Interacting Electrons in Graphene: Fermi Velocity Renormalization and Optical Response

Area of Science:

• Condensed Matter Physics
• Quantum Mechanics
• Materials Science

Background:

• Graphene's unique electronic properties, particularly Fermi velocity renormalization, remain a challenge.
• Existing models often require fitting parameters, limiting their predictive power.

Purpose of the Study:

• To develop a parameter-free Hartree-Fock theory for electrons on a honeycomb lattice.
• To accurately model Fermi velocity renormalization in graphene.
• To provide a theoretical framework for understanding electron-electron interactions in 2D materials.

Main Methods:

• Developed a novel Hartree-Fock theory incorporating a topological invariant (crystal structure function).
• Ensured the Hartree-Fock sublattice spinor is independent of electron-electron interactions.
• Applied static self-screening and local field effects for model validation.

Main Results:

• Achieved agreement with experimental data without using fitting parameters.
• Derived an explicit expression for optical conductivity.
• Demonstrated renormalization of the Drude weight.
• Quantum Monte Carlo calculations validated the mean-field approach.

Conclusions:

• The developed parameter-free theory successfully explains Fermi velocity renormalization in graphene.
• The model provides a robust method for calculating optical conductivity and Drude weight.
• This approach offers new insights into electron-electron interactions in topological materials.