  In this manuscript, we demonstrate a novel technique to probe the electronic
structure of the top-most atomic layer of a solid using the virtual photon
exchange between a positron and a valence band electron. This process, termed
Auger-mediated positron sticking, is initiated by the coupling of the energy
and momentum associated with the trapping of a positron in an
image-potential-induced surface state to an electron in the material. We have
used this quantum sticking of low-energy positrons to probe the valence band
density of states of single-layer graphene and copper. The measured
positron-induced electron spectra were successfully reproduced using a model
which is principally composed of the valence band density of states. Our
results demonstrate that Auger-mediated positron sticking is a top-most atomic
layer selective probe of the electronic structure of fragile two dimensional
surfaces which can complement existing photoemission spectroscopy techniques.
The exceptional surface selectivity of Auger-mediated positron sticking arises
because the excitation depth is limited to the Thomas-Fermi screening length.
Finally, the analysis of the Cu spectrum in terms of the partial density of
states reveals matrix element effects that suppress the contribution of valence
3d electrons relative to the 4s and 4p electrons.
