Unveiling Berry curvature contributions to Hall current in $C_4K$ materials

Abstract: We identify a new contribution to the conventional Hall effect that emerges in materials with $C_4K$ symmetry. This contribution originates from the modification of phase space density due to the Berry curvature, as we demonstrate using semiclassical equations of motion for band electrons. As an illustration, we build a minimal two-band tight-binding model with altermagnetic order that breaks $C_4$ and $K$ symmetries while preserving $C_4K$. The resulting Hall conductivity shows a square-root feature at the altermagnetic phase transition, which is due to the novel Berry curvature-driven contribution emerging below the critical temperature. This effect may offer a simple transport-based signature of an altermagnetic phase transition.