Scanning tunneling microscopy studies of topological crystalline insulators

Recent theoretical studies and experimental findings suggest the existence of a new topological phase: topological crystalline insulators (TCI). In contrast to the Z$_{2}$ topological insulators, where the time-reversal symmetry warrants the topological protection of the gapless surface states, in the TCI phase the protection is based on the crystal symmetry. Pb$_{1-x}$Sn$_{x}$Se and Pb$_{1-x}$Sn$_{x}$Te alloys are promising candidates for the TCI state: both of them have the rock-salt crystal structure (at certain doping values) with spatial mirror symmetry, and as a function of doping level the band structure can be changed from normal to inverted bandgap state. We present scanning tunneling microscopy/spectroscopy measurements on these alloys as a function of doping. Similar to previous experiments on spin-orbit coupled topological insulators [1], spectroscopic mapping with the STM can be used to establish the presence of topological properties through examining allowed and disallowed scattering transitions.\\[4pt][1] P. Roushan et al, Nature \textbf{460} 1106 (2009).