A comparative analysis of the accuracy of Kubo formulations for graphene plasmonics

In recent years, there has been a growing need for the design and fabrication of smaller, faster, low-consumption and high-performance devices, as well as the technology approaches to the integration of electronics and photonics. This has led to the wide use of plasmonic structures. On the other hand, the excellent optical and electrical properties of graphene have made it a suitable material for plasmonic applications. The graphene properties can be manipulated by operation frequency and tuning its Fermi energy. Fermi energy of graphene can be tuned through electric gating or chemical doping. A phenomenon called Pauli blocking governs the interband transitions in graphene, and it is worth noting that since Pauli blocking is directly related to the Fermi energy of graphene, all parameters tuning the Fermi energy of graphene lead to variation of the imaginary parts of graphene's permittivity and refractive index. Many applications of graphene in plasmonics rely on this property. Since the permittivity and refractive index formulas of graphene are extracted from its two-dimensional conductivity called the Kubo formulation, the accurate calculation of graphene's two-dimensional conductivity is very important. In this paper, for the first time to our knowledge, the available Kubo formulations have been analyzed and compared so that the most accurate Kubo formulation could be chosen for plasmonic applications. Also, a comprehensive and detailed study about the properties of graphene including surface conductivity, permittivity, refractive index and plasma frequency, along with a sensitivity analysis for its refractive index and plasma frequency are accomplished.