Circular Drude conductivity with a positive-frequency convention (${\sigma }_{\pm }={\sigma }_0/[1+i(\omega \mp {\omega }_c)\tau ]$)

For charge $-e$, field $B\hat{z}$, time dependence $e^{i\omega t}$ and circular components $E_{\pm }=E_x\pm i{E}_y$, the active positive-frequency response is the plus component and its denominator contains $\omega -{\omega }_c$. Reversing the field or exchanging helicity labels swaps the signs. A printed circular conductivity must state those conventions together.