Quantization Rules for Topological Surface States*

Recently, a new class of chiral electronic states on the surface of insulators with strong spin-orbit interaction has been discovered [1,2]. One of the unusual properties of this material is the elimination of the possibility of backscattering between states of orthogonal spins [3]. An unexplored aspect of these materials is the question of how the absence of backscattering affects the energy quantization in a confined geometry. We have studied the variations in the local density of states in the regions confined between adjacent atomic step edges on Sb(111) using a low temperature scanning tunneling microscopy. We have found a remarkably Dirac-like quantization with E$_{n}$= nE$_{0}$ (n=integer) for the confined surface states of Sb over a wide range of energies. Our experiments also demonstrate the absence of confinement and quantization in the regime where backscattering cannot occur. [1] L. Fu, C. L. Kane, and E. J. Mele, Phys. Rev. Lett. 98, 106803 (2007) [2] D. Hsieh \textit{et al.}, Nature 452, 970 (2008) [3] P. Roushan et al., Nature 460, 1106 (2009)