  Stacking order plays a crucial role in determining the crystal symmetry and
has significant impacts on electronic, optical, magnetic, and topological
properties. Electron-phonon coupling, which is central to a wide range of
intriguing quantum phenomena, is expected to be intricately connected with
stacking order. Understanding the stacking order-dependent electron-phonon
coupling is essential for understanding peculiar physical phenomena associated
with electron-phonon coupling, such as superconductivity and charge density
waves. In this study, we investigate the effect of stacking order on
electron-infrared phonon coupling in graphene trilayers. By using gate-tunable
Raman spectroscopy and excitation frequency-dependent near-field infrared
nanoscopy, we show that rhombohedral ABC-stacked trilayer graphene has a
significantly stronger electron-infrared phonon coupling strength than the
Bernal ABA-stacked trilayer graphene. Our findings provide novel insights into
the superconductivity and other fundamental physical properties of rhombohedral
ABC-stacked trilayer graphene, and can enable nondestructive and
high-throughput imaging of trilayer graphene stacking order using Raman
scattering.
