The modern theory of orbital magnetization (OM) was developed by using Wannier function method, which has a formalism similar with the Berry phase. In this manuscript, we perform a numerical study on the fate of the OM under disorder, by using this method on the Haldane model in two dimensions, which can be tuned between a normal insulator or a Chern insulator at half filling. The effects of increasing disorder on OM for both cases are simulated. Energy renormalization shifts are observed in the weak disorder regime and topologically trivial case, which was predicted by a self-consistent T-matrix approximation. Besides this, two other phenomena can be seen. One is the localization trend of the band orbital magnetization. The other is the remarkable contribution from topological chiral states arising from nonzero Chern number or large value of integrated Berry curvature. If the fermi energy is fixed at the gap center of the clean system, there is an enhancement of |M| at the intermediate disorder, for both cases of normal and Chern insulators, which can be attributed to the disorder induced topological metal state before localization.

中文翻译：

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二维轨道磁化无序的数值研究

现代轨道磁化（OM）理论是利用万尼尔函数方法发展起来的，其形式与贝里相类似。在这份手稿中，我们通过在二维霍尔丹模型上使用这种方法对无序状态下 OM 的命运进行了数值研究，该模型可以在正常绝缘体或半填充时的陈绝缘体之间进行调整。模拟了两种情况下增加的无序对 OM 的影响。在弱无序状态和拓扑微不足道的情况下观察到能量重整化转移，这是通过自洽 T 矩阵近似预测的。除此之外，还可以看到另外两个现象。一是能带轨道磁化的局域化趋势。另一个是由非零陈数或大值积分贝里曲率引起的拓扑手征状态的显着贡献。如果费米能量固定在清洁系统的间隙中心，则|M| 有增强。在中间无序时，对于正常和陈绝缘体的两种情况，这可归因于定位前无序诱导的拓扑金属状态。