  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 [arXiv:2404.17146
(2024)]. Here, we propose a way for achieving valley polarization in twisted
altermagnetism by applying out-of-plane external electric field. Since the
out-of-plane electric field creates a layer-dependent electrostatic potential,
the valleys form 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 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 $\mathrm{Ca(CoN)_2}$ as a special twisted altermagnet. These findings
provide new opportunities for innovative spintronics, twistronics and
valleytronics applications.
