Dynamical screening and excitonic bound states in biased bilayer graphene

Abstract: Excitonic bound states are characterised by a binding energy $\epsilon_b$ and a single-particle band gap $\Delta_b$. This work provides a theoretical description for both strong ($\epsilon_b\sim\Delta_b$) and weak ($\epsilon_b\ll\Delta_b$) excitonic bound states, with particular application to biased bilayer graphene. Standard description of excitons is based on a wave function that is determined by a Schr\"odinger-like equation with screened attractive potential. The wave function approach is valid only in the weak binding regime $\epsilon_b\ll\Delta_b$. The screening depends on frequency (dynamical screening) and this implies retardation. In the case of strong binding, $\epsilon_b\sim\Delta_b$, a wave function description is not possible due to the retardation. Instead we appeal to the Bethe-Salpeter equation, written in terms of the electron-hole Green's function, to solve the problem. So far only the weak binding regime has been achieved experimentally. Our analysis demonstrates that the strong binding regime is also possible and we specify conditions in which it can be achieved for the prototypical example of biased bilayer graphene. The conditions concern the bias, the configuration of gates, and the substrate material. To verify the accuracy of our analysis we compare with available data for the weak binding regime. We anticipate applying the developed dynamical screening Bethe-Salpeter techniques to various 2D materials with strong binding.