  Electron tunneling spectroscopy measurements on van der Waals
heterostructures consisting of metal and graphene (or graphite) electrodes
separated by atomically thin hexagonal boron nitride tunnel barriers are
reported. The tunneling conductance dI/dV at low voltages is relatively weak,
with a strong enhancement reproducibly observed to occur at around |V| ~ 50 mV.
While the weak tunneling at low energies is attributed to the absence of
substantial overlap, in momentum space, of the metal and graphene Fermi
surfaces, the enhancement at higher energies signals the onset of inelastic
processes in which phonons in the heterostructure provide the momentum
necessary to link the Fermi surfaces. Pronounced peaks in the second derivative
of the tunnel current, are observed at voltages where known phonon modes in the
tunnel junction have a high density of states. In addition, features in the
tunneling conductance attributed to single electron charging of nanometer-scale
defects in the boron nitride are also observed in these devices. The small
electronic density of states of graphene allows the charging spectra of these
defect states to be electrostatically tuned, leading to Coulomb diamonds in the
tunneling conductance.
