Perfectly matched layers for the Dirac equation in general electromagnetic texture.

Area of Science:

• Computational Physics
• Condensed Matter Physics
• Electromagnetism

Background:

• Simulating Dirac fermion systems requires effective boundary conditions to handle wave propagation.
• Traditional methods like the imaginary-potential method can suffer from back-reflection issues.

Purpose of the Study:

• To construct and implement Perfectly Matched Layer (PML) boundary conditions for the Dirac equation.
• To evaluate the performance of PML for electromagnetic potentials and finite-difference schemes.

Main Methods:

• Developed PML extension for the Dirac equation and staggered-grid finite-difference schemes.
• Computed PML auxiliary functions using Crank-Nicholson or integral solution methods.
• Analyzed stability conditions and spectral properties of the PML scheme.

Main Results:

• PML boundary conditions demonstrate effective damping of out-propagating waves.
• Numerical tests with topological insulator surface parameters show superior wave absorption compared to the imaginary-potential method.
• PML significantly suppresses back-reflection, even for time-dependent electromagnetic textures.

Conclusions:

• PML offers a robust and efficient approach for simulating wave phenomena in Dirac systems.
• The method is particularly advantageous for transient transport simulations due to its excellent absorption properties.