Abstract
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.
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