Piezoelectric polarizations and valley-related multiple Hall effects in TiAlX3 monolayers (X = Se, Te)†

Valleytronics, spintronics and piezotronics are emerging fields that aim to manipulate the valley, spin and charge degrees of freedom to control related transport properties in condensed matter. Here, we predict that TiAlX₃ (X = Se, Te) are multifunctional ferromagnetic semiconductors with large valley polarization up to 179.7 meV and a large in-plane piezoelectric response up to −66.02 pm V⁻¹. Strain-induced topological phase transitions and the quantum anomalous valley Hall effect (QAVHE) can be found in TiAlSe₃, where 100% valley- and spin-polarization can be generated by half-valley metallic (HVM) states. Combining the sequent band inversions of the d_x²−y²/d_xy and d_z² orbitals at K and K′ valleys with a two-band strained k·p model, the physical mechanism in topological phase transitions is illuminated. Finally, based on the coexistence of the anomalous valley Hall effect (AVHE) and piezoelectric transport in ferrovalley systems, we propose the piezoelectric-AVHE (PAVHE) in which the carriers from the polarized-valleys are driven by the intrinsic polarized electric field established by the piezoelectric response. Our work enriches the valley-related multiple Hall effect and stimulates further experimental works related to the valley physics.