Combined piezoelectricity and ferrovalley properties in Janus monolayer VClBr

Recently, the concept of ferrovalley materials has been proposed. These systems, in which ferromagnetism or ferroelectricity triggers spontaneous valley polarization, can be applied to nonvolatile valleytronic devices. In addition, a fabricated Janus transition metal dichalcogenide has been attracting immense attention due to its intrinsic valley properties and piezoelectricity. Inspired by these works, we predict a ferrovalley material, Janus VClBr monolayer, by performing first-principles calculations. The Janus VClBr monolayer possesses a large valley polarization due to the spin-orbit coupling coexisting with the intrinsic exchange interaction of vanadium $3d$ electrons, which can be illustrated by a $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ model. Combining the valley band structures with group theory analysis, we also find the chirality-dependent optical band gap that could be used to detect the valley state of the system. An anomalous valley Hall effect is confirmed by calculating the Berry curvatures in such a material system. Meanwhile, mirror symmetry breaking along the perpendicular direction not only results in an emergent internal electric dipole and a giant in-plane piezoelectricity, but also generates an out-of-plane second-harmonic-generation coefficient. Our findings of these distinctive properties, particularly the coupling of piezoelectricity and valley, could pave the way to design the Janus ferrovalley material as multifunctional valleytronics and optoelectronics devices.