此論文主要以緊束模型研究單層石墨在外加均勻和調制磁場共存的磁光學性質。單層石墨在均勻磁場之下存在著高簡併態的藍道能階。這些能階為完全平坦的能帶，態密度顯現出強烈的對稱峰結構，表現出零維系統特徵。藍道能階擁有特殊的空間對稱波函數，這些波函數為一維諧振子的解。均勻磁場下的單層石墨在光學吸收譜上呈現許多顯著的對稱吸收峰，且這些吸收峰擁有單一特定的光學選擇定則，這些定則已經被實驗所證實。而在調制磁場加入之後，藍道能階將以原本的能量為中心點分裂為成對的拋物線能帶。每條拋物線能帶具有一個新的邊界態，這些邊界態在態密度上表現出顯著的不對稱尖峰。此外，態密度也呈現出特別的雙峰結構，這是由於成對的邊界態所引起。這些不對稱峰為一維系統的特徵。換句話說，原本在均勻磁場下具有零維特徵的系統，其有效維度因調制磁場而提升。除了能帶特徵改變之外，波函數的對稱性也預期將會受到影響。由於光吸收譜的特性主要決定於波函數的特徵，所以我們也預測它會受到調制磁場強烈影響，包含吸收峰的頻率改變以及光學選擇律的消失等。這些理論上的預測可以經由光學實驗的量測得到驗證。

This work studies the magneto-optical properties of monolayer graphene under the influence of both uniform and modulated magnetic fields using the tight-binding model. In the presence of uniform magnetic fields, graphene displays the Landau energy levels of high degeneracy. These purely plat bands result in the significant structure of symmetric peaks, exhibiting features of the zero-dimensional systems. These Landau levels correspond to the symmetric wave functions of one-dimensional oscillators. A great number of pronounced symmetric peaks exist in the optical absorption spectrum when applying uniform magnetic fields to graphene. According to our calculations, these peaks obey one specific selection rule, which has been confirmed by experiments. When modulated magnetic fields are exerted along with uniform ones, the Landau levels will split into pairs of parabolic bands centered around the original energy levels. Each parabolic band possesses a new band-edge state contributing to the prominent asymmetric peaks in the DOS. Moreover, the twin-peak structures in the DOS owes to the band-edge-state pairs. The asymmetric peaks characterize the one-dimensional system. In other words, the effective dimension of the system with zero-dimensional features will increase due to modulated fields. In addition to the energy bands, the symmetry of wave functions is also expected to be influenced. The optical absorption spectra are mainly decided by the features of wave functions and therefore are strongly affected by magnetic fields, including the frequencies of absorption peaks and the disappearance of optical selection rules. These predictions can be verified through optical measurements.

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