Theory of optical activity in doped systems with application to twisted bilayer graphene

We theoretically study the optical activity in a doped system and derive tensor from light wavevector-dependent linear conductivity. Although light-matter interaction is introduced through velocity gauge minimal coupling Hamiltonian, we find that well-known ``false divergences'' problem can be avoided practice if electronic states are described by finite band effective such as few-band tight-binding model. The expression obtain for good numerical agreement with recent theory derived an undoped topologically trivial gapped system. apply our to of gated twisted bilayer graphene, detailed discussion dependence results on twist angle, chemical potential, gate voltage, location rotation center forming graphene.