Layering effects on low frequency modes in n-layered MX2 transition metal dichalcogenides.

n-Layered (n = 2, 3, 4) MX2 transition metal dichalcogenides (M = Mo, W; X = S, Se, Te) have been studied using DFT techniques. Long-range van der Waals forces have been modeled using the Grimme correction to capture interlayer interactions. We study the dynamic and electronic dependence of atomic displacement on the number of layers. We find that the displacement patterns mainly affected by a change in the layer number are low-frequency modes at Γ and A k-points; such modes are connected with the intrinsic tribological response. We disentangle electro-phonon coupling by combining orbital polarization, covalency and cophonicity analysis with phonon band calculations. We find that the frequency dependence on the number of layers and the atomic type has a non-trivial relation with the electronic charge distribution in the interlayer region. We show that the interlayer electronic density can be adjusted by appropriately tuning M-X cophonicity, acting as a knob to control vibrational frequencies, hence the intrinsic frictional response. The present results can be exploited to study the electro-phonon coupling effects in TMD-based materials beyond tribological applications.