(a) Schematic illustrating the separation of the top contact and the tunneling region to avoid perturbing the surface state in the tunneling region. The structure in (a) could have mirror symmetry or it could have a wrap-around contact or a wrap-around tunnel region as shown in (b). (b) Symmetric implementation of (a) with a wrap-around tunnel region. Magnetic doping of the surface and edges prevents leakage around the edges from the top surface to the bottom surface. The bottom contact could be the vacuum chuck of the probe station. The high specific contact resistance of the weakly coupled back-side contact could be compensated by its large area.
Dispersion of a 6 nm TI thin film and the corresponding inter-surface transmission spectrum plotted on a logarithmic scale. (a) Dispersion close to the Dirac point when the surfaces are at equal potential (U = 0) such that the top and bottom Dirac cones align. (b) Dispersion close to the Dirac point with an inter-surface potential difference of U = 80 meV giving an effective Rashba-like splitting. For both cases, a small 3.5 meV band gap is opened due to the surface-surface coupling. (c) Transmission spectrum for the equal-potential case. The white lines indicate the corresponding band structure. (d) Transmission spectrum and the corresponding Rashba-like split dispersion when U = 80 meV.
Schematic of band alignments illustrating the quantum number selection rules. The blue bands with the down arrows indicate negative spin states, while the red bands with the up arrows correspond to positive spin states. The gray region in between represents the bulk material. (a) and (b) illustrate the alignment of the surface Dirac cones when the two surfaces are at the same potential, U = 0. (c) Overlay of the top and bottom surface bands when U = 0. The cones are slightly offset to demonstrate the mismatch of spin for each and ϵ except at . Energy, momentum, and spin can only be conserved at . (d) and (e) show the shifted top and bottom surface states when the surface-surface potential is nonzero. (f) Overlay of (d) and (e) in which the intersection of the Dirac cones is indicated by the dashed line. The intersection of the two Dirac cones forms a circle in the plane. Energy, momentum, and spin are only conserved on this circle. The small bandgap of a few meV resulting from the intersurface coupling is not shown.
Total, integrated transmission spectrum . (a) Thickness dependence of on a logarithmic scale in the absence of bias (U = 0). The energy reference is set at the band edge ( ) of the 6.0 nm thin film. (b) The effect of bias on the transmission of the 6.0 nm film. The potential of the top surface is raised by U/2 and the potential of the bottom surface is lowered by U/2.
Temperature response from 1.8 K to 77 K of the tunneling conductance for different alignments of as shown in the legend of (a) for three film thicknesses of (a) 6.0 nm, (b) 7.5 nm, and (c) 9.0 nm. (d) The effect of a surface-surface potential difference of U = 30 meV on the temperature dependence of the tunneling conductance is compared with the U = 0 case for the 6.0 nm film. The dotted curves are the same as in (a) with U = 0. The solid curves are with U = 30 meV.
Current voltage response of the tunneling current at 77 K with a built-in, inter-surface potential difference of . The number beside each I–V curve indicates the peak-to-valley current ratio. (a) Current-voltage response when the equilibrium Fermi level is aligned at the valence band edge, , for 4 different film thicknesses as shown in the legend. (b) Current-voltage response of the 6.0 nm thin film for three different alignments of the equilibrium Fermi levels, , as shown in the legend. (c) An illustration of the Dirac cone alignments for three different biases: , and . The top Dirac cone is denoted by the red color, while the bottom one is denoted by blue.
Definition of the surface Green's function based on the tight-binding model. Two semi-infinite interfaces are solved to simulate the surface eigenstate injection and absorption at the top (a) and the bottom (b) surfaces.
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