Official Resources
- Repository: https://github.com/ChristopheBerthod/MagnetoTransport.jl
- License: MIT License
Overview
MagnetoTransport.jl is a specialized Julia package for calculating the linear magneto-transport properties of two-dimensional quantum systems. It implements the Kubo-Bastin formalism to evaluate the longitudinal ($\sigma_{xx}$) and transverse/Hall ($\sigma_{xy}$) conductivity tensors. Unlike general transport codes, it specifically targets the accurate computation of orbital magnetic effects, including Hofstadter butterfly physics and quantum Hall plateaus, taking into account energy-dependent self-energies.
Scientific domain: Quantum Hall Effect, Topological Matter, 2D Materials
Target user community: Theorists investigating topological transport in lattice models
Theoretical Methods
- Kubo-Bastin Formula: A formulation of the Kubo formula that is robust for dissipative systems and captures both Fermi sea and Fermi surface contributions.
- Streda Formula: Used for the thermodynamic part of the Hall conductivity.
- Peierls Substitution: Models the orbital magnetic field effects on lattice hoppings.
- Self-Energy: Incorporates disorder/scattering via a complex self-energy $\Sigma(E)$.
Capabilities
- Observables:
- Longitudinal Conductivity ($\sigma_{xx}$).
- Hall Conductivity ($\sigma_{xy}$, quantized in units of $e^2/h$).
- Density of States (DOS).
- Integrated Berry curvature.
- Models:
- Square, Honeycomb (Graphene), and Triangular lattices.
- User-defined tight-binding Hamiltonians.
Key Strengths
- Julia Efficiency: Leverages Julia's JIT compilation for fast numerical integration over the Brillouin zone.
- Precision: Capable of resolving fine spectral features (Landau levels) using high-resolution grids or adaptive integration (
QuadGK).
- Focus: Dedicated solely to the conductivity tensor, ensuring correct implementation of the often-tricky Kubo terms.
Inputs & Outputs
- Inputs:
- Julia scripts defining the lattice parameters ($a, t$).
- Magnetic flux per plaquette ($\phi$).
- Scattering rate ($\eta$ or $\Sigma$).
- Outputs:
- Conductivity tensors as a function of Fermi energy or Chemical potential.
- Plots of $\sigma_{xy}$ showing integer quantization.
Interfaces & Ecosystem
- Julia: Fully integrated with the Julia scientific stack (
LinearAlgebra, Plots).
- Quantica.jl: Can potentially use Hamiltonians constructed in Quantica (with conversion).
Performance Characteristics
- Speed: Vectorsized operations over k-space make it highly efficient for 2D bulk systems.
- Scalability: Limited to effective single-particle models (non-interacting or mean-field).
Comparisons with Other Codes
- vs. Kwant: Kwant calculates Hall conductance for finite bars using leads. MagnetoTransport.jl calculates the bulk Hall conductivity tensor using the Kubo formula.
- vs. LinReTraCe: Both usage Kubo formulas; MagnetoTransport.jl is Julia-based and specialized for 2D magnetic response, while LinReTraCe is C++ and more general (3D, thermoelectrics).
Community and Support
- Development: Christophe Berthod (University of Geneva).
- Source: GitHub.
Verification & Sources