There are two absorption properties that are involved in light-graphene interaction, interband and intraband absorption for small signals. This is described by the complex conductivity, \[\sigma_g=\sigma_{intra}(\omega,\mu_c,\Gamma,T)+\sigma_{inter}(\omega,\mu_c,\Gamma,T)\], where \(\omega\) is the angular frequency of light, \(\mu_c\) is the chemical potential, \(\Gamma\) is scattering rate, and \(T\) is the temperature [1].Whats interesting is that the chemical potential can be tuned with electrical gating, thus the conductivity can be controlled by the same process. Chemical potential also controls what absorption process is occurring.Interband corresponding to absorption from the valence band to conduction band and intraband absoprtion corresponding to absoprtion from a semiconductor like optical property to a metal like optical property [2]. For incoming light with energy \(\hbar \omega\), interband absoprtion dominates when \(\mu_c < \frac{\hbar \omega}{2}\) and intraband dominates when \(\mu_c > \frac{\hbar \omega}{2}\) and it is theoretically predicted that intraband absoprtion would be dominate when \(\mu_c \approx \frac{\hbar \omega}{1.67}\) [2]. Zhaolin Lu et al investigates graphene conductivty at \(T=300 K\) with a scattering rate \(\hbar \Gamma=5 meV\). Figure 1 plots real and imaginary parts of conductivity vs chemical potential and the dielectric constant as a funciton of chemical potential. Notice the sensitivity of conductivity with little change in chemical potential. Here \(\epsilon_{eff}=1-\frac{\delta_g}{i\omega\epsilon_0\Delta}\) where \(\Delta=0.7 nm\) is the effective thickness of graphene. Notice the dip in in the magnitude of the effective dielectric constant, it is near zero at \(\mu_t\). Physically this is the marking of the transition from a dielectric type graphene to a metal type graphene. The transition chemical potential is \(\mu_t=0.515 eV\) for this experiment. Theoretical value from [1] predicts \(\mu_t=0.479 eV\) which has about 7 \(\%\) error. Since conductivity can be tuned by electrical gating so too can the effective dielectric constant.

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