Detecting the Six Polytypes of Five-Layer Graphite

Graphene layers can assemble in two shifted metastable positions per interface, leading to eight possible structural arrangements in five-layer graphene, six of which correspond to distinct periodic crystals. These polytypes exhibit diverse symmetries, interlayer electronic hybridization, van der Waals adhesion, and optical responses. Arrangements lacking inversion [I] and mirror [M_z] symmetries host intrinsic polarizations, while those with sufficiently flat electronic bands display orbital magnetization, unconventional superconductivity, and anomalous fractional quantum Hall states. Here, a detailed comparative study of these polytypes is presented, examining their Raman scattering spectra, second-harmonic optical emission microscopy, and surface electric potential maps. Each configuration is deterministically identified, its natural abundance is quantified, and its relative stability is assessed. Understanding these stacking-dependent properties is a critical step toward the development of multiferroic devices that leverage sliding transitions between structural configurations.