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Complex band structure with non-orthogonal basis set: analytical properties and implementation in the SIESTA code.

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  • 1School of Physics and CRANN, Trinity College, College Green, Dublin 2, Ireland.

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|December 8, 2021
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Summary

This study extends the transfer matrix method to compute complex band structures (CBS) in materials with non-orthogonal atomic basis sets. It identifies and analyzes spurious features arising from overlap matrices, offering a new computational tool for materials science.

Keywords:
complex band structuredensity functional theorynon-orthogonal basis sets

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Area of Science:

  • Condensed matter physics
  • Materials science
  • Computational materials science

Background:

  • Complex band structure (CBS) is crucial for understanding materials with broken periodicity, such as surfaces, interfaces, and defects.
  • CBS aids in interpreting electronic transport calculations and studying topological materials.
  • Existing methods for computing CBS often assume orthogonal atomic basis sets.

Purpose of the Study:

  • To extend the transfer matrix method for computing CBS in systems with non-orthogonal atomic basis sets.
  • To identify and characterize spurious features in the analytic continuation of band structures due to non-orthogonality.
  • To develop a practical computational tool for extracting CBS from density functional theory calculations.

Main Methods:

  • Extension of the transfer matrix method to handle non-orthogonal atomic basis sets.
  • Numerical and analytical investigation of spurious features in the complex band structure.
  • Development of a post-processing tool for density functional theory (DFT) calculations.

Main Results:

  • Demonstrated the appearance of spurious features in CBS when using non-orthogonal basis sets.
  • Characterized the properties of these spurious features both numerically and analytically.
  • Presented a numerical implementation for extracting CBS from DFT calculations.

Conclusions:

  • The transfer matrix method can be adapted for non-orthogonal basis sets, but requires careful handling of spurious features.
  • The developed tool facilitates high-throughput studies of complex band structures in insulators and semiconductors.
  • This work provides a valuable method for analyzing electronic properties in a wider range of materials.