Hofstadter-type spectral diagrams for the Bloch electron in three dimensions
Hofstadter-type spectral diagrams for the Bloch electron in three dimensions
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布洛赫电子的霍夫施塔特型三维谱图
DOI：
10.1103/physrevb.69.033202
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发表时间：
2004
影响因子：
3.7
通讯作者：
V. Geyler
中科院分区：
文献类型：
--
作者：
J. Brüning;V. Demidov;V. Geyler
本文分析了均匀磁场中布洛赫电子精确三维哈密顿量的通量-能量图和角-能量图。的依赖关系的结构图上的方向的字段，的几何形状的布拉维晶格，和原子的数量在一个基本的细胞被认为是。数值结果表明，即使在立方晶格的情况下，角能图也可能具有分形结构。结果表明，忽略朗道带的耦合会显著改变图的形状。最低朗道带对应的霍尔电导率进行了简要讨论。
Flux-energy and angle-energy diagrams for an exact three-dimensional Hamiltonian of the Bloch electron in a uniform magnetic field are analyzed. The dependence of the structure of the diagrams on the direction of the field, the geometry of the Bravais lattice, and the number of atoms in an elementary cell is considered. Numerical evidence is given to show that the angle-energy diagram may have a fractal structure even in the case of a cubic lattice. It is shown that neglecting coupling of Landau bands changes considerably the shape of the diagrams. The Hall conductivity corresponding to the lowest Landau band is briefly discussed.