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 $90^{ o}$. The results are discussed in terms of overlapping wave functions with $p_x; p_y$ orbital character.
Categories: cond-mat.str-el