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