Realization of the Tunable Multivalley System in a GeSe Monolayer by Atomic Substitution

A significant family of ferrovalley systems, 2D Group IV monochalcogenides (MX; M = Ge, Sn, Pb; X = S, Se, Te), have two inequivalent valleys, V_x and V_y, whose valley polarization results from the reduction of lattice symmetry caused by ferroelectric polarization. Another class is the ferromagnetic honeycomb materials, which have two inequivalent valleys of K₊ and K_- points and concurrently break the time and space symmetry. When the characteristics of the two ferrovalley material classes are combined, four unequal valleys (V_±x and V_±y) can be formed. Drawing from this concept, we analyze the symmetry of the GeSe monolayer and list the conditions necessary to introduce valley polarization of V₊ and V_- valleys. Finally, we demonstrate our prediction using atomic substitution in a GeSe monolayer and then combine four unequal valleys to form 16 states that can be switched using ferroelasticity, ferroelectricity, and ferromagnetism. Our research can help to comprehend ferrovalley materials and discover ferrovalley systems with multiple coexisting ferroic properties and also the implement and manage of multivalley systems.