Official Resources
- Homepage: https://github.com/ricardoribeiro-2020/berry
- Repository: https://github.com/ricardoribeiro-2020/berry
- License: MIT License
Overview
Berry is a Python package designed to calculate the Berry phase, Berry curvature, and related topological properties of crystalline materials directly from Density Functional Theory (DFT) wavefunctions, without relying on Maximally Localized Wannier Functions (MLWFs). It specifically interfaces with Quantum ESPRESSO to extract Bloch states and compute topological invariants and optical responses, such as the Anomalous Hall Conductivity (AHC) and Circular Dichroism.
Scientific domain: Topological Physics, Non-linear Optics
Target user community: DFT users studying topology and optical responses
Theoretical Methods
- Berry Connection & Curvature: Direct calculation using finite differences of Bloch states in k-space.
- Wavefunction Gauge: Uses graph-based or AI-enhanced algorithms to ensure smooth gauge choices across the Brillouin Zone.
- Optical Response:
- Anomalous Hall Conductivity (linear response).
- Circular Dichroism (differential absorption of polarized light).
- Second Harmonic Generation (SHG) ($\chi^{(2)}$ tensor).
Capabilities
- DFT Interface:
- Reads Quantum ESPRESSO
save directories and XML files.
- Handles spinor wavefunctions (SOC).
- Calculations:
- Berry curvature vectors $\mathbf{\Omega}(\mathbf{k})$.
- Chern numbers of 2D planes.
- Optical conductivity spectra $\sigma_{\alpha\beta}(\omega)$.
- SHG susceptibility tensor.
- Tools:
- Band unfolding for supercells.
- Visualization of curvature fields.
Key Strengths
- Direct Basis: By working directly with DFT wavefunctions, it avoids potential artifacts or loss of information associated with Wannierization, especially for entangled bands where Wannier projection is difficult.
- Optical Focus: Specialized modules for Circular Dichroism and SHG make it unique among topological tools, which often focus only on static invariants.
- Gauge Fixing: Implements robust algorithms to handle the "random gauge" problem inherent in DFT codes, essential for numerical differentiation.
Inputs & Outputs
- Inputs:
- Quantum ESPRESSO output (
prefix.save, wfc files).
- Python configuration script.
- Outputs:
- NumPy arrays of curvature and conductivity.
- Plots of 2D/3D curvature distribution.
Interfaces & Ecosystem
- Upstream: Quantum ESPRESSO.
- Dependencies: NumPy, SciPy.
Performance Characteristics
- Memory: High. Processing full DFT wavefunctions requires significant RAM compared to tight-binding models.
- Connectivty: Requires dense k-grids in the DFT step for accurate derivatives.
Comparison with Other Codes
- vs. Wannier90: Wannier90 interpolates bands to ultra-dense grids cheaply. Berry works on the original grid (or requires a dense DFT run), which is more expensive but stays "closer to the truth" of the DFT basis.
- vs. Yambo: Yambo is a full Many-Body/Optics code. Berry is a lighter, specialized tool for topological optics.
Application Areas
- Chiral Semimetals: Calculating circular dichroism in enantiomorphic crystals.
- Magnetic Topology: AHC in ferromagnetic Weyl semimetals.
Community and Support
- Development: Ricardo Mendes Ribeiro (University of Minho).
- Source: GitHub.
Verification & Sources