2D spontaneous valley polarization from inversion symmetric single-layer lattices

2D spontaneous valley polarization attracts great interest both for its fundamental physics and for its potential applications in advanced information technology, but it can only be obtained from inversion asymmetric single-layer crystals, while the possibility to create 2D spontaneous valley polarization from inversion symmetric single-layer lattices remains unknown. Here, starting from inversion symmetric single-layer lattices, a general design principle for realizing 2D spontaneous valley polarization based on van der Waals interaction is mapped out. Using first-principles calculations, we further demonstrate the feasibility of this design principle in a real material of T-FeCl2. More remarkably, such design principle exhibits the additional exotic out-of-plane ferroelectricity, which could manifest many distinctive properties, for example, ferroelectricity-valley coupling and magnetoelectric coupling. The explored design-guideline and phenomena are applicable to a vast family of 2D materials. Our work not only opens up a platform for 2D valleytronic research but also promises the fundamental research of coupling physics in 2D lattices.