Coulomb Impurity Problem in Graphene
Vitor M. PereiraDepartment of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USAJohan NilssonDepartment of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USAA. H. Castro NetoDepartment of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
2007en
ABI
Abstract
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.
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