SlateKoster

Official Resources

• Homepage: https://tight-binding.com/ (TBStudio)
• Source Repository: https://github.com/mohammadnakhaee/tbstudio
• Documentation: https://tight-binding.com/tutorials
• License: TBStudio: Free for academic use; tightbinder: GPL v3

Overview

SlateKoster tools encompass software packages for constructing tight-binding (TB) models using the Slater-Koster approximation, which expresses Hamiltonian and overlap matrix elements between atomic orbitals as products of radial functions and angular-dependent Slater-Koster coefficients. These tools enable the generation of TB Hamiltonians from first-principles calculations for electronic structure studies of nano-scale materials.

Key implementations include TBStudio, a cross-platform GUI application that constructs TB models using the Slater-Koster approach with nonlinear fitting to reproduce first-principles data, and tightbinder, a Python library for electronic structure calculations based on Slater-Koster tight-binding models. TBStudio supports s, p, and d orbitals with or without spin-orbit coupling and can generate code in C++, C, Fortran, Mathematica, Matlab, and Python. The tightbinder library provides tools to build, modify, and characterize crystalline or disordered materials with SK models up to d orbitals.

Scientific domain: Tight-binding methods, electronic structure, nanoscale materials
Target user community: Computational physicists and materials scientists using tight-binding models

Theoretical Methods

• Slater-Koster two-center approximation
• Linear combination of atomic orbitals (LCAO)
• Nonlinear fitting to first-principles band structures
• Orthogonal and non-orthogonal basis sets
• Spin-orbit coupling in tight-binding
• Levenberg-Marquardt and genetic algorithm fitting
• Scaling factors for distance-dependent hopping

Capabilities (CRITICAL)

• Construction of Slater-Koster tight-binding Hamiltonians
• Fitting to first-principles (DFT) band structures
• Support for s, p, and d orbitals
• Spin-orbit coupling support
• Orthogonal and non-orthogonal basis sets
• Code generation in multiple languages (C++, C, Fortran, Matlab, Python, Mathematica)
• Amorphous material modeling with modified hoppings
• Predefined models (Haldane, BHZ) and custom model support
• Berry phase quantities (Berry curvature, Zak phase, Z2 index, Chern number)

Inputs & Outputs

Input formats:

• TBStudio: Model files (.tbm), first-principles band structure data
• tightbinder: Configuration files with SK parameters, crystal structure
• TBFIT: Input files with atomic/electronic configuration, target band structure

Output data types:

• Slater-Koster tight-binding parameters
• Tight-binding Hamiltonian and overlap matrices
• Generated code in multiple programming languages
• Band structures and density of states
• Berry phase related quantities

Interfaces & Ecosystem

• TBStudio: C++ with wxWidgets GUI, OpenGL, LAPACK
• tightbinder: Python (pip install tightbinder), GPL v3
• TBFIT: Fortran with MINPACK and PIKAIA libraries
• First-principles interfaces: OpenMX, VASP output compatibility
• Platforms: Cross-platform (TBStudio); Python packages for tightbinder

Limitations & Known Constraints

• Two-center approximation neglects three-center integrals
• Fitting quality depends on choice of reference systems and orbitals
• Transferability limited to chemical environments similar to fitting data
• SK parameter sets are system-specific
• GUI tools may have platform dependencies

Performance Characteristics

• Fitting algorithms converge in minutes to hours depending on system complexity
• TB Hamiltonian evaluation is extremely fast (much faster than DFT)
• Code generation enables efficient downstream calculations
• Python library suitable for moderate system sizes

Comparison with Other Codes

• vs Wannier90: Wannier90 uses maximally localized Wannier functions; SlateKoster tools use SK parameterization
• vs TBmodels: TBmodels works with Wannier function output; SK tools fit directly to band structure
• vs PythTB: PythTB is a simple TB toolkit; tightbinder offers SK fitting and more features

Best Practices

• Use sufficient k-point sampling in reference DFT calculations for accurate fitting
• Include enough orbitals to capture relevant physics (d orbitals for transition metals)
• Test transferability by comparing TB results with DFT for different configurations
• Use spin-orbit coupling for heavy elements
• Generate code in your preferred language for integration with existing workflows

Verification & Sources

Primary sources:

1. TBStudio website: https://tight-binding.com/
2. tightbinder GitHub: https://github.com/alejandrojuria/tightbinder
3. TBFIT GitHub: https://github.com/CaiCheng-sicnu/TBFIT
4. J.C. Slater and G.F. Koster, Phys. Rev. 94, 1498 (1954)

Confidence: VERIFIED - Multiple implementations with websites and GitHub repositories confirmed