A closed-form approximate expression for the optical conductivity of graphene

Area of Science:

• Condensed Matter Physics
• Materials Science
• Nanotechnology

Background:

• Accurate optical conductivity models are crucial for understanding graphene's electronic properties.
• Existing methods for calculating optical conductivity often involve complex, singular integrals.
• Graphene's unique one-atom-thick structure presents challenges in electromagnetic simulations.

Purpose of the Study:

• To develop a closed-form approximate expression for graphene's optical conductivity.
• To provide a computationally efficient and reliable alternative to existing methods.
• To validate the utility of the derived optical conductivity in electromagnetic simulations.

Main Methods:

• Derivation of a closed-form approximate expression for optical conductivity.
• Inclusion of key physical parameters: wavelength, temperature, chemical potential, and hopping parameter.
• Numerical validation against established methods, assessing accuracy for wavelengths greater than 250 nm.

Main Results:

• The developed expression achieves less than 0.8% maximum absolute error for λ>250 nm.
• The formula offers a fast, easy, and reliable calculation, avoiding singular integrals.
• Effective complex electrical permittivity derived from the conductivity accurately models graphene in 3D simulations.

Conclusions:

• The novel approximate expression provides a highly accurate and efficient method for calculating graphene's optical conductivity.
• This simplified approach facilitates the integration of graphene into electromagnetic simulations and device analyses.
• The findings contribute to the broader understanding and application of graphene in optoelectronics and photonics.