Gate-Tunable Resonance State and Screening Effects for Proton-Like Atomic Charge in Graphene.

The ability to create a robust and well-defined artificial atomic charge in graphene and understand its carrier-dependent electronic properties represents an important goal toward the development of graphene-based quantum devices. Herein, we devise a new pathway toward the atomically precise embodiment of point charges into a graphene lattice by posterior (N) ion implantation into a back-gated graphene device. The N dopant behaves as an in-plane proton-like charge manifested by formation of the characteristic resonance state in the conduction band. Scanning tunneling spectroscopy measurements at varied charge carrier densities reveal a giant energetic renormalization of the resonance state up to 220 meV with respect to the Dirac point, accompanied by the observation of gate-tunable long-range screening effects close to individual N dopants. Joint density functional theory and tight-binding calculations with modified perturbation potential corroborate experimental findings and highlight the short-range character of N-induced perturbation.

Numerical package for QFT calculations of defect-induced phenomena in graphene.

We introduce a computationally efficient method based on the path integral formalism to describe defect-modified graphene. By taking into account the entire Brillouin zone, our approach respects the lattice symmetry and can be used to investigate both short-range and long-range effects. The proposed method's key advantage is that the computational complexity does not increase with the system size, scaling, instead, with the number of defects. Our aim is to make the quantum-field calculations in graphene accessible to the experimental community. We demonstrate our method's capabilities by exploring the well-known graphene-mediated Ruderman-Kittel-Kasuya-Yoshida interaction and by performing a detailed study of the atomic collapse in the presence of defects.