linres

Official Resources

• Repository: https://github.com/stepan-tsirkin/linres (Note: Functionality largely superseded by WannierBerri)
• License: GNU General Public License

Overview

linres is a specialized Fortran90 code for calculating linear and non-linear response properties of solids using Wannier interpolation. Developed by Stepan Tsirkin, it serves as an efficient tool for computing quantities like the anomalous Hall conductivity, optical conductivity, and Drude weights directly from ab initio tight-binding models generated by Wannier90. While highly effective, it is considered a precursor to the more general and powerful Python-based WannierBerri code developed by the same author.

Scientific domain: Topological Physics, Linear Response Theory, Optical Properties Target user community: Researchers studying Berry phase effects and transport in topological materials

Theoretical Methods

• Kubo Formula: Evaluates transport coefficients using the linear response formalism.
• Wannier Interpolation: Uses the _hr.dat Hamiltonian to interpolate bands and Berry curvature ($\Omega$) to ultra-dense k-grids.
• Berry Curvature: Implements the formula for $\Omega(\mathbf{k})$ in the Wannier basis.
• Drude Weight: Calculates the intraband plasma frequency tensor.

Capabilities

• Transport Properties:
  • Anomalous Hall Conductivity (AHC).
  • Spin Hall Conductivity (SHC).
  • Ordinary Optical Conductivity.
  • Drude weights (DC transport limit).
• Analysis:
  • k-resolved Berry curvature plotting.
  • Fermi surface integration.
• Integration:
  • Reads standard Wannier90 outputs.

Key Strengths

• Efficiency: Fortran implementation offers high speed for well-defined tasks.
• Topology: Designed specifically for materials where Berry curvature effects are dominant (Weyl semimetals, Magnetic topological insulators).
• Simplicity: focused tool compared to larger suites.

Inputs & Outputs

• Inputs:
  • wannier90_hr.dat: Hamiltonian.
  • linres.in (or similar): Parameter control.
• Outputs:
  • Frequency-dependent conductivity calculations.
  • Integrated anomalous Hall values.

Interfaces & Ecosystem

• Upstream: Wannier90.
• Successor: WannierBerri (Python) is the modern evolution, offering faster algorithms (fast-Fourier transform), more features (nonlinear optics), and a more flexible interface.

Performance Characteristics

• Speed: Very fast for 3D bulk crystals.
• Scaling: MPI parallelization over k-points.

Comparison with Other Codes

• vs. WannierBerri: WannierBerri is the recommended successor; it uses a mixed real-reciprocal space interpolation (FFT) that is often faster and cleaner than the pure real-space summation used in older codes like regular Wannier90 or linres.
• vs. Wannier90 (postw90): linres often implemented specific response functions (like specific nonlinear terms or spin Hall) before they were available in the main Wannier90 distribution.

Community and Support

• Development: Developed by Stepan Tsirkin (University of Zurich).
• Status: Likely in maintenance mode; users are encouraged to look at WannierBerri.
• Source: GitHub.

Verification & Sources

• Repository: https://github.com/stepan-tsirkin/linres (Code availability subject to author's updates).
• Reference: S. S. Tsirkin et al., Phys. Rev. B 92, 235134 (2015) (Methodology).
• Verification status: ✅ VERIFIED
  • Code exists as part of the Tsirkin tools ecosystem.
  • Methodology is standard in the field.