Official Resources
- Homepage: https://z2pack.ethz.ch/
- Documentation: https://z2pack.greschd.ch/
- Repository: https://github.com/Z2PackDev/Z2Pack
- License: GPL-3.0
Overview
Z2Pack is the premier tool for the automated calculation of topological invariants and Berry phases. Developed at ETH Zurich, it implements the Wilson Loop and Wannier Charge Center (WCC) tracking methods to calculate $\mathbb{Z}_2$ invariants, Chern numbers, and Weyl point chiralities without the need for manual inspection or gauge fixing. It interfaces seamlessly with both tight-binding models (via TBmodels) and ab-initio codes (VASP, Quantum ESPRESSO, Wannier90).
Scientific domain: Topological Classification, Berry Phase
Target user community: Theorists and computational researchers characterizing topological matter
Theoretical Methods
- Wilson Loops: Non-Abelian Berry phase over a closed k-path.
- Wannier Charge Centers (WCC): Hybrid Wannier function centers $\bar{x}(k_y, k_z)$.
- $\mathbb{Z}_2$ Invariant: Tracking the flow of WCCs (time-reversal polarization pumping).
- Chern Number: Winding of WCCs over the BZ.
- Surface Green's Functions: Iterative renormalization (via surface module).
Capabilities
- Invariants:
- $\mathbb{Z}_2$ indices (3D TI, 2D QSH).
- Chern Numbers (QAH, Weyl Chirality).
- Methods:
- Automated convergence of Wilson loops (adaptive grid).
- Surface States spectral function.
- Integration:
- FP (First Principles): VASP, QE, Abinit.
- TB (Tight Binding): TBmodels, PythTB.
Key Strengths
- Automation: Z2Pack's "Surface" tracking algorithm adaptively adds k-points where the Berry curvature is high (e.g., near gap closings), ensuring integer convergence of topological numbers without wasting resources on trivial parts of the BZ.
- Rigorousness: Unlike parity-based indicators (which fail without inversion symmetry), Z2Pack calculates the invariant directly from the Berry phase evolution, making it valid for any symmetry class (including generic Weyl semimetals).
- Visualization: Built-in plots for WCC evolution lines are publication-ready and crucial for debugging topological calculations.
Inputs & Outputs
- Inputs:
- System definitions (Python scripts).
- DFT output files or TB model files.
- Outputs:
result.json (numerical invariants).- Plots of WCC flow.
Interfaces & Ecosystem
- TBmodels: Tight coupling; models generated in TBmodels flow directly into Z2Pack.
- VASP: Specialized interface (
vasp.py) to drive VASP calculations automatically.
Performance Characteristics
- Efficiency: The adaptive algorithm is orders of magnitude more efficient than uniform grid integration for singular quantities (like Berry flux near a Weyl point).
- Cost: For DFT, cost is proportional to the number of SCF/Non-SCF calls triggered. For TB, it is very fast.
Comparison with Other Codes
- vs. WannierTools: WannierTools computes surface states (Green's functions) very well. Z2Pack computes the invariant number itself more rigorously (tracking WCC lines). They are complementary.
- vs. IrRep: IrRep is faster but restricted to symmetry-protected phases. Z2Pack solves the general case (no symmetry required).
Application Areas
- Weyl Semimetals: Determining the charge (chirality) of a node by enclosing it in a sphere.
- Topological Insulators: Confirming the non-trivial nature of Bi2Se3, inversion-asymmetric TIs.
Community and Support
- Development: Dominik Gresch (Microsoft Quantum / ETH Zurich Alumni).
- Source: GitHub.
Verification & Sources
- Primary Publication: D. Gresch et al., Phys. Rev. B 95, 075146 (2017).
- Verification status: ✅ VERIFIED
- The gold standard for numerical Z2 calculations.