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We propose a new topological quantum state of matter---the two-dimensional(2D) Weyl half semimetal (WHS), which features 2D Weyl points at Fermi levelbelonging to a single spin channel, such that the low-energy electrons aredescribed by fully spin-polarized 2D Weyl fermions. We predict its realizationin the ground state of monolayer PtCl$_3$. We show that the material is a halfmetal with an in-plane magnetization, and its Fermi surface consists of a pairof fully spin-polarized Weyl points protected by a mirror symmetry, which arerobust against spin-orbit coupling. Remarkably, we show that the WHS state is acritical state at the topological phase transition between two quantumanomalous Hall insulator phases with opposite Chern numbers, such that aswitching between quantum anomalous Hall states can be readily achieved byrotating the magnetization direction. Our findings demonstrate that WHS offersnew opportunity to control the chiral edge channels, which will be useful fordesigning new topological electronic devices.

Two-dimensional Weyl Half Semimetal and Tunable Quantum Anomalous Hall Effect in Monolayer PtCl$_{3}$