Intrinsic Layer-Dependent Surface Energy and Exfoliation Energy of van der Waals Materials

Stacking and twisting 2D van der Waals (vdW) layers have become versatile platforms to tune the electron correlation. These platforms rely on exfoliating vdW materials down to a single vdW layer and a few vdW layers. We calculate the intrinsic layer-dependent surface and exfoliation energies of typical vdW materials such as graphite, h-BN, black P, MX₂ (M = Mo or W; X = S, Se, or Te), MX (M = Ga or In; X = S, Se, or Te), Bi₂Te₃, and MnBi₂Te₄ using density functional theory. For exchange-correlation functionals with explicit vdW interaction, a single vdW layer always has the smallest surface energy, giving a surface energy reduction when compared to that of thicker vdW layers. However, the magnitude of this surface energy reduction quickly decreases with an increase in the number of atomic layers inside the single vdW layer for different vdW materials. Such atomic-layer dependence in surface energy reduction helps explain the different effectiveness of exfoliation for different vdW materials down to a single vdW layer.