Graphite under uniaxial compression along c-axis: a new parameter relates out-of-plane strain to in-plane phonon frequency

Stacking graphene sheets forms graphite. Two in-plane vibrational modes of graphite, E1u and E2g(2), are derived from graphene E2g mode, the shifts of which under compression are all considered as results of in-plane bond shortening. Values of Gruneisen parameter have been reported to quantify such relation. However, the reason why the shift rates of these three modes with pressure differ is unclear. In this work, we introduce a new parameter to quantify the contribution of out-of-plane strain to the in-plane vibrational frequencies, suggesting that the compression of \pi-electrons plays a non-negligible part in both graphite and graphene under high pressure.