Prediction of half-valley metallic and valley semiconducting features in monolayer Ti3X3Y2 (X=S, Se; Y=S, Se, Te)

Developing two-dimensional valleytronic materials with spin-valley coupling attracts great interest in the field of valleytronics and spintronics devices. Here, starting from a tight-binding model based on a colorful triangle lattice, we suggest that the valley polarization can be realized in monolayer ${\mathrm{Ti}}_{3}{X}_{3}{Y}_{2}$ ($X$ = S, Se; $Y$ = S, Se, Te) by using first-principles calculations. Our results show that the proposed monolayer exhibits intrinsic ferrovalley with large valley polarization, derived from the time-reversal and ${C}_{2}$ symmetry broken, which is beneficial for observing the anomalous valley hall effect in these systems. Furthermore, strain engineering can induce the ferrovalley semiconductor to half-valley metal transition in monolayer ${\mathrm{Ti}}_{3}{X}_{3}{Y}_{2}$. Our work not only provides a platform for two-dimensional (2D) valleytronic research but also promises the fundamental research of coupling physics in 2D lattices.