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 the crystalline insulator $Pb_{0.7}Sn_{0.3}Se(001)$ has been studied systematically by scanning tunneling spectroscopy. Our results reveal that coupling adjacent sets in at a step{to{step distance $d_{ss} < 25$ nm, resulting characteristic splitting single peak Dirac point spectra. Whereas energy exponentially increases with decreasing $d_{ss}$ for running almost parallel, we find no step edges under an angle $90^{o}$. are discussed terms overlapping wave functions $p_x; p_y$ orbital character.