The interaction between the Fermi sea of conduction electrons and a non-adiabatic attractive impurity potential can lead to a power-law divergence in the tunneling probability of charge through the impurity. The resulting effect, known as the Fermi edge singularity (FES), constitutes one of the most fundamental many-body phenomena in quantum solid state physics. Here we report the first observation of FES for Dirac Fermions in graphene driven by isolated Coulomb impurities in the conduction channel. In high-mobility graphene devices on hexagonal boron nitride substrates, the FES manifests in abrupt changes in conductance with a large magnitude $approx e^{2}/h$ at resonance, indicating total many-body screening of a local Coulomb impurity with fluctuating charge occupancy. Furthermore, we exploit the extreme sensitivity of graphene to individual Coulomb impurities, and demonstrate a new defect-spectroscopy tool to investigate strongly correlated phases in graphene in the quantum Hall regime.
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