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

TL;DR

This study systematically investigates how one-dimensional topological edge states in a topological crystalline insulator interact, revealing that coupling occurs at close step distances and depends on the step orientation, affecting spectral features.

Contribution

It provides a detailed analysis of the coupling mechanisms between 1D edge states in a topological crystalline insulator using scanning tunneling spectroscopy, highlighting the role of step distance and orientation.

Findings

Coupling occurs at step distances less than 25 nm.

Energy splitting increases exponentially with decreasing step distance.

No splitting observed for steps at 90° orientation.

Abstract

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.