# Symmetry dictated grain boundary state in a two-dimensional topological insulator

## TL;DR

This study demonstrates that lattice symmetry dictates the presence of a topologically protected metallic state along grain boundaries in a 2D topological insulator, confirmed through experiments and simulations.

## Contribution

First direct measurement showing symmetry-enforced topological metallic states at grain boundaries in a 2D TI, linking lattice symmetry to electronic properties.

## Key findings

- Metallic state observed along non-symmorphic grain boundary
- Absence of metallic state along symmorphic boundary
- Simulations reveal hourglass nodal-line semimetallic states

## Abstract

Structural imperfections such as grain boundaries (GBs) and dislocations are ubiquitous in solids and have been of central importance in understanding nature of polycrystals. In addition to their classical roles, advent of topological insulators (TIs) offers a chance to realize distinct topological states bound to them. Although dislocation inside three-dimensional TIs is one of the prime candidates to look for, its direct detection and characterization are challenging. Instead, in two-dimensional (2D) TIs, their creations and measurements are easier and, moreover, topological states at the GBs or dislocations intimately connect to their lattice symmetry. However, such roles of crystalline symmetries of GBs in 2D TIs have not been clearly measured yet. Here, we present the first direct evidence of a symmetry enforced Dirac type metallic state along a GB in 1T'-MoTe$_2$, a prototypical 2D TI. Using scanning tunneling microscope, we show a metallic state along a grain boundary with non-symmorphic lattice symmetry and its absence along the other boundary with symmorphic one. Our large scale atomistic simulations demonstrate hourglass like nodal-line semimetallic in-gap states for the former while the gap-opening for the latter, explaining our observation very well. The protected metallic state tightly linked to its crystal symmetry demonstrated here can be used to create stable metallic nanowire inside an insulator.