  With considering the great success of scanning tunnelling microscopy (STM)
studies of graphene in the past few years, it is quite surprising to notice
that there is still a fundamental contradiction about the reported tunnelling
spectra of quasi-free-standing graphene monolayer. Many groups observed V-shape
spectra with linearly vanishing density-of-state (DOS) at the Dirac point,
whereas, the others reported spectra with a gap of 60 meV pinned to the Fermi
level in the quasi-free-standing graphene monolayer. Here we systematically
studied the two contradicted tunnelling spectra of the quasi-free-standing
graphene monolayer on several different substrates and provided a consistent
interpretation about the result. The gap in the spectra arises from the
out-of-plane phonons in graphene, which mix the Dirac electrons at the
Brillouin zone corners with the nearly free-electron states at the zone center.
Our experiment indicated that interactions with substrates could effectively
suppress effects of the out-of-plane phonons in graphene and enable us to
detect only the DOS of the Dirac electrons in the spectra. We also show that it
is possible to switch on and off the out-of-plane phonons of graphene at the
nanoscale, i.e., the tunnelling spectra show switching between the two distinct
features, through voltage pulses applied to the STM tip.
