Systematic Investigation of the Coupling between One-Dimensional Edge States of a Topological Crystalline Insulator

The interaction of spin-polarized one-dimensional (1D) topological edge modes localized along single-atomic steps of the topological crystalline insulator Pb_{0.7}Sn_{0.3}Se(001) has been studied systematically by scanning tunneling spectroscopy. Our results reveal that the coupling of adjacent edge modes sets in at a step-to-step distance d_{ss}≤25  nm, resulting in a characteristic splitting of a single peak at the Dirac point in tunneling spectra. Whereas the energy splitting exponentially increases with decreasing d_{ss} for single-atomic steps running almost parallel, we find no splitting for single-atomic step edges under an angle of 90°. The results are discussed in terms of overlapping wave functions with p_{x}, p_{y} orbital character.