Valley polarization in twisted altermagnetism

The combination of altermagnetism, twistronics, and valleytronics is of great significance for potential applications in advanced electronic devices. Twisted magnetic van der Waals bilayers have been identified as an ideal platform for altermagnetism of any type, such as $d$ wave, $g$ wave, and $i$ wave, by choosing the constituent monolayer with specific symmetry [Y. Liu et al., Phys. Rev. Lett. 133, 206702 (2024)]. Here, we propose a way for achieving valley polarization in twisted altermagnetism by applying an out-of-plane external electric field. Since the out-of-plane electric field creates a layer-dependent electrostatic potential, the valleys from different layers will stagger, producing valley polarization. We also demonstrate the effectiveness of our proposed way using the twisted tight-binding model. It is found that the applied electric field can also induce a valley/spin-gapless semiconductor and half metal besides valley polarization. Based on first-principles calculations, our proposed way to achieve valley polarization can be verified in twisted bilayer VOBr and monolayer $\mathrm{Ca}{(\mathrm{CoN})}_{2}$ as a special twisted altermagnet. These findings provide different opportunities for innovative spintronics, twistronics, and valleytronics applications.