Optical conductivity signature of Van Hove singularity in altermagnetic topological systems

Abstract

We investigate the topological phases, joint density of states (JDOS), optical conductivities, and magneto-optical responses of a two-dimensional $d$-wave altermagnet with spin-orbit coupling and Zeeman splitting. The system hosts Dirac gaps at the high-symmetry points $Γ$, $\textrm{M}$, $\textrm{X}$, and $\textrm{Y}$. We show that the JDOS exhibits kinks at the corresponding Dirac gap frequencies and pronounced peaks at Van Hove singularities, whose positions can be tuned by the altermagnetic order. These features are reflected in the optical conductivities, with complementary signatures in their real and imaginary parts. Particularly, the Van Hove signatures in the transverse optical conductivity disappear in the absence of $d$-wave altermagnetism, revealing an altermagnet-induced optical signature of the Van Hove singularity. Finally, the Faraday and Kerr rotations inherit characteristic features of the optical conductivity. Our results establish optical and magneto-optical spectroscopy as sensitive probes of Dirac gaps and Van Hove singularities in altermagnetic topological systems.