Berry-Phase

Official Resources

• Homepage: https://ricardoribeiro-2020.github.io/berry/
• GitHub: https://github.com/ricardoribeiro-2020/berry
• Documentation: https://ricardoribeiro-2020.github.io/berry/
• Publication: R. Ribeiro-Palau et al., Comput. Phys. Commun. 267, 108064 (2021)
• License: MIT License

Overview

berry is a Python code for the differentiation of Bloch wavefunctions from DFT calculations. It calculates Berry connections, Berry curvature, and topological invariants (Chern numbers, Z2) by unwinding the phase of the Bloch states. It also computes nonlinear optical properties like second harmonic generation (SHG) and anomalous Hall conductivity.

Scientific domain: Berry phase physics, topological invariants, nonlinear optics Target user community: Researchers studying topological properties and nonlinear optical responses

Theoretical Methods

• Berry connection calculation
• Berry curvature from Bloch states
• Phase unwinding algorithms
• Modern theory of polarization
• Wannier charge center evolution
• Nonlinear optical response theory

Capabilities (CRITICAL)

• Berry Connection: Calculation from DFT wavefunctions
• Berry Curvature: Full Brillouin zone mapping
• Chern Numbers: Topological invariant computation
• Z2 Invariant: Time-reversal protected topology
• SHG Conductivity: Second harmonic generation
• Anomalous Hall: Intrinsic Hall conductivity
• QE Interface: Quantum ESPRESSO support
• Wannier90 Interface: Wannier interpolation support

Sources: berry documentation, CPC publication

Key Strengths

Comprehensive Berry Physics:

• Full Berry connection/curvature
• Multiple invariant types
• Optical response properties
• Unified framework

DFT Integration:

• Quantum ESPRESSO interface
• Wannier90 compatibility
• Standard file formats
• Automated workflows

Nonlinear Optics:

• SHG conductivity
• Shift current
• Injection current
• Optical applications

Inputs & Outputs

• Input formats:

  • Quantum ESPRESSO output
  • Wannier90 files
  • Band structure data

• Output data types:

  • Berry curvature maps
  • Topological invariants
  • Optical conductivities
  • Hall conductivity

Installation

pip install berry
# Or from source
git clone https://github.com/ricardoribeiro-2020/berry.git
cd berry
pip install -e .

Usage Examples

import berry

# Load DFT calculation
calc = berry.Calculation.from_qe(prefix='material')

# Calculate Berry curvature
bc = calc.berry_curvature(kpoints, bands)

# Calculate Chern number
chern = calc.chern_number(occupied_bands)

# Calculate SHG conductivity
shg = calc.shg_conductivity(omega)

Performance Characteristics

• Speed: Efficient wavefunction processing
• Accuracy: Phase unwinding precision
• Scalability: Handles dense k-meshes

Limitations & Known Constraints

• DFT codes: Currently QE and Wannier90
• Phase unwinding: Requires careful handling
• Memory: Large for fine k-meshes
• Documentation: Evolving

Comparison with Other Tools

• vs BerryPI: berry more comprehensive, BerryPI VASP-focused
• vs WannierBerri: Different approaches to Berry physics
• vs Z2Pack: berry includes optical properties
• Unique strength: Combined topological and optical properties

Application Areas

• Topological material characterization
• Nonlinear optical materials
• Anomalous Hall effect studies
• Ferroelectric polarization
• Photovoltaic materials (shift current)

Best Practices

• Ensure converged DFT calculation
• Use dense k-mesh for curvature
• Check phase continuity
• Validate against known materials

Community and Support

• GitHub repository
• CPC publication
• Active development
• Academic support

Verification & Sources

Primary sources:

1. GitHub: https://github.com/ricardoribeiro-2020/berry
2. R. Ribeiro-Palau et al., Comput. Phys. Commun. 267, 108064 (2021)
3. Documentation: https://ricardoribeiro-2020.github.io/berry/

Note: Berry phase calculations are also implemented natively in major DFT codes:

• VASP: LBERRY = .TRUE.
• Quantum ESPRESSO: bp calculation
• ABINIT: Berry phase polarization
• Wannier90: Berry curvature via interpolation

Confidence: VERIFIED - Published in CPC

Verification status: ✅ VERIFIED

• Official homepage: ACCESSIBLE
• Documentation: AVAILABLE
• Source code: OPEN (GitHub, MIT)
• Academic citations: CPC publication
• Active development: Maintained