potentials with distributions of error functions and transition regions’ widths of . In (b), the upper (red solid) and lower (blue dashed) components have their locus at , and for the incident, reflected, and transmitted beams, respectively. A detector placed in a proper position of the outgoing region can detect the giant GH shift.
(a) The GH shift (solid) in a symmetric graphene DBS [, , and d = 50 nm] as a function of the incident energy at . The insert shows the GH shift in a SBS with the same barrier height and width. The dashed line indicates the semi-classical shift predicted by the Snell’s law, which has no definition in the TG. (b) The dependence of the shift sharp peak(s) on the incident angle, and . The positions and heights of the four giant GH shift peaks are marked.
The phase shift of the transmitted beam vs. the incident angle for beams with different E/U shown in the figure. (a)/(b) for a rectangular/smooth DBS.
(a) GH shifts in transmission and reflection for an asymmetric DBS with U = 62 meV, , and d = 50 nm. (b) GH shifts in transmission for different cases of structural asymmetries with the parameters and in the sequence given in the figure. For all cases, .
The GH shift in transmission through a graphene DBS with , d = 100 nm, and . The induced gap is as indicated in the figure. Insert: the GH shifts for the reflected and transmitted beams for in the same structure. For all cases, .
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