  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.
