Official Resources
- Repository: https://github.com/Frost-group/PolaronMobility.jl
- Documentation: https://github.com/Frost-group/PolaronMobility.jl (README)
- License: MIT License
Overview
PolaronMobility.jl is a Julia package dedicated to calculating polaron properties—specifically mobility and effective mass—in polar semiconductors and ionic crystals. It implements Feynman's variational path-integral approach to the Fröhlich polaron problem, which describes the interaction of an electron with macroscopic optical phonons. It also extends to the Holstein polaron model, making it a versatile tool for studying charge transport limits in materials like halide perovskites and organic semiconductors.
Scientific domain: Carrier Transport, Polarons, Condensed Matter
Target user community: Researchers studying mobility limits in polar materials
Theoretical Methods
- Feynman Path Integral: Variational solution to the Fröhlich Hamiltonian.
- Finite Temperature: Calculation of free energies and thermal averages at $T > 0$.
- Mobility Theories:
- FHIP: Feynman-Hellwarth-Iddings-Platzman (limit of low temperature/weak coupling).
- Kadanoff: Boltzmann equation approach suitable for intermediate temperatures.
- Holstein Model: Small polaron physics (lattice discreteness).
Capabilities
- Observables:
- DC Mobility $\mu(T)$.
- Optical Conductivity $\sigma(\omega)$ (AC response).
- Effective Mass $m^*$.
- Materials: Input of $\epsilon_0, \epsilon_\infty$, and $\omega_{LO}$ allows simulation of specific compounds (e.g., CsPbBr$_3$).
- Analysis:
- Crossover from large to small polarons.
Key Strengths
- Speed: Variational minimization is computationally inexpensive compared to Monte Carlo or Green's function methods, allowing near-instant results for material screening.
- Material-Specific: Designed to take material parameters directly, bridging model physics with real material contexts.
- Julia Implementation: Clean code that is easy to integrate into larger material screening pipelines.
Inputs & Outputs
- Inputs: Dielectric constants, Phonon frequency, Effective mass (band mass).
- Outputs: Mobility values, plots of $\mu$ vs $T$.
Interfaces & Ecosystem
- Dependencies: Julia scientific stack (
Optim.jl, QuadGK.jl).
Performance Characteristics
- Efficiency: Very high. Solving the variational equations takes milliseconds.
- Scalability: trivially parallelizable over different materials or temperatures.
Comparison with Other Codes
- vs. EPW: EPW is a first-principles code that calculates $g_{mn\nu}(k,q)$. PolaronMobility.jl uses a continuum model (Fröhlich). EPW is more accurate for specific band structures; PolaronMobility.jl captures the non-perturbative polaron state better in the continuum limit.
- vs. DiagMC: Diagrammatic Monte Carlo is exact but slow. This code is approximate (variational) but fast.
Application Areas
- Halide Perovskites: Explaining the modest mobility and "phonon glass" behavior.
- Organics: Understanding transport in soft polar lattices.
Community and Support
- Development: Frost Group (Imperial College London).
- Source: GitHub.
Verification & Sources