Scanning tunneling spectroscopy of exciton condensate in graphene double-layers

Fermions can form a condensate by pairing up into composite bosons, such as in superconductors and superfluid He₃. Interlayer exciton condensate is one of the few demonstrated fermionic condensates, where electrons and holes reside in spatially separated parallel layers couple to form excitons that condense at low temperatures. Previous transport measurements have established exciton condensation in graphene double-layer devices. However, there has not been spectroscopic measurements of this exotic state. Here we use scanning tunneling spectroscopy to probe the graphene double-layer devices under strong magnetic fields. In addition to incompressible states at the integer and fractional fillings of each layer, we observed gapped states when the total filling factor of the two layers is an integer as interlayer charge imbalance is continuously varied. These gaps, which are smaller than the those of integer quantum Hall states in individual layers, correspond to exciton condensates. Our spectroscopic measurements reveal information on the strength of the condensate states at different charge imbalance, the evolution of fractional quantum Hall states with changing dielectric environments, and competition between exciton condensation and fractional quantum Hall states of each layer. Future spectroscopic imaging experiments may uncover signatures of other remarkable electron behaviors in the double-layer system, such as exciton solids and topological excitations.