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Chirality or handedness in condensed matter induces anomalous opticalresponses such as natural optical activity, rotation of the plane of lightpolarization, as a result of breaking of spatial-inversion symmetry. In thisstudy, optical properties of a Weyl spin-orbit system with quadraticdispersion, a typical chiral system invariant under time-reversal, areinvestigated theoretically by deriving an effective Hamiltonian based on animaginary-time path-integral formalism. We show that the effective Hamiltoniancan be indeed written in terms of an optical chirality order parametersuggested by Lipkin. The natural optical activity is discussed based on theHamiltonian.

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