kdotp-symmetry

Official Resources

• Homepage: https://kdotp-symmetry.greschd.ch/
• GitHub: https://github.com/greschd/kdotp-symmetry
• Documentation: https://kdotp-symmetry.greschd.ch/
• PyPI: https://pypi.org/project/kdotp-symmetry/
• Publication: D. Gresch et al., Phys. Rev. Materials 2, 103805 (2018)
• License: Apache License 2.0

Overview

kdotp-symmetry is a Python tool for calculating the general form of a k·p Hamiltonian under given symmetry constraints. It automatically derives the allowed terms in an effective Hamiltonian near a high-symmetry k-point by analyzing the little group symmetry operations and basis function transformations.

Scientific domain: k·p perturbation theory, effective mass theory, band structure modeling Target user community: Researchers developing effective models for semiconductors and topological materials

Theoretical Methods

• k·p perturbation theory
• Little group symmetry analysis
• Invariant theory for Hamiltonians
• Representation theory
• Löwdin partitioning basis

Capabilities (CRITICAL)

• Symmetry-constrained k·p: Derive allowed Hamiltonian terms
• Arbitrary Order: k-expansion to any order
• General Symmetries: Works with any little group
• Basis Functions: Custom orbital/spin basis support
• Spin-Orbit Coupling: SOC-compatible formulation
• Symbolic Output: Mathematica-compatible expressions

Sources: kdotp-symmetry documentation, Phys. Rev. Materials publication

Key Strengths

Automatic Derivation:

• No manual symmetry analysis needed
• Systematic term generation
• Complete basis for allowed terms
• Verified by symmetry

Flexible Framework:

• Any little group
• Arbitrary k-expansion order
• Custom basis functions
• SOC inclusion

Integration:

• Works with Z2Pack
• TBmodels compatible
• Symbolic output
• Python ecosystem

Inputs & Outputs

• Input formats:

  • Symmetry operations (rotation matrices)
  • Basis function representations
  • Expansion order specification

• Output data types:

  • Symbolic Hamiltonian terms
  • Coefficient matrices
  • Basis function list
  • Mathematica expressions

Installation

pip install kdotp-symmetry

Usage Examples

import kdotp_symmetry as kp
import numpy as np

# Define symmetry operations (e.g., C3 rotation)
symmetries = [
    kp.SymmetryOperation(
        rotation_matrix=np.array([[0, -1, 0], [1, -1, 0], [0, 0, 1]]),
        repr_matrix=np.array([[np.exp(-1j*np.pi/3), 0], [0, np.exp(1j*np.pi/3)]])
    )
]

# Generate k.p Hamiltonian to second order
basis = kp.monomial_basis(dim=2)  # 2D k-space
hamiltonian = kp.symmetric_hamiltonian(
    symmetries=symmetries,
    kp_variable='k',
    order=2
)
print(hamiltonian)

Performance Characteristics

• Speed: Fast symbolic computation
• Accuracy: Exact symmetry constraints
• Scalability: Higher orders computationally heavier

Limitations & Known Constraints

• Symbolic focus: Not for numerical band structure
• Input format: Requires explicit symmetry matrices
• Learning curve: Representation theory knowledge helpful

Comparison with Other Tools

• vs kdotp-generator: kdotp-symmetry original, kdotp-generator extends
• vs MagneticKP: kdotp-symmetry non-magnetic focus
• vs manual derivation: Automated and systematic
• Unique strength: Rigorous symmetry-based k·p derivation

Application Areas

• Semiconductor effective mass models
• Topological semimetal models
• Weyl/Dirac point Hamiltonians
• Quantum well structures
• Band edge modeling

Best Practices

• Verify symmetry operation matrices
• Check basis function representations
• Validate against known models
• Use appropriate expansion order

Community and Support

• GitHub issue tracker
• Published methodology
• Z2Pack ecosystem

Verification & Sources

Primary sources:

1. GitHub: https://github.com/greschd/kdotp-symmetry
2. D. Gresch et al., Phys. Rev. Materials 2, 103805 (2018)

Confidence: VERIFIED - Published in Phys. Rev. Materials

Verification status: ✅ VERIFIED

• Official homepage: ACCESSIBLE
• Documentation: COMPREHENSIVE
• Source code: OPEN (GitHub, Apache-2.0)
• Academic citations: Phys. Rev. Materials
• Active development: Maintained