Abstract:This is the last paper in a series of three in which we have studied the Peierls substitution in the case of a weak magnetic field. Here we deal with two $2d$ Bloch eigenvalues which have a conical crossing. It turns out that in the presence of an almost constant weak magnetic field, the spectrum near the crossing develops gaps which remind of the Landau levels of an effective mass-less magnetic Dirac operator.

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中文翻译：

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弱非恒定磁场中狄拉克型交叉点附近的光谱分析

摘要：这是我们研究弱磁场情况下的 Peierls 替代的三篇系列论文中的最后一篇。在这里，我们处理两个具有圆锥形交叉点的 $2d$ Bloch 特征值。事实证明，在几乎恒定的弱磁场存在的情况下，交叉点附近的光谱会产生间隙，这让人想起有效的无质量磁性狄拉克算子的朗道能级。

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