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 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.

Automated summary

This paper theoretically studies the optical activity in a doped system and derives the optical activity tensor from a light wave vector dependent linear optical conductivity. The obtained expression for the optical activity tensor is in good numerical agreement with a recent theory for an undoped topologically trivial gapped system. The theory is applied to the optical activity of a gated twisted bilayer graphene, with a detailed discussion of the dependence on various factors.