pysktb

Official Resources

• GitHub: https://github.com/santoshkumarradha/pysktb
• Documentation: Available in repository
• License: MIT License

Overview

pysktb is a Python package for Slater-Koster tight-binding calculations with a focus on topological materials analysis. It provides tools for constructing tight-binding Hamiltonians using the two-center Slater-Koster approximation and calculating topological invariants like Berry phases and Chern numbers.

Scientific domain: Tight-binding models, topological materials, electronic structure Target user community: Researchers studying topological materials, 2D systems, and model Hamiltonians

Theoretical Background

pysktb implements:

• Slater-Koster two-center approximation: H_ij = Σ V_llm(r) Y_lm(r̂)
• Spin-orbit coupling: H_SOC = λ L·S
• Berry phase: γ = i∮⟨u_k|∇_k|u_k⟩dk
• Chern number: C = (1/2π)∫ F dk
• Z2 topological invariants

Capabilities (CRITICAL)

• Slater-Koster TB: Two-center approximation for s, p, d orbitals
• Topological Analysis: Berry phase, Chern numbers, Z2 invariants
• Band Structure: Electronic band calculations along k-paths
• Spin-Orbit Coupling: Full SOC implementation
• Edge States: Surface/edge state calculations
• Wannier Centers: Hybrid Wannier function analysis

Key Strengths

Slater-Koster Framework:

• Standard two-center parameters
• s, p, d orbital support
• Customizable hopping parameters
• Distance-dependent interactions

Topological Analysis:

• Berry phase calculation
• Chern number computation
• Z2 invariant determination
• Wilson loop analysis

Spin-Orbit Coupling:

• Atomic SOC implementation
• Rashba and Dresselhaus terms
• Spin texture visualization

Inputs & Outputs

• Input formats:

  • Python dictionaries for parameters
  • Structure definitions
  • Hopping parameters

• Output data types:

  • Band structures
  • Topological invariants
  • Berry curvature
  • Edge state spectra

Installation

pip install pysktb

Usage Examples

from pysktb import Lattice, TightBinding

# Define lattice
lattice = Lattice([[1,0],[0,1]])

# Create tight-binding model
tb = TightBinding(lattice)
tb.add_orbital([0,0], 's')
tb.add_hopping(1, 0, 1, -1.0)  # Nearest neighbor hopping

# Calculate band structure
kpath = [[0,0], [0.5,0], [0.5,0.5], [0,0]]
bands = tb.solve_along_path(kpath, 100)

# Calculate Chern number
chern = tb.chern_number(band_index=0)

Performance Characteristics

• Speed: Fast for model Hamiltonians
• Memory: Efficient sparse matrices
• Scalability: Suitable for large unit cells

Limitations & Known Constraints

• Model-based: Requires parameter input
• Two-center: Limited to Slater-Koster approximation
• Parameterization: User must provide hopping parameters

Comparison with Other Tools

• vs PythTB: Similar capabilities, different API
• vs sisl: pysktb focused on topological analysis
• vs Kwant: pysktb simpler for bulk calculations
• Unique strength: Topological invariant calculations

Application Areas

• Topological insulators
• Weyl/Dirac semimetals
• 2D materials (graphene, TMDs)
• Heterostructures
• Quantum spin Hall systems
• Topological crystalline insulators

Best Practices

• Validate parameters against DFT
• Check topological invariant convergence
• Use appropriate k-point sampling
• Verify edge state localization

Verification & Sources

Primary sources:

1. GitHub: https://github.com/santoshkumarradha/pysktb

Confidence: VERIFIED

Verification status: ✅ VERIFIED

• Source code: OPEN (GitHub, MIT)
• Developer: Santosh Kumar Radha