# Topological properties of multilayers and surface steps in the SnTe material class

## TL;DR

This paper explores the topological properties of surface steps in SnTe multilayers, revealing how symmetries and invariants influence low-energy states and potential instabilities like magnetization, with implications for experimental observations.

## Contribution

It identifies the topological invariants governing step states in SnTe multilayers and demonstrates their dependence on layer number and symmetry protections.

## Key findings

- Step states occur when mirror- and spin-resolved Chern numbers differ across steps.
- Particle-hole symmetry can protect Weyl points at surface steps.
- Magnetic domain walls support low-energy bound states due to topological distinctions.

## Abstract

Surfaces of multilayer semiconductors typically have regions of atomically flat terraces separated by atom-high steps. Here we investigate the properties of the low-energy states appearing at the surface atomic steps in \snte. We identify the important approximate symmetries and use them to construct relevant topological invariants. We calculate the dependence of mirror- and spin-resolved Chern numbers on the number of layers and show that the step states appear when these invariants are different on the two sides of the step. Moreover, we find that a particle-hole symmetry can protect one-dimensional Weyl points at the steps. Since the local density of states is large at the step the system is susceptible to different types of instabilities, and we consider an easy-axis magnetization as one realistic possibility. We show that magnetic domain walls support low-energy bound states because the regions with opposite magnetization are topologically distinct in the presence of non-symmorphic chiral and mirror symmetries, providing a possible explanation for the zero-bias conductance peak observed in the recent experiment [Mazur et al., Phys. Rev. B 100, 041408(R) (2019)]