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Nodal loops in two-dimensional (2D) systems are typically vulnerable againstspin-orbit coupling (SOC). Here, we explore 2D systems with a type of doublydegenerate nodal loops that are robust under SOC and feature an hourglass typedispersion. We present symmetry conditions for realizing such hourglass Weylloops, which involve nonsymmorphic lattice symmetries. Depending on thesymmetry, the loops may exhibit different patterns in the Brillouin zone. Basedon first-principles calculations, we identify the monolayer GaTeI-familymaterials as a realistic material platform to realize such loops. Thesematerials host a single hourglass Weyl loop circling around a high-symmetrypoint. Interestingly, there is also a spin-orbit Dirac point enabled by anadditional screw axis. We show that the hourglass Weyl loop and the Dirac pointare robust under a variety of applied strains. By breaking the screw axis, theDirac point can be transformed into a second Weyl loop. Furthermore, bybreaking the glide mirror, the hourglass Weyl loop and the spin-orbit Diracpoint can both be transformed into a pair of spin-orbit Weyl points. Our workoffers guidance and realistic material candidates for exploring fascinatingphysics of several novel 2D emergent fermions.

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