Tunneling and Fluctuating Electron-Hole Cooper Pairs in Double Bilayer Graphene.

A strong low-temperature enhancement of the tunneling conductance between graphene bilayers has been reported recently, and interpreted as a signature of electron-hole pairing. The pairing in electron-hole double layers was first predicted more than forty years ago but has since avoided observation. Here we provide a detailed theory of conductance enhanced by electron-hole Cooper pair fluctuations, which are a precursor to equilibrium pairing, that reflects specific details of double graphene bilayer systems. Above the equilibrium condensation temperature, the pairs have finite temporal coherence and do not support dissipationless tunneling. Instead they strongly boost the tunneling conductivity via a fluctuational internal Josephson effect. We find dependences of the zero-bias peak in the differential tunneling conductance on temperature and electron-hole density imbalance that are in an enough good agreement with experiment.