Signatures of optical conductivity in double-layer graphene excitonic condensate

Signatures of the excitonic condensation state and its optical properties in biased double-layer graphene (DLG) are discussed. In the framework of the generic bilayer graphene model involving a Coulomb interaction between electrons in one layer and holes in the opposite layer, we have derived a set of self-consistent equations determining the excitonic condensate order parameter by use of the projector-based renormalization method. Based on the Kubo theory of the linear optical response, a formula of the optical conductivity is also obtained with full contributions of the quantum fluctuations. Our results elucidate a possibility of the excitonic condensation formation in the biased system once the dielectric thickness is sufficiently small. As a function of the external electric field, the excitonic condensation dome suppresses rapidly as enlarging the dielectric thickness. The impression of the dielectric thickness and external electric field affecting the excitonic condensate is also addressed in the signature of the optical conductivity. Our findings are worthwhile to understand the formation and stability of the excitonic condensation states not only in DLG but also in other double-layer systems or in semimetal-semiconductor transition materials.