Local-gauge finite-element method for electron waves in magnetic fields.

Area of Science:

• Condensed matter physics
• Computational physics
• Materials science

Background:

• The finite-element method (FEM) is used to analyze electron wave transport in 2D systems under magnetic fields.
• Existing FEM formulations face challenges with accuracy in large systems and strong magnetic fields.
• Gauge selection in FEM can significantly impact numerical results.

Purpose of the Study:

• To identify limitations of conventional FEM for realistic 2D electron systems in magnetic fields.
• To propose a novel FEM formulation that addresses convergence issues.
• To demonstrate the improved accuracy and efficiency of the new formulation.

Main Methods:

• Conventional finite-element method (FEM) formulations.
• A new FEM formulation incorporating the Peierls phase into matrix elements.
• Numerical simulations of electron transport properties.

Main Results:

• Conventional FEM formulations yield inaccurate results for large systems and strong magnetic fields.
• The choice of gauge significantly affects numerical outcomes in standard FEM.
• The proposed FEM formulation with the Peierls phase demonstrates improved convergence and accuracy.

Conclusions:

• A novel, conceptually different FEM formulation enhances the analysis of electron transport in 2D systems.
• The Peierls phase incorporation offers a solution to the poor convergence problem in FEM.
• This improved FEM is suitable for analyzing realistic systems under magnetic fields.