2007/06/27 by Vitor M. Pereira, Johan Nilsson, A. H. Castro Neto · 9 citations
Materials Science · Physics and Astronomy · #Bound state #Condensed matter physics #Coulomb #Coulomb barrier #Dirac equation #Graphene #Graphene research and applications #Gravitational singularity #Lattice (music) #Physics #Quantum and electron transport phenomena #Quantum mechanics #Renormalization #Topological Materials and Phenomena #cond-mat.mes-hall #cond-mat.str-el
paper · pdf · doi:10.1103/physrevlett.99.166802
published as Phys. Rev. Lett. 99, 166802 (2007) · 3 Figures; minor typo corrections and minor update in Fig. 3d
arxiv created 2007/06/27 · openalex publication_date 2007/10/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We address the problem of an unscreened Coulomb charge in graphene and calculate the local density of states and displaced charge as a function of energy and distance from the impurity. This is done nonperturbatively in two different ways: (1) solving the problem exactly by studying numerically the tight-binding model on the lattice and (2) using the continuum description in terms of the 2D Dirac equation. We show that the Dirac equation, when properly regularized, provides a qualitative and quantitative low energy description of the problem. The lattice solution shows extra features that cannot be described by the Dirac equation: namely, bound state formation and strong renormalization of the van Hove singularities.