Coexisting Giant\nTunable Valley Polarization and Piezoelectric\nResponse in FeO<sub>2</sub>SiGeN<sub>2</sub> Monolayers

The valley-related multiple Hall\neffect and piezoelectric response\nare interesting transport characteristics in low-dimensional systems;\nhowever, few studies have reported their coexistence in a single system\nas well as their coupling relationships. By first-principles calculations,\nwe propose a multifunctional Janus semiconductor, i.e., an FeO<sub>2</sub>SiGeN<sub>2</sub> monolayer with a large valley polarization\nof about 120 meV and in-plane piezoelectric polarization with a <i>d</i><sub>11</sub> of −0.71–4.03 pm/V. The magnetic\nanisotropy energy can be significantly regulated by the electronic\ncorrelation strength and strain, which can be attributed to the change\nin the competitive relationship with respect to the Fe-3d-resolved\nmagnetic anisotropy energy brought about by external regulatory means.\nElectronic correlation strength can induce phase transitions in the\nJanus FeO<sub>2</sub>SiGeN<sub>2</sub> monolayer from a ferrovalley\nto the quantum anomalous Hall phase, while the half-valley metallic\nstate as the boundary of the phase transition can generate 100% spin\nand valley polarization. The related phase transition mechanism is\nanalyzed based on the two-band strained <i>k · p</i> model. The presence of the piezoelectric strain coefficient <i>d</i><sub>11</sub> in valleytronic materials makes the coupling\nbetween charge degrees of freedom and valley degrees of freedom possible,\nand the intrinsic electric field caused by the in-plane piezoelectric\nresponse provides a way to realize the piezoelectric anomalous valley\nHall effect. This work may pave a way to find interesting materials\nwith the valley-related multiple Hall effect and stimulate further\nexperimental work related to valleytronics and piezotronics.