Motivated by some earlier experimental observations on the magneto-optical absorption and cyclotron resonance in graphene, we carry out systematically a theoretical investigation of the magneto-optical absorption in graphene monolayer situated on a substrate. The effect of electron–impurity scattering is considered at low temperatures. The magneto-optical absorption coefficient (AC) is calculated using the perturbation theory taking account of both one– and two–photon absorption processes. Numerical results are obtained for the SiO₂, SiC, and h-BN substrates to compare and show effects of the substrate. There appear the cyclotron–impurity resonance peaks in the AC which show a blue-shift with increasing magnetic field strength. In general, the absorption intensity, the resonance energy and the FWHM depend strongly on the substrate. Also, the FWHM increases with increasing the impurity density by the law FWHM$=\beta \sqrt{n_i}$, where $\beta$ is a constant whose value is different in different substrates and $n_i$ the impurity density. In particular, the resonance energy versus magnetic field strength and the full width at half maximum (FWHM) for the SiO₂ substrate are in good agreement with those obtained by earlier experiments.

出于对石墨烯中磁光吸收和回旋加速器共振的一些较早实验观察的推动，我们系统地对位于基底上的石墨烯单层中的磁光吸收进行了理论研究。在低温下考虑了电子杂质散射的影响。磁光吸收系数（AC）是根据扰动理论计算的，同时考虑了一个和两个光子的吸收过程。获得了SiO _2的数值结果，SiC和h-BN基板进行比较并显示基板的效果。交流电中出现回旋加速器-杂质共振峰，随着磁场强度的增加，其出现蓝移。通常，吸收强度，共振能量和半高宽均强烈取决于基底。同样，随着定律FWHM的增加，FWHM随着杂质密度的增加而增加。$=\beta \sqrt{{ñ}_{\mathrm{一世}}}$，在哪里 $\beta$ 是一个常数，其值在不同的基质中不同，并且 ${ñ}_{\mathrm{一世}}$杂质密度。尤其是，SiO ₂衬底的共振能量对磁场强度以及半高全宽（FWHM）与通过早期实验获得的共振良好。