# Hourglass Weyl loops in two dimensions: Theory and material realization in monolayer GaTeI family

## TL;DR

This paper introduces a new class of hourglass Weyl loops in 2D materials, specifically in monolayer GaTeI-family, which are robust under spin-orbit coupling and can be manipulated via symmetry breaking.

## Contribution

It provides symmetry conditions for hourglass Weyl loops, identifies monolayer GaTeI as a material platform, and explores their robustness and tunability through strain and symmetry breaking.

## Key findings

- Monolayer GaTeI hosts a robust hourglass Weyl loop.
- The Weyl loop and Dirac point are stable under strain.
- Breaking symmetries transforms loops into Weyl points or pairs.

## Abstract

Nodal loops in two-dimensional (2D) systems are typically vulnerable against spin-orbit coupling (SOC). Here, we explore 2D systems with a type of doubly degenerate nodal loops that are robust under SOC and feature an hourglass type dispersion. We present symmetry conditions for realizing such hourglass Weyl loops, which involve nonsymmorphic lattice symmetries. Depending on the symmetry, the loops may exhibit different patterns in the Brillouin zone. Based on first-principles calculations, we identify the monolayer GaTeI-family materials as a realistic material platform to realize such loops. These materials host a single hourglass Weyl loop circling around a high-symmetry point. Interestingly, there is also a spin-orbit Dirac point enabled by an additional screw axis. We show that the hourglass Weyl loop and the Dirac point are robust under a variety of applied strains. By breaking the screw axis, the Dirac point can be transformed into a second Weyl loop. Furthermore, by breaking the glide mirror, the hourglass Weyl loop and the spin-orbit Dirac point can both be transformed into a pair of spin-orbit Weyl points. Our work offers guidance and realistic material candidates for exploring fascinating physics of several novel 2D emergent fermions.