Benzene on graphene: Types of domain boundaries

It is shown that for the system of benzene molecules adsorbed on the graphene surface there is a rich set of linear topological defects—domain boundaries. This is a typical van der Waals system. We have previously introduced a vector order parameter (OP) as a transition from a symmetric (hollow) to a non-symmetric (top) position and have shown the existence of left and right domains connected to a graphene’s two-atomic unit cell. Here, we have found the existing of the 180°, 120°, 60°, and 0° domain boundaries for the relative orientation of OP vectors. We have shown that the domain boundary description requires the topology of the neighboring domains (left or right), the relative OP vectors direction and length. Additional information can be obtained from the boundary line direction and length. Topological selection rules for possible and forbidden angles of the domain boundaries have been introduced. The number of possible domain pairs (boundaries) and the number of domain boundaries types are calculated. It is noted that the domain and domain boundaries in this system can be artificially created as well as arise naturally. They can be used for modification of electronic and mechanical properties of graphene.