Official Resources
- Homepage: https://sourceforge.net/projects/py-nodes/
- Repository: https://sourceforge.net/projects/py-nodes/
- License: GPL-3.0
Overview
PY-Nodes is a Python-based computational tool designed to automatically search for and classify band degeneracy points (nodes) in the Brillouin zone of topological semimetals. Specifically tailored for the all-electron DFT code WIEN2k, it uses a simplex optimization algorithm (Nelder-Mead) to minimize the energy gap function $\Delta E(\mathbf{k}) = |E_{n+1}(\mathbf{k}) - E_n(\mathbf{k})|$. This allows it to locate Weyl points, Dirac points, and nodal lines with high precision without computationally expensive dense grid scans.
Scientific domain: Topological Semimetals, Optimization
Target user community: WIEN2k users searching for Weyl points
Theoretical Methods
- Optimization: Nelder-Mead method to find local minima of the gap function.
- Topological Nodes:
- Weyl Points: Two-band crossings in 3D.
- Dirac Points: Four-band crossings (typically protected by symmetry).
- Nodal Lines: Continuous loops of degeneracy.
- DFT backend: WIEN2k (FLAPW method).
Capabilities
- Search:
- Automatic detection of gap closing points.
- Can trace nodal lines by following the degeneracy valley.
- Classification:
- Distinguishes between point nodes and lines based on the Hessian of the gap.
- precision: Finds coordinates to machine precision, unrestricted by a pre-defined k-mesh.
Key Strengths
- All-Electron Accuracy: By using WIEN2k, it is suitable for f-electron systems and heavy metals where pseudopotential errors might shift node positions.
- Efficiency: Much faster than grid-based methods ($O(N_{iter})$ vs $O(N_k^3)$), essential for searching the full 3D BZ.
- Automation: Can be scripted to scan multiple band pairs.
Inputs & Outputs
- Inputs:
- WIEN2k
case.energy files.
- Search configuration (start points, bands).
- Outputs:
- List of node coordinates ($k_x, k_y, k_z$) and residual gaps.
Interfaces & Ecosystem
- Upstream: WIEN2k.
- Dependencies: NumPy.
Performance Characteristics
- Speed: The search algorithm is very fast; the bottleneck is typically reading the initial DFT data or running the DFT steps if on-the-fly calculation is needed (optional workflow).
- Reliability: Requires reasonable starting guesses to avoid getting stuck in local (non-zero) minima.
Comparison with Other Codes
- vs. WannierTools: WannierTools finds nodes using a tight-binding model. PY-Nodes works directly with the DFT eigenvalues, avoiding Wannierization errors but limited by DFT cost if dynamic recalculation is needed.
- vs. IrRep: IrRep finds nodes at high symmetry points via representations. PY-Nodes searches for accidental crossings at generic k-points (Weyl points).
Application Areas
- Weyl Semimetals: TaAs, NbP.
- Nodal Line Semimetals: ZrSiS family.
Community and Support
- Development: V. Pandey and S.K. Pandey.
- Source: SourceForge.
Verification & Sources
- Primary Publication: V. Pandey et al., Comput. Phys. Comm. (2023).
- Verification status: ✅ VERIFIED