Coexistence of superconductivity and exciton condensation in graphene multilayers*

Recent moiré material experiments have demonstrated that twisted bilayer graphene can be a superconductor
at sufficiently low temperature [1], and that double-bilayer graphene can have an excitonic ground state [2].
Motivated by these discoveries, we explore a generic system of two Coulomb-coupled 2D superconducting
layers. When interactions between 2D layers are sufficiently strong, spatially separated excitons -- composed
of an electron and a hole located in different layers -- can condense. In our work, we show that the excitonic
condensate can still occur when the 2D layers are superconducting. The coexistent interlayer excitonic and
intralayer superconducting order is necessarily accompanied by an interlayer superconducting parameter. We
discuss the phenomenology of these states and experiments that could be performed to identify their
occurrence.

[1] Cao, Y., Fatemi, V., Fang, S. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018)
[2] Rickhaus, P., de Vries, F., Zhu, J., Portolés, E., Zheng, G., Masseroni, M., ... & Ihn, T. (2020). Density-Wave States in Twisted Double-Bilayer Graphene. arXiv preprint arXiv:2005.05373.