LAUSR

We have proposed a topological carbon allotrope, named Hopfene, which has three-dimensional (3D) arrays of Hopf-links to bind 2D Graphene layers both horizontally and vertically without forming strong σ bonds between layers. Tight-binding calculations show unique band structures of this crystal, which predicts semi-metal characteristics with the existence of both Weyl and Dirac Fermions depending on the Fermi energy. Here, we have theoretically examined superconductivity of Hopfene based on the attractive Hubbard model. Regardless of its simplicity of the model, we found non-trivial competitions between Hartree–Fock mean-field contributions and Cooper-paring interactions to open semiconductor and superconducting energy gaps, respectively. Consequently, the superconducting order parameters are significantly reduced at every quarterly doping concentration, where the system is in the close vicinity of the quantum critical point, and we found superconductor-insulator transition in the strong coupling limit. Upon doping, we confirmed a classical scenario of a smooth crossover from weak coupling Bardeen-Cooper-Schrieffer (BCS) superconductivity to strong coupling Bose–Einstein Condensation (BEC) of preformed pairs by increasing the interaction strength. We think the proposed Hopfene is a useful platform to investigate the impacts of the topological nature of the Fermi surfaces on the superconductivity and other orders, including charge-density-waves and magnetic orders, and possible quantum phase transitions among them.