Topological surface states are a class of novel electronic states that are of potential interest in quantum computing or spintronic applications1, 2, 3, 4, 5, 6, 7. Unlike conventional two-dimensional electron states, these surface states are expected to be immune to localization and to overcome barriers caused by material imperfection8, 9, 10, 11, 12, 13, 14. Previous experiments have demonstrated that topological surface states do not backscatter between equal and opposite momentum states, owing to their chiral spin texture15, 16, 17, 18. However, so far there is no evidence that these states in fact transmit through naturally occurring surface defects. Here we use a scanning tunnelling microscope to measure the transmission and reflection probabilities of topological surface states of antimony through naturally occurring crystalline steps separating atomic terraces. In contrast to non-topological surface states of common metals (copper, silver and gold)19, 20, 21, 22, 23, which are either reflected or absorbed by atomic steps, we show that topological surface states of antimony penetrate such barriers with high probability. This demonstration of the extended nature of antimony’s topological surface states suggests that such states may be useful for high current transmission even in the presence of atomic-scale irregularities—an electronic feature sought to efficiently interconnect nanoscale devices.
Figures at a glance
Figure 1: The topological surface states of Sb(111) on atomic terraces. 
a, STM topographic image (Vbias = 1 V, I = 8 pA) of a 2,500 Å-by-1,250 Å area showing terraces of various widths separated by 3.7 Å-high single atomic steps. b, The dI/dV measurement averaged over each terrace shows quantized peaks. The spectra are offset vertically for clarity. c, Spatially and energetically resolved dI/dV measurements taken along the dotted arrow in a demonstrate the interference in space and the quantization in energy.
Figure 2: Allowed scattering wavevectors and their quantization. 
a, The dI/dV measurement on a 390 Å-wide terrace. b, Energy-resolved Fourier transform of the spatial modulation of the data in a reveals the quantization of scattering wavevectors qA and qB. c, The dispersions of qA and qB match the dispersion of the surface bands as measured by ARPES along the high-symmetry directions (solid lines) and extend it above the Fermi level (dotted lines). d, Contours of constant energy of the antimony surface state (ARPES measurements from ref. 8). The contours consist of a central electron pocket and six surrounding hole pockets. The coloured arrows represent spin texture of the surface state. The scattering wavevectors qA and qB indicate allowed scattering processes.
, 
and 
are the high-symmetry points of the first Brillouin zone, with 
located at the centre of the zone, 
located in the middle of each side of this six-fold symmetric zone, and 
located at the vertex.
Figure 3: Lifetime and leakage of quantized quasiparticles. 
Each resonant peak is fitted to a Lorentzian function to yield the full-width at half-maximum of the quantized energy peaks, Γ (inset). The plot shows the energy dependence of Γ for two different terraces. The dashed lines are parabolic fits, and ΓL is the peak broadening at the Fermi energy. The error bars are from the fitting process of the resonant peaks and are mainly due to the measurement resolution.
Figure 4: Resonant tunnelling between adjacent terraces. 
a, STM topographic image of a narrow terrace (L = 110 Å) and an adjacent wide terrace (L = 2,500 Å). Only part of the wide terrace is displayed. The colour scale shows the height variations in the topographic image. b, On the narrow terrace, the dI/dV measurement shows the quantization of the energy levels. c, The dI/dV measurement on the wide terrace shows sudden phase shifts and suppressions of the dI/dV intensities at around +5 meV and −70 meV due to resonant tunnelling. The averaged background conductance at each energy has been subtracted. d, The Fourier transform of the spatial modulation of the data in c. The grey markers indicate suppression of modulation intensities. e, Spectral weight of the scattering wavevector qB as extracted from d. The dashed line corresponds to the background spectral weight in the absence of resonance tunnelling. f, Spectral weight (circles) normalized by the background. The best fit (red line) yields ~42% reflection, ~35% transmission and ~23% bulk absorption from the scattering process at the boundary. The blue line, which is the fit based on a model without bulk absorption, is displayed for comparison.
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