# Implementation of Atomically Thick Graphene and Its Derivatives in Electromagnetic Absorbers
## 1 Introduction  
Graphene is a two-dimensional (2D) material exhibiting an ambipolar electrical field effect [1]. For a long time in history, 2D materials with single-atom thickness like graphene were theoretically predicted as thermaldynamically unstable due to the strong thermal fluctuations. In 2004, [PERSON] and [PERSON] from University of Manchester experimentally proved the existence of graphene with samples achieved with the scotch tape method [1]. Since then, a series of 2D materials such as hBN [2] and silicene [3] were also synthesized. On one hand, the ultrahigh carrier mobility of graphene, far beyond any other semiconductors, makes it an ideal channel material for the development of high-speed field-effect transistors [4]. On the other hand, the strong electrical field effect of graphene can be implemented to realize reconfigurable electromagnetic (EM) devices [5; 6; 7].  
According to [PERSON]'s formula, the conductivity of graphene (\(\sigma_{s}\)), consisting of both intraband and interband terms, is calculated as [8]  
\[\sigma_{s}=\sigma_{intra}+\sigma_{inter}, \tag{1}\]  
where  
\[\sigma_{intra}=\frac{e^{2}k_{B}T}{\pi\hbar^{2}(j\omega-2\tau)}\times\left( \frac{|E_{F}|}{k_{B}T}+2\ln(e^{-\frac{E_{F}}{k_{B}T}}+1)\right), \tag{2}\]  
\[\sigma_{inter}=\frac{e^{2}}{4\pi\hbar}\times\ln\left(\frac{2|E_{F}|-(\omega-2j \Gamma)\,\hbar}{2|E_{F}|+(\omega-2j\Gamma)\,\hbar}\right). \tag{3}\]\(e\) is the elementary electron charge, \(k_{B}\) is the Boltzmann constant, \(T\) is the temperature, \(\hbar\) is the reduced Planck's constant, \(\omega\) is the angular frequency, \(\Gamma\) is the carrier scattering rate and \(E_{F}\) is the chemical potential. For frequency below 10 THz, the intraband term dominates, hence \(\sigma_{total}\approx\sigma_{intra}\). The chemical potential \(E_{F}\) can be tuned through chemical or electrostatic doping. The electrostatic doping is achieved by sandwiching a dielectric layer between graphene and a conductive (e.g., metal) electrode. When the bias voltage is applied between graphene and the electrode, the carriers (i.e., holes or electrons) are injected into (or extracted from) graphene, resulting in a varying \(\sigma_{s}\) against the variation of bias voltage. It is noted that a strong electric field in the range of V/nm is usually required in electrostatic doping, resulting in a dielectric layer with thickness varying from several to at most a few hundred nanometers under a practical bias voltage.  
Over the past decade, graphene-based waveguide modulators operating at optical frequencies have been reported [9; 10; 11]. In addition, graphene-based been-steering devices operating at mid-infrared frequency have also been proposed, demonstrating effective control over the reflection angle of the incident wave [12; 13]. Moreover, graphene and its derivatives such as reduced graphene oxide (rGO) have also been utilized along with other materials to realize EM absorbers with fixed wave absorption and operation frequencies [14; 15; 16; 17; 18; 19]. Meanwhile, graphene-based reconfigurable EM absorbers have also been proposed, paving the way for the development of smart EM absorbing materials. [20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31]. Generally, there are two types of graphene EM absorbers, namely, quarter-wavelength absorber and metasurface absorber. As they exhibit different EM absorption performance, the graphene-based quarter-wavelength and metasurface absorbers are introduced separately in this work.