Optical rotation in thin chiral/twisted materials and the gyrotropic magnetic effect

The rotation of the plane of polarization of light passing through a non-magnetic material is known as natural optical activity or optical gyrotropy. The behavior of this effect in thin chiral conductors is of current interest. For example, the low frequency limit of gyrotropy in chiral 3D crystals, known as the gyrotropic magnetic effect (GME), is controlled by the orbital magnetic moment of electrons, which has been proposed to be relevant to current-induced switching in twisted bilayer graphene. We show that the GME is not limited to bulk materials but also appears for quasi-2d systems with minimal structure incorporated in the third direction. Starting from multi-band Kubo formula, we derive a generic expression for GME current in quasi-2d materials induced by low-frequency light, and provide a Feynman-diagrammatic interpretation. The relations between the 2d finite layered formula and 3d bulk formula are also discussed.