Atomic-scale insights into the origin of rectangular lattice in nanographene probed by scanning tunneling microscopy

We conducted atomic-scale scanning tunneling microscopy of a graphene nanosheet on graphite. In addition to a rhombus lattice representing the $\left(\sqrt{3}\times \sqrt{3}\right)R{30}^{\circ }$ superstructure, we resolved another quadrangle lattice similar to a rectangle in the sheet. Its lattice size was approximately $0.37\times 0.22\mathrm{n}{\mathrm{m}}^2$. To clarify the origin of this unique rectangular lattice, the overlap of the $\sqrt{3}\times \sqrt{3}$ superstructures along the direction of their long diagonals was theoretically examined using a simple model. The electron distribution with high energy in the occupied states of armchair-edged graphene nanoribbons (AGNRs) was calculated based on first principles. A rectangular lattice, resembling the one observed experimentally, was found to form on the AGNR under a specific width condition. This finding was also analyzed in terms of Clar's theory and the scattering of electron waves. We propose that wrinkles and adsorbates in graphene play a role similar to an armchair edge, resulting in the $\sqrt{3}\times \sqrt{3}$ phase. If these local defects are in close proximity, the rhombus phases interact to generate electronic structures predicted for AGNRs. This is probably the reason why a rectangular lattice was imaged on the graphene sheet that is not an ideal AGNR.