Practical band interpolation with a modified tight-binding method.

Area of Science:

• Condensed matter physics
• Materials science
• Computational materials science

Background:

• Accurate calculation of electronic band structures is crucial for understanding material properties.
• Traditional methods for dense k-point sampling can be computationally expensive.

Purpose of the Study:

• To develop a computationally efficient scheme for interpolating crystal energy bands.
• To enable fast and accurate determination of Hamiltonians and overlap matrices at arbitrary k-points.

Main Methods:

• Combining pseudopotential plane-wave calculations with a modified tight-binding Hamiltonian approach.
• Utilizing matrix manipulation to integrate plane-wave eigenvalues into the tight-binding framework.
• Employing three-dimensional Fourier interpolation for Hamiltonians and overlap matrices.

Main Results:

• A scheme that generates modified tight-binding Hamiltonians on a coarse k-point grid.
• Fast and accurate interpolation of Hamiltonians and overlap matrices to arbitrary k-points.
• Successful application to density functional calculations for germanium, graphite, graphene, copper, and SiGe superlattices.

Conclusions:

• The presented method offers a significant speed-up for electronic band structure calculations.
• This approach provides an accurate alternative for interpolating crystal energy bands.
• The scheme is versatile and applicable to a range of crystalline materials.