Optical response of alternating twisted trilayer graphene

We study the optical response of the alternating twisted trilayer graphene by making use of a unitary transformation for the trilayer Hamiltonian and the Kubo formulation of linear response theory. The layer-resolved optical conductivities are expressed in terms of contributions from effective twisted bilayer and single-layer systems along with their coupling. We show that the in-plane magnetic response is proportional to this coupling between the twisted bilayer and single-layer systems; and, due to the different energy scales, the in-plane magnetic response is negligibly small. We also formulate a local electro-magnetic response that involves the vertical gradients of the magnetic field and moment.