Fig. 4: Signs of the acid intercalation of the 2D sheets.

An AFM image of exfoliated graphene (a) and hBN (b) revealing cleaving edges (marked with green dashed lines). c The histogram of the cleaved edge angles for the exfoliated graphene, hBN (grey), and MoS₂ (green). Insets: Corresponding examples of the exfoliated 2D sheets. d The wavelength dependence of the optical contrast for tape (solid curves) and acid-assisted (circles) exfoliated graphene 2D sheets with a different number of layers. Error bars represent one standard deviation. Dashed curves represent the prediction of the Fresnel law. Inset: Optical (left) and AFM (right) images of the graphene sheet. Scale bars in a–c: 1 µm. e AFM thickness versus the number of layers determined from the optical contrast of the tape exfoliated graphene and hBN (open symbols) compared to the acid-exfoliated graphene (solid circles) and hBN (solid squares). The linear regressions determine the effective monolayer thickness. XRD pattern of exfoliated hBN (f) and graphene (g) exhibiting the reflections expected for the bulk crystals (black font) along with the series reflections correspondent to the Stage I in hBN and Stage II in graphene intercalated nanosheets with the effective \(d\)-spacing, \(d = nc_0 + d_{\rm{i}}\), where \(c_0 =\) 3.35 Å, n is the stage number and \(d_{\rm{i}}\) is the intercalant size. The reflection at around 44° originates from the metallic sample holder. h XRD data for the exfoliated MoS₂. i AFM thickness for tape (open symbols) and acid-assisted (solid symbols) exfoliated MoS₂ vs. the number of layers determined from the contrast measurements and corresponding linear regression. Error bars in e and i are one standard deviation approximated from AFM height profiles (Supplementary Fig. 10) and Fresnel-law model analysis (Supplementary Figs 11 and 12).