In this work the role of magnetic Landau quantization in the dynamics and spectrum of Diced Lattice charge carriers is studied in terms of the associated pseudospin 1 Green function. The equations of motion for the 9 matrix elements of this Green function are formulated in position/frequency representation and are solved explicitly in terms of a closed form integral representation involving only elementary functions. The latter is subsequently expanded in a Laguerre eigenfunction series whose frequency poles identify the discretized energy spectrum for the Landau quantized Diced Lattice as ε_(n) = ±√(2(2n + 1)α²eB) (α√(2) is the characteristic speed for the Diced Lattice), which differs significantly from the non-relativistic linear dependence of ε_(n) on B, and is similar to the corresponding √(B)-dependence of other Dirac materials (Graphene, Group VI Dichalcogenides).

中文翻译：

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切块晶格的朗道量化动力学和谱

在这项工作中，根据相关的赝自旋 1 格林函数研究了磁性朗道量子化在切块晶格电荷载流子的动力学和光谱中的作用。该格林函数的 9 个矩阵元素的运动方程以位置/频率表示形式表达，并根据仅涉及初等函数的封闭形式积分表示形式明确求解。后者随后在 Laguerre 特征函数系列中扩展，其频率极点将 Landau 量化分块晶格的离散能谱标识为 ε_(n) = ±√(2(2n + 1)α²eB) （α√(2) 是特征切点晶格的速度），这与 ε_(n) 对 B 的非相对论线性相关性显着不同，并且类似于其他 Dirac 材料（石墨烯，