## 1 Introduction
During the reconstruction process, the electromagnetic properties of an antenna can be changed by applying the properties of the materials in the antenna structure (such as permeability, electric-magnetic field effects) with external control without adding any elements. These antenna structures are mostly used in the patch or substrate parts that make up the antennas. Graphene is a great material because it has excellent optical and electronic properties [25; 26; 27] and also because its resonance properties can be easily changed by applying an external voltage [28; 29; 30]. Using graphene provides a great advantage to antenna designs because it has an efficient dynamic tuning [31; 32]. The frequency-dependent surface conductivity of graphene can be easily changed by causing changes in its chemical potential due to applying a gate voltage. While this important feature of graphene provides an advantage in adjusting the resonance frequencies of antennas, this situation provides the chance to easily manufacture antennas that can be used, especially at microwave frequencies. The frequency-dependent two-dimensional surface conductivity of single-layer graphene is expressed by the Kubo formula (Equation (1)) [33]:  
\[\sigma(\omega,\mu_{c},\Gamma,\Upsilon)\approx-j\frac{q_{c}^{2}k_{B}\Upsilon}{ \pi\hbar^{2}(\omega-2j\Gamma)}\times\left(\frac{\mu_{c}}{k_{B}\Upsilon}+2 \ln(e^{-\frac{\kappa_{c}}{k_{B}\Upsilon}}+1)\right) \tag{1}\]  
\(\omega\): the angular frequency  
\(\mu_{c}\): the chemical potential  
\(\Gamma\): the scattering rate  
\(\Upsilon\): the temperature  
\(\tau\): the relaxation time  
\(k_{B}\): the Boltzmann  
\(\mu^{2}\): the reduced Planck constant. The effect of changing graphene's chemical potential (\(\mu_{c}\)) on the surface conductivity has been studied [34]. This effect varies depending on the carrier density, which can be controlled by gate voltage, electric bias field, or chemical doping. Increasing the chemical potential also causes an increase in graphene surface conductivity. In other words, this causes a shift in antenna resonances at higher frequencies. On the other hand, it allows the emergence of flexible antenna designs that can be changed by the shift in antenna resonance caused by the chemical potential change. The value in chemical potential can be controlled electrically by varying the gate voltage (\(V_{g}\)). The formula explaining this situation is given below (Equation (2)). Graphene conductivity ranges are given according to the relevant frequency bands in the study of [PERSON] et al. [34]. \[V_{g}=\left[\frac{q_{e}h_{c}^{2}h}{\pi\hbar^{2}v_{f}^{2}e_{0}e_{r}}\right] \tag{2}\]  
[PERSON] et al. give the real and imaginary values of the surface conductivity of graphene depending on the frequency for a changing chemical potential and a constant relaxation time at their study [33]. They show that the chemical potential and the conductivity change point are important parameters to adjust the resonance frequency. In a study [35], the antenna produced with graphene was compared with the other antennas with different metals instead of graphene. When the results are examined, it is seen that the reflection coefficients of the metal-based antenna are less adapted than the graphene. On the other hand, graphene performs better in terms of reflection coefficient, decreasing from \(-6.440\) to \(-15.125\) dB. Graphene shows better results than metal in terms of performance with a well-adapted resonance frequency. [PERSON] and [PERSON] [36] examined the \"Effect of Copper and Graphene Material Bow-tie Structured Antenna for 1.2 GHz Application.\" It is seen that graphene performs better in antennas, since its conductivity is much better than copper. In addition, resistance and stub-matching problems are significantly reduced compared to copper and offer better bandwidth. All these situations suggest that using graphene is more functionally effective than copper.