  The Weyl semimetals represent a distinct category of topological materials
wherein the low-energy excitations appear as the long-sought Weyl fermions.
Exotic transport and optical properties are expected because of the chiral
anomaly and linear energy-momentum dispersion. While three-dimensional Weyl
semimetals have been successfully realized, the quest for their two-dimensional
(2D) counterparts is ongoing. Here, we report the realization of 2D Weyl
fermions in monolayer PtTe$_{1.75}$, which has strong spin-orbit coupling and
lacks inversion symmetry, by combined angle-resolved photoemission
spectroscopy, scanning tunneling microscopy, second harmonic generation, X-ray
photoelectron spectroscopy measurements, and first-principles calculations. The
giant Rashba splitting and band inversion lead to the emergence of three pairs
of critical Weyl cones. Moreover, monolayer PtTe$_{1.75}$ exhibits excellent
chemical stability in ambient conditions, which is critical for future device
applications. The discovery of 2D Weyl fermions in monolayer PtTe$_{1.75}$
opens up new possibilities for designing and fabricating novel spintronic
devices.
