Klimchitskaya G L, Malyi V S, Mostepanenko V M, Petrov V M
Central Astronomical Observatory at Pulkovo of the Russian Academy of Sciences, St.Petersburg, 196140, Russia. Institute of Physics, Nanotechnology and Telecommunications, Peter the Great Saint Petersburg Polytechnic University, St.Petersburg, 195251, Russia.
J Phys Condens Matter. 2019 Dec 18;31(50):505003. doi: 10.1088/1361-648X/ab4000.
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 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.
我们研究了涂覆有石墨烯片的介电板的反射率，该石墨烯片在任何温度下都具有非零能隙和化学势。在狄拉克模型的框架下，给出了使用极化张量计算反射率的一般形式。它允许基于量子电动力学的第一原理计算任何涂覆有真实石墨烯片的材料板的反射率特性。对涂覆有石墨烯的SiO板在室温、液氮温度和液氦温度下进行了反射率的数值计算。我们证明，化学势、能隙、频率和温度在它们对涂覆有石墨烯的板的反射率的联合作用中存在非平凡的相互作用。具体而言，结果表明，在入射光频率固定的情况下，化学势和能隙的增加分别通过增加和降低反射率而对其产生相反方向的影响。根据我们的结果，对于任何化学势和能隙值，反射率在足够低的频率下趋近于1，而在高频下下降到未涂覆板的反射率。发现温度对反射率的影响对于化学势较小的石墨烯涂层更为明显。所得结果可用于优化利用石墨烯涂层的光学探测器和其他器件。
