Reflectance of graphene-coated dielectric plates in the framework of Dirac model: joint action of energy gap and chemical potential

Abstract

We investigate the reflectance of a dielectric plate coated with a graphene sheet which possesses the nonzero energy gap and chemical potential at any temperature. The general formalism for the reflectance using the polarization tensor is presented in the framework of Dirac model. It allows calculation of the reflectivity properties for any material plate coated with real graphene sheet on the basis of first principles of quantum electrodynamics. Numerical computations of the reflectance are performed for the graphene-coated SiO 2 plate at room, liquid-nitrogen, and liquid-helium temperatures. We demonstrate that there is a nontrivial interplay between the chemical potential, energy gap, frequency, and temperature in their joint action on the reflectance of a graphene-coated plate. Specifically, it is shown that at the fixed frequency of an incident light an increase of the chemical potential and the energy gap affect the reflectance in opposite directions by increasing and decreasing it, respectively. According to our results, the reflectance approaches unity at sufficiently low frequencies and drops to that of an uncoated plate at high frequencies for any values of the chemical potential and energy gap. The impact of temperature on the reflectance is found to be more pronounced for graphene coatings with smaller chemical potentials. The obtained results could be applied for optimization of optical detectors and other devices exploiting graphene coatings.

Casimir and Casimir-Polder Forces in Graphene Systems: Quantum Field Theoretical Description and Thermodynamics

“…Equations ( 27)-( 30) have been used in calculations of the Casimir interaction in graphene systems [108][109][110][111][112][113]. After an analytic continuation to the real frequency axis, they were also applied for investigation of the electrical conductivity [114][115][116][117] and reflectances of graphene [118][119][120][121][122][123]. This allows us to compare the longitudinal and transverse dielectric permittivities of graphene ε ,⊥ , which are directly expressed via the respective conductivities σ ,⊥ , with the dielectric permittivity of the Drude model ε D .…”

“…This representation was generalized for the case of graphene with nonzero µ [107]. The results of [106,107] have also been used in investigation of the Casimir effect [108][109][110][111][112][113], electrical conductivity [114][115][116][117] and reflectivity [118][119][120][121][122][123] in graphene systems. The polarization tensor for a strained graphene was also derived [124].…”

Casimir and Casimir-Polder Forces in Graphene Systems: Quantum Field Theoretical Description and Thermodynamics

“…Equations ( 27)-( 30) have been used in calculations of the Casimir interaction in graphene systems [108][109][110][111][112][113]. After an analytic continuation to the real frequency axis, they were also applied for investigation of the electrical conductivity [114][115][116][117] and reflectances of graphene [118][119][120][121][122][123]. This allows to compare the longitudinal and transverse dielectric permittivities of graphene ε ,⊥ , which are directly expressed via the respective conductivities σ ,⊥ , with the dielectric permittivity of the Drude model ε D .…”

Quantum field theoretical description of the Casimir effect between two real graphene sheets and thermodynamics

“…This form of the polarization tensor was also successfully used in calculations of the Casimir force in various graphene systems [52][53][54][55][56][57] , as well as for investigation of the reflectivity and conductivity properties of graphene [58][59][60][61].…”