Thickness-dependent phase transition in graphite under high magnetic field

Various electronic phases emerge when applying high magnetic fields in graphite. However, the origin of a semimetal-insulator transition at $B \simeq 30\; \textrm{T}$ is still not clear, while an exotic density-wave state is theoretically proposed. In order to identify the electronic state of the insulator phase, we investigate the phase transition in thin-film graphite samples that were fabricated on silicon substrate by a mechanical exfoliation method. The critical magnetic fields of the semimetal-insulator transition in thin-film graphite shift to higher magnetic fields, accompanied by a reduction in temperature dependence. These results can be qualitatively reproduced by a density-wave model by introducing a quantum size effect. Our findings establish the electronic state of the insulator phase as a density-wave state standing along the out-of-plane direction, and help determine the electronic states in other high-magnetic-field phases.