Quantum geometry and elliptic optical dichroism in $p$-wave magnets

The quantum geometric tensor is composed of the Berry curvature and the quantum metric, which is observable by means of optical absorption of elliptically polarized light. Especially, the quantum geometric tensor at the zero-momentum is observable by the optical absorption at the optical band edge. In this context, we study optical absorption of a $p$-wave magnet under irradiation of elliptically polarized light. The $p$-wave magnet has a band splitting along one axis, which we choose the $x$ axis. We obtain analytic formulae for the optical conductivity up to the second order in the magnitude of the N\'{e}el vector. In particular, the optical conductivity is exactly obtained when the N\'{e}el is along the $x$, $y$ and $z$ axis. It shows strong ellipticity a dependence of the light polarization, which is an elliptic dichroism. Especially, there is a perfect elliptic optical dichroism when the N\'{e}el vector is along the $y$ axis. It is possible to determine the N\'{e}el vector by measuring the ellipticity of the perfect elliptic dichroism.