Emergence of net chirality in a two-dimensional Dirac fermion system with altermagnetic mass

In two-dimensional lattice systems, massless Dirac fermions undergo doubling, leading to the cancellation of net chirality. We demonstrate that the recently discovered altermagnetism can induce a unique mass term, the altermagnetic mass term, which gaps out Dirac cones with one chirality while maintaining the other gapless, leading to the emergence of net chirality. The surviving gapless Dirac cones retain identical winding numbers and exhibit the quantum anomalous Hall effect in the presence of the trivial constant mass term. When subjected to an external magnetic field, the altermagnetic mass induces Landau level asymmetry in Dirac fermions, resulting in fully valley-polarized quantum Hall edge states. Our findings reveal that Dirac fermions with the altermagnetic mass harbor rich physical phenomena warranting further exploration.