  The response of Dirac fermions to a Coulomb potential is predicted to differ
significantly from the behavior of non-relativistic electrons seen in
traditional atomic and impurity systems. Surprisingly, many key theoretical
predictions for this ultra-relativistic regime have yet to be tested in a
laboratory. Graphene, a 2D material in which electrons behave like massless
Dirac fermions, provides a unique opportunity to experimentally test such
predictions. The response of Dirac fermions to a Coulomb potential in graphene
is central to a wide range of electronic phenomena and can serve as a sensitive
probe of graphene's intrinsic dielectric constant, the primary factor
determining the strength of electron-electron interactions in this material.
Here we present a direct measurement of the nanoscale response of Dirac
fermions to a single Coulomb potential placed on a gated graphene device.
Scanning tunneling microscopy and spectroscopy were used to fabricate tunable
charge impurities on graphene and to measure how they are screened by Dirac
fermions for a Q = +1|e| impurity charge state. Electron-like and hole-like
Dirac fermions were observed to respond very differently to tunable Coulomb
potentials. Comparison of this electron-hole asymmetry to theoretical
simulations has allowed us to test basic predictions for the behavior of Dirac
fermions near a Coulomb potential and to extract the intrinsic dielectric
constant of graphene: {\epsilon}_g= 3.0 \pm 1.0. This small value of
{\epsilon}_g indicates that microscopic electron-electron interactions can
contribute significantly to graphene properties.
