HopTB.jl

**HopTB.jl** is a Julia package designed for constructing and analyzing tight-binding Hamiltonians, with a unique focus on **non-orthogonal bases**. It serves as a bridge between first-principles Density Functional Theory (DFT) codes and…

4. TIGHT-BINDING 4.2 Model Hamiltonians VERIFIED
Back to Mind Map Official Website

Overview

**HopTB.jl** is a Julia package designed for constructing and analyzing tight-binding Hamiltonians, with a unique focus on **non-orthogonal bases**. It serves as a bridge between first-principles Density Functional Theory (DFT) codes and model physics, allowing users to import Hamiltonians from **Wannier90**, **OpenMX**, and **FHI-aims**. Beyond standard band structures, HopTB.jl provides a powerful suite of tools for calculating linear and **non-linear response functions**, including optical co

Reference Papers

Reference papers are not yet linked for this code.

Full Documentation

Official Resources

  • Homepage: https://hoptb.github.io/HopTB.jl/dev/
  • Repository: https://github.com/HopTB/HopTB.jl
  • License: MIT License

Overview

HopTB.jl is a Julia package designed for constructing and analyzing tight-binding Hamiltonians, with a unique focus on non-orthogonal bases. It serves as a bridge between first-principles Density Functional Theory (DFT) codes and model physics, allowing users to import Hamiltonians from Wannier90, OpenMX, and FHI-aims. Beyond standard band structures, HopTB.jl provides a powerful suite of tools for calculating linear and non-linear response functions, including optical conductivity, Hall effects, and second harmonic generation.

Scientific domain: Theoretical Materials Science, Non-Linear Optics Target user community: Researchers bridging DFT and effective model calculations

Theoretical Methods

  • Tight-Binding: Supports both standard orthogonal ($S_{ij} = \delta_{ij}$) and generalized non-orthogonal ($S_{ij} \neq 0$) tight-binding models.
  • Linear Response: Kubo formula implementation for conductivity tensors.
  • Geometric Phase: Calculation of Berry curvature, Berry connection, and their dipole moments.
  • Non-Linear Optics:
    • Shift Current (bulk photovoltaic effect).
    • Second Harmonic Generation (SHG).
    • Injection Current.

Capabilities

  • Interfaces:
    • Read generic Wannier90 outputs (_hr.dat, .win).
    • Read OpenMX and FHI-aims tight-binding formats.
  • Observables:
    • Band structures, Fermi surfaces.
    • Optical Conductivity $\sigma(\omega)$.
    • Anomalous Hall Continuity.
    • Spin Hall Conductivity.
    • Non-linear conductivities (Shift, Berry Dipole).
  • Symmetrization: Tools to enforce crystal symmetries on tight-binding models derived from numerical data.

Key Strengths

  • Non-Orthogonality: One of the few transport/response codes that correctly handles the overlap matrix $S$ from local-orbital DFT codes (OpenMX/FHI-aims) without assuming orthogonality.
  • Non-Linear Optics: Specialized features for the emerging field of non-linear Hall effects and shift currents, which are not found in standard TB packages.
  • Julia Performance: Exploits Julia's JIT compilation for efficient integration over dense k-grids.

Inputs & Outputs

  • Inputs:
    • DFT output files (Wannier/OpenMX/FHI-aims).
    • Julia scripts defining calculation parameters.
  • Outputs:
    • Computed tensors (conductivity, etc.).
    • Plotting objects.

Interfaces & Ecosystem

  • Upstream: Wannier90, OpenMX, FHI-aims.
  • Downstream: Julia plotting libraries (Plots.jl, Makie.jl).

Performance Characteristics

  • Efficiency: Highly optimized for k-point summation.
  • Parallelism: Julia multi-threading support.

Comparison with Other Codes

  • vs. WannierBerri: WannierBerri is the gold standard for Berry phase properties from Wannier90. HopTB.jl offers similar capabilities around optics and Hall effects but adds support for non-orthogonal bases (non-Wannier90 sources).
  • vs. TB2J: TB2J calculates magnetic parameters; HopTB.jl calculates optical/electronic response.

Application Areas

  • Topological Photovoltaics: Studying shift currents in Weyl semimetals.
  • Spintronics: Spin Hall effect in complex oxides.
  • Methodology: Testing the validity of orthogonal approximations in tight-binding.

Community and Support

  • Development: HopTB team (GitHub).
  • Source: GitHub.

Verification & Sources

Related Tools in 4.2 Model Hamiltonians