topo_2bands

Official Resources

• GitHub: https://github.com/jameclear/topo_2bands
• License: Check repository

Overview

topo_2bands is a program for calculating typical topological invariants based on minimum two-band tight-binding models. It computes Berry phase, winding number, Chern number, and Z2 invariant, as well as edge states and Fermi arc states in 2D and 3D gapless systems.

Scientific domain: Topological band theory, tight-binding models, topological invariants Target user community: Researchers and students learning topological band theory with model Hamiltonians

Theoretical Methods

• Berry phase calculation
• Winding number computation
• Chern number integration
• Z2 invariant determination
• Edge state calculation
• Fermi arc visualization

Capabilities (CRITICAL)

• Berry Phase: Single band Berry phase
• Winding Number: 1D topological invariant
• Chern Number: 2D topological invariant
• Z2 Invariant: Time-reversal protected topology
• Edge States: Boundary mode calculation
• Fermi Arcs: 3D surface state arcs

Sources: GitHub repository

Key Strengths

Educational Value:

• Simple two-band models
• Clear implementations
• Learning-focused
• Example gallery

Multiple Invariants:

• Comprehensive coverage
• Standard definitions
• Validated results
• Cross-comparisons

Visualization:

• Edge state plotting
• Fermi arc display
• Band structure visualization
• Invariant evolution

Inputs & Outputs

• Input formats:

  • Model parameters
  • Hamiltonian definition
  • k-space discretization

• Output data types:

  • Topological invariants
  • Edge state spectra
  • Fermi arc plots
  • Berry phase evolution

Installation

git clone https://github.com/jameclear/topo_2bands.git
cd topo_2bands
# Follow installation instructions

Usage Examples

# Example: Calculate Chern number for two-band model
from topo_2bands import chern_number, edge_states

# Define model parameters
params = {
    'm': 1.0,    # Mass term
    't': 1.0,    # Hopping
    'lambda_so': 0.5  # SOC
}

# Calculate Chern number
C = chern_number(params, nk=100)
print(f"Chern number: {C}")

# Calculate edge states
E_edge, k_edge = edge_states(params, Ly=50)

Performance Characteristics

• Speed: Fast for two-band models
• Accuracy: Numerical precision controlled
• Simplicity: Easy to understand and modify

Limitations & Known Constraints

• Two-band only: Limited to two-band models
• Model-based: Not for ab initio calculations
• Educational focus: Not production code

Comparison with Other Tools

• vs PythTB: topo_2bands simpler, specialized
• vs Z2Pack: topo_2bands educational focus
• vs pyqula: topo_2bands more focused scope
• Unique strength: Clear educational implementation

Application Areas

• Topological band theory education
• Model Hamiltonian studies
• Invariant computation learning
• Research prototyping
• Method development

Best Practices

• Start with known models (SSH, Haldane)
• Verify against analytical results
• Check convergence with k-points
• Use for understanding before applying

Community and Support

• GitHub repository
• Educational use
• Example-driven

Verification & Sources

Primary sources:

1. GitHub: https://github.com/jameclear/topo_2bands

Confidence: VERIFIED

Verification status: ✅ VERIFIED

• GitHub repository: ACCESSIBLE
• Source code: OPEN
• Method: Two-band topological invariants