In this work we study the topologically protected states of the Sb(111) surface by using ab initio transport theory. In the presence of a strong surface perturbation we obtain standing-wave states resulting from the superposition of spin-polarized surface states. By Fourier analysis, we identify the underlying two dimensional scattering processes and the spin texture. We find evidence of resonant transmission across surface barriers at quantum well state energies and evaluate their lifetimes. Our results are in excellent agreement with experimental findings. We also show that despite the presence of a step edge along a different high-symmetry direction, the surface states exhibit unperturbed transmission around the Fermi energy for states with near to normal incidence. Introduction. In the past few years topological insulators (TIs) have become an intensely studied field of condensed matter physics. 1,2 The unique metallic states at the surface of a TI can be used both as a tabletop playground to prove fundamental concepts developed for particle physics and also as a new materials platform for intriguing quantum applications in both spin electronics and quantum computing. [3][4][5] The first three-dimensional TI to be experimentally realized was a Bi-Sb alloy, 6 following a theoretical prediction by Fu and Kane. 7 The topological nature of the alloy is inherited from the parent element antimony, which has a nontrivial principal topological invariant ν 0 , whereas bismuth has a trivial Z 2 invariant. 8 Although Sb itself is a semimetal, its (111) surface hosts two spin-polarized bands, which extend around the Fermi energy E F . These form a single distorted Dirac cone where the lower bands are lifted upwards. The electronic properties of Sb(111) thin films have been investigated both theoretically and experimentally. [9][10][11][12] In a recent experiment, Seo et al. demonstrated that the topological surface states are extraordinarily insensitive to the presence of surface barriers. 13 They probed the extended nature of Sb(111) surface states by using a scanning tunneling microscope (STM) and found that these transmit across surface atomic steps with a high probability. Their analysis of the standing-wave states on surface terraces revealed the novel chiral spin texture of the two surface states, consistent with earlier angle-resolved photoemission spectroscopy (ARPES) measurements. 14 In this Rapid Communication we seek to theoretically recreate the above-mentioned experiment by using ab initio transport theory, and show that we can reproduce the formation of quantum well states and their lifetimes, as well as the wavelengths and phase shifts of the scattering states. Thereby we demonstrate that by first-principles calculations one can describe the correct scattering properties of such topologically protected surface states. In addition to comparing our results favorably to the experiments, we predict the scattering properties of these states in the presence of a surface perturbation along a direction orthogonal...