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Charge response function and a novel plasmon mode in graphene.

S Gangadharaiah1, A M Farid, E G Mishchenko

  • 1Department of Physics, University of Utah, Salt Lake City, Utah 84112, USA.

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Summary

Vertex corrections are crucial for understanding 2D Dirac electrons near the electron-hole excitation threshold. Analytical summation reveals a strong plasmon resonance due to these corrections, impacting electron-electron interactions.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Field Theory in Many-Body Systems

Background:

  • Noninteracting 2D Dirac electrons exhibit a 1/√|qν-ω| singularity in polarizability at the electron-hole excitation boundary.
  • Screening of this singularity by electron-electron interactions is typically approximated using the random phase approximation (RPA), valid for infinite color degeneracy (N→∞).

Purpose of the Study:

  • To investigate the crucial role of ladder-type vertex corrections beyond the random phase approximation for 2D Dirac electrons.
  • To analytically sum the infinite series of ladder diagrams describing the excitonic effect near the excitation threshold.
  • To analyze the impact of these corrections on the polarization operator and plasmon resonance.

Main Methods:

  • Calculation of the ratio of ladder terms to RPA contributions, highlighting the importance of vertex corrections near the threshold.
  • Analytical summation of an infinite series of ladder diagrams to capture the excitonic effect.
  • Analysis of the polarization operator beyond the threshold (qν > ω).

Main Results:

  • Ladder-type vertex corrections become significant near the threshold, with their contribution growing as ln(n)|qν-ω|/N(n) compared to RPA.
  • Analytical summation confirms the crucial role of these corrections in describing the excitonic effect.
  • Beyond the threshold, the real part of the polarization operator is positive, leading to a strong, narrow plasmon resonance.

Conclusions:

  • Vertex corrections are essential for accurately describing the polarizability of 2D Dirac electrons and screening effects.
  • The study reveals a strong plasmon resonance arising from electron-electron interactions beyond the random phase approximation.
  • These findings are critical for understanding the collective electronic excitations in 2D Dirac materials.