  We present a comparative measurement of the G-peak oscillations of phonon
frequency, Raman intensity and linewidth in the Magneto-Raman scattering of
optical E2g phonons in mechanically exfoliated ABA- and ABC-stacked trilayer
graphene (TLG). Whereas in ABA-stacked TLG, we observe magnetophonon
oscillations consistent with single-bilayer chiral band doublets, the features
are flat for ABC-stacked TLG up to magnetic fields of 9 T. This suppression can
be attributed to the enhancement of band chirality that compactifies the
spectrum of Landau levels and modifies the magnetophonon resonance properties.
The drastically different coupling behaviour between the electronic excitations
and the E2g phonons in ABA- and ABC-stacked TLG reflects their different
electronic band structures and the electronic Landau level transitions and thus
can be another way to determine the stacking orders and to probe the
stacking-order-dependent electronic structures. In addition, the sensitivity of
the magneto-Raman scattering to the particular stacking order in few layers
graphene highlights the important role of interlayer coupling in modifying the
optical response properties in van der Waals layered materials.
