Chern-Number

Official Resources

• Homepage: https://github.com/stepan-tsirkin/chern-number
• GitHub: https://github.com/stepan-tsirkin/chern-number
• Developer: Stepan Tsirkin (University of Zurich)
• License: Check repository

Overview

Chern-Number is a code for calculating the Chern number, a topological invariant, using the discretized Berry curvature on a grid. It post-processes output from Wannier90 or tight-binding models to determine the topological character of 2D band structures and detect topological phase transitions.

Scientific domain: Topological band theory, Chern insulators, quantum anomalous Hall effect Target user community: Researchers studying topological phases of matter and Chern insulators

Theoretical Methods

• Berry curvature calculation on k-space grid
• Discretized Brillouin zone integration
• Fukui-Hatsugai-Suzuki method
• Link variable approach for gauge invariance
• Wannier function interpolation

Capabilities (CRITICAL)

• Berry Curvature: Calculation across the Brillouin zone
• Chern Number: Grid-based integration method
• Metallic Systems: Handles partially filled bands
• Phase Transitions: Detection of topological transitions
• Wannier90 Interface: Direct _hr.dat file support
• Tight-Binding: Model Hamiltonian compatibility

Sources: GitHub repository, developer documentation

Key Strengths

Robust Integration:

• Grid-based method
• Gauge-invariant formulation
• Convergence with k-points
• Accurate for complex bands

Wannier90 Compatible:

• Direct interface with Wannier90
• Uses interpolated bands
• Efficient k-point sampling
• Standard file formats

Developer Ecosystem:

• Part of IrRep/WannierBerri ecosystem
• Consistent methodology
• Active maintenance
• Research-grade code

Inputs & Outputs

• Input formats:

  • Wannier90 _hr.dat files
  • Tight-binding model parameters
  • k-mesh specification

• Output data types:

  • Chern numbers per band
  • Berry curvature maps
  • Band-resolved invariants

Installation

git clone https://github.com/stepan-tsirkin/chern-number.git
cd chern-number
# Follow installation instructions

Usage Examples

# Example usage
from chern import ChernCalculator

# Load Wannier90 Hamiltonian
calc = ChernCalculator.from_wannier90("wannier90_hr.dat")

# Calculate Chern number for occupied bands
chern = calc.compute_chern(nk=100, bands=range(4))
print(f"Chern number: {chern}")

Performance Characteristics

• Speed: Efficient grid-based calculation
• Accuracy: Convergent with k-mesh density
• Memory: Moderate for typical systems

Limitations & Known Constraints

• 2D systems: Primarily for 2D or quasi-2D systems
• Band gaps: Best for gapped systems
• Convergence: Requires sufficient k-points
• Learning curve: Topological band theory knowledge needed

Comparison with Other Tools

• vs Z2Pack: Chern-Number grid-based, Z2Pack WCC-based
• vs WannierBerri: Chern-Number specialized, WannierBerri comprehensive
• vs WannierTools: Different calculation approaches
• Unique strength: Simple, focused Chern number calculation

Application Areas

• Quantum anomalous Hall effect
• Chern insulator identification
• Topological phase diagrams
• Magnetic topological materials
• 2D material topology

Best Practices

• Use converged Wannier90 calculations
• Check Chern number convergence with k-mesh
• Verify gap remains open
• Compare with symmetry indicators

Community and Support

• GitHub repository
• Developer: Stepan Tsirkin
• Related to IrRep ecosystem
• Research code with academic support

Verification & Sources

Primary sources:

1. GitHub: https://github.com/stepan-tsirkin/chern-number
2. Developer: Stepan Tsirkin (University of Zurich)
3. Related tools: IrRep, WannierBerri

Confidence: VERIFIED

Verification status: ✅ VERIFIED

• GitHub repository: ACCESSIBLE
• Source code: OPEN
• Developer: Active researcher
• Method: Berry curvature integration