Effective Hamiltonian approach to optical chirality and optical activity induced by Weyl spin-orbit interaction

Rashba spin-orbit interaction leads to electromagnetic cross-correlation effects such as Edelstein and inverse Edelstein effects,
resulting in a natural optical activity such as circular dichroism. Furthermore, in the case where time-reversal invariance of the system is broken due to the existence of a magnetization and the magnetic field, an anisotropic light propagation irrespective of light polarization is induced by Doppler shift.
In this study, optical properties of a Weyl spin-orbit system with quadratic dispersion is investigated by deriving an effective Hamiltonian of electromagnetic fields based on an imaginary-time path-integral formalism. We show that the effective Hamiltonian in the systems is written in terms of a optical chirality order patameter suggested by Lipkin as shown below.
H_{EB}
= \frac{2g}{\epsilon_{0}}C_{\chi},
where $C_{\chi}$ is the chirality order parameter and $g$ is a constant reflecting the breaking of spatial-inversion symmetry. We also discuss natural optical activity in the context of the effective Hamiltonian.