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Coulomb impurity problem in graphene.

Vitor M Pereira1, Johan Nilsson, A H Castro Neto

  • 1Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA.

Physical Review Letters
|November 13, 2007
PubMed
Summary
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We studied unscreened Coulomb charge effects in graphene using two methods. The Dirac equation offers a good low-energy approximation, but lattice models reveal additional phenomena like bound states.

Area of Science:

  • Condensed Matter Physics
  • Materials Science
  • Theoretical Physics

Background:

  • Graphene exhibits unique electronic properties due to its 2D Dirac cone structure.
  • Understanding impurity effects is crucial for graphene-based electronic devices.
  • Unscreened Coulomb interactions present a significant theoretical challenge.

Purpose of the Study:

  • To investigate the impact of an unscreened Coulomb impurity in graphene.
  • To calculate the local density of states and displaced charge.
  • To compare nonperturbative lattice and continuum models.

Main Methods:

  • Numerical study of the tight-binding model on a lattice.
  • Continuum description using the 2D Dirac equation.
  • Nonperturbative calculations of electronic properties.

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Main Results:

  • The 2D Dirac equation, when regularized, accurately describes low-energy phenomena.
  • Lattice model reveals bound state formation not predicted by the Dirac equation.
  • Strong renormalization of van Hove singularities observed in the lattice solution.

Conclusions:

  • The continuum Dirac model provides a valuable, albeit incomplete, low-energy approximation for graphene impurities.
  • Lattice models are necessary to capture all emergent phenomena, including bound states and singularity renormalization.
  • Accurate modeling of Coulomb impurities is essential for predicting graphene's electronic behavior.