  ABC-stacked trilayer graphene (TLG) are predicted to exhibit novel many-body
phenomena due to the existence of almost dispersionless flat-band structures
near the charge neutrality point (CNP). Here, using high magnetic field
scanning tunneling microscopy, we present Landau Level (LL) spectroscopy
measurements of high-quality ABC-stacked TLG. We observe an approximately
linear magnetic-field-scaling of the valley splitting and orbital splitting in
the ABC-stacked TLG. Our experiment indicates that the valley splitting
decreases dramatically with increasing the LL index. When the lowest LL is
partially filled, we find an obvious enhancement of the orbital splitting,
attributing to strong many-body effects. Moreover, we observe linear energy
scaling of the inverse lifetime of quasiparticles, providing an additional
evidence for the strong electron-electron interactions in the ABC-stacked TLG.
These results imply that interesting broken-symmetry states and novel electron
correlation effects could emerge in the ABC-stacked TLG in the presence of high
magnetic fields.
