Transforming Two-Dimensional Carbon Allotropes into Three-Dimensional Ones through Topological Mapping: The Case of Biphenylene Carbon (Graphenylene)

In this work, we propose a new methodology for obtaining three-dimensional (3D) carbon allotrope structures from 2D ones through topological mapping. The idea is to select a 3D target structure and "slice" it along different structural directions, creating a series of 2D structures. As a proof of concept, we chose the tubulane structure 12-hexa(3,3) as a target. Tubulanes are 3D carbon allotropes based on cross-linked carbon nanotubes. One of the obtained 2D "sliced" structures was mapped into the biphenylene carbon (BPC). We showed that compressing BPC in-plane, biaxially, followed by compression along the