Local Gauge Finite Element Method for Electron Waves in Magnetic Fields
Local Gauge Finite Element Method for Electron Waves in Magnetic Fields
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磁场中电子波的局域规范有限元法
DOI：
10.1103/physreve.86.026707
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
Tsuyoshi Ueta and Yuu Miyagawa
中科院分区：
文献类型：
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作者：
奥野智貴;植田 毅;西村直志;Tsuyoshi Ueta and Yuu Miyagawa
有限元法已被推广到分析磁场中二维电子系统的电子波输运性质。虽然许多研究人员已经创建了新的公式或改进这种方法，很少有人分析这种方法是如何应用到现实系统。本文认为，传统的公式的有限元法不给大系统或强磁场的准确结果，此外，它表明，所选的规范显着影响的数值结果。此外，本文提出了一个概念上不同的制定解决收敛性差的问题的有限元。这个公式很简单：在没有磁场的情况下，矩阵元素乘以Peierls相位。为了显示这种提法的优点，数值例子。
The finite-element method (FEM) has already been extended to analyze transport properties of electron waves of two-dimensional electron systems in magnetic fields. Although many researchers have created new formulations or improvements to this method, few have analyzed how this method is applied to realistic systems. The present paper suggests that conventional formulations of the FEM do not give accurate results for large systems or for strong magnetic fields; in addition, it suggests that the selected gauge significantly influences the numerical results. Furthermore, this paper proposes a conceptually different formulation of the FEM that solves the poor convergence problem. This formulation is simple: matrix elements are multiplied by the Peierls phase in the absence of a magnetic field. To show the advantages of this formulation, numerical examples are presented.