Effective Hamiltonian approach to optical activity in Weyl spin-orbit system

Chirality or handedness in condensed matter induces anomalous optical responses such as natural optical activity, rotation of the plane of light polarization, as a result of breaking of spatial-inversion symmetry. In this study, optical properties of a Weyl spin-orbit system with quadratic dispersion, a typical chiral system invariant under time-reversal, are investigated theoretically by deriving an effective Hamiltonian based on an imaginary-time path-integral formalism. We show that the effective Hamiltonian can be indeed written in terms of an optical chirality order parameter suggested by Lipkin. The natural optical activity is discussed based on the Hamiltonian.