3D integration of graphene has attracted attention for realizing carbon‐based electronic devices. While the 3D integration can amplify various excellent properties of graphene, the influence of 3D curved surfaces on the fundamental physical properties of graphene has not been clarified. The electronic properties of 3D nanoporous graphene with a curvature radius down to 25–50 nm are systematically investigated and the ambipolar electronic states of Dirac fermions are essentially preserved in the 3D graphene nanoarchitectures, while the 3D curvature can effectively suppress the slope of the linear density of states of Dirac fermion near the Fermi level are demonstrated. Importantly, the 3D curvature can be utilized to tune the back‐scattering‐suppressed electrical transport of Dirac fermions and enhance both electron localization and electron–electron interaction. As a result, nanoscale curvature provides a new degree of freedom to manipulate 3D graphene electrical properties, which may pave a new way to design new 3D graphene devices with preserved 2D electronic properties and novel functionalities.

We propose a way to improve energy density functionals (EDFs) in the density functional theory based on the combination of the inverse Kohn-Sham method and the density functional perturbation theory. Difference between the known EDF and the exact one is treated as the first-order perturbation. As benchmark calculations, we reproduce the theoretical exchange and correlation functionals in the local density approximation. Systems of noble-gas atoms are used for benchmark calculations, and the ground-state energies and densities, as well as the functionals, are reproduced with good accuracies.

The functional-renormalization-group aided density-functional theory (FRG-DFT) is applied to the two-dimensional homogeneous electron gas (2DHEG). The correlation energy of the 2DHEG is derived as a function of the Wigner-Seitz radius rs directly. We find that our correlation energy completely reproduces the exact behavior at the high-density limit. For finite density, the result of FRG-DFT shows good agreement with the Monte Carlo (MC) results in the high-density region, although the discrepancy between FRG-DFT and MC results becomes larger as the system becomes more dilute. Our study is the first example in which the FRG-DFT is applied to more-than-onedimensional models, and shows that the FRG-DFT is a feasible and promising method even for the analysis of realistic models for quantum many-body systems.