Possible electronic state quasi-half-valley metal in a VGe2P4 monolayer

One of the key problems in valleytronics is to realize valley polarization. Ferrovalley semiconductors and half-valley metals (HVM) have been proposed, which possess intrinsic spontaneous valley polarization. Here, we propose the concept of a quasi-HVM (QHVM), including electron and hole carriers with only a type of carriers being valley polarized. The QHVM may realize the separation function of the electron and hole. A concrete example of the ${\mathrm{VGe}}_{2}{\mathrm{P}}_{4}$ monolayer is used to illustrate our proposal through first-principle calculations. To better realize QHVM, the electric field is applied to tune related valley properties of ${\mathrm{VGe}}_{2}{\mathrm{P}}_{4}$. Within the considered electric field range, ${\mathrm{VGe}}_{2}{\mathrm{P}}_{4}$ adopts a ferromagnetic (FM) ground state, which possesses out-of-plane magnetization, as confirmed by calculating magnetic anisotropy energy including magnetic shape anisotropy and magnetocrystalline anisotropy energies. These out-of-plane FM properties guarantee intrinsic spontaneous valley polarization in ${\mathrm{VGe}}_{2}{\mathrm{P}}_{4}$. Within a certain range of electric field, the QHVM can be maintained, and the related polarization properties can be effectively tuned. In this paper, we pave the way toward two-dimensional functional materials design of valleytronics.