elphbolt

Official Resources

• Repository: https://github.com/nakib/elphbolt
• License: GNU General Public License v3.0

Overview

elphbolt is a state-of-the-art solver for the coupled electron-phonon Boltzmann Transport Equations (BTE). Unlike standard transport codes that treat electrons and phonons separately or use the relaxation time approximation, elphbolt solves the full system iteratively to capture complex non-equilibrium phenomena such as phonon drag (the dragging of electrons by a non-equilibrium phonon flux) and electron drag. It utilizes Wannier90 for efficient interpolation of electronic bands and electron-phonon matrix elements, enabling first-principles calculations of thermoelectric and hydrodynamic transport in real materials.

Scientific domain: Thermoelectrics, Hydrodynamic Transport, Electron-Phonon Physics Target user community: Researchers designing high-efficiency thermoelectric materials or studying non-equilibrium carrier dynamics

Theoretical Methods

• Coupled BTE: Simultaneously solves the Boltzmann equations for electron distribution $f_{nk}$ and phonon distribution $n_{q\nu}$.
• Wannier Interpolation: Uses Maximally Localized Wannier Functions (MLWFs) to interpolate electron eigenvalues and electron-phonon matrix elements to dense k/q-grids.
• Iterative Solver: Self-consistently updates the distributions to converge the drag terms.
• Eliashberg Theory: Includes a module (superconda) for calculating phonon-mediated superconducting properties.

Capabilities

• Transport Coefficients:
  • Electrical Conductivity ($\sigma$).
  • Seebeck Coefficient ($S$) with full phonon drag contribution.
  • Electronic Thermal Conductivity ($\kappa_e$).
  • Lattice Thermal Conductivity ($\kappa_{ph}$) with electron-phonon scattering.
• Microscopic Analysis:
  • Mode-resolved contributions to conductivity and drag.
  • Visualization of non-equilibrium distributions.
  • Lifetimes/Mean-free-paths for both carriers.
• Superconductivity: Calculation of $T_c$ and gap functions (via superconda).

Key Strengths

• Drag Physics: One of the few public codes explicitly designed to capture phonon drag, which is dominant in many semiconductors at low/intermediate temperatures.
• Ab Initio Accuracy: No empirical parameters; inputs come directly from DFT/DFPT (e.g., Quantum ESPRESSO).
• Efficiency: OpenMP/MPI hybrid parallelization allows scaling to large grids necessary for transport convergence.

Inputs & Outputs

• Inputs:
  • Wannier90 files (_hr.dat, _chk).
  • EPW files (.epmatwp) or similar electron-phonon element representations.
  • elphbolt.in: Control inputs.
• Outputs:
  • onsager_coefficients.dat: Full tensor of transport coefficients.
  • linewidths: Lifetimes of electrons/phonons.
  • spectral_function: Mode-resolved transport data.

Interfaces & Ecosystem

• Upstream:
  • Quantum ESPRESSO: Generates the ground state and phonons (PHonon).
  • EPW: Often used to generate the initial coarse grid electron-phonon vertices.
  • Wannier90: Provides the tight-binding basis.
• Parallelism: Efficient handling of large memory requirements for coupled matrices.

Performance Characteristics

• Computational Cost: More expensive than constant-time approximation codes (like BoltzTraP) but essential for accuracy in high-mobility or high-drag interactions.
• Scaling: Scales well with core count; memory bandwidth is often the bottleneck due to large interpolation tables.

Limitations & Known Constraints

• Input Complexity: Requires a complex chain of preceding calculations (DFT -> PHonon -> Wannier90 -> EPW setup).
• Validity: BTE assumes well-defined quasiparticles; breaks down in the bad-metal or strongly correlated hopping regime (though elphbolt focuses on band transport).

Comparison with Other Codes

• vs. EPW: EPW also calculates transport but elphbolt specializes in the coupled solution (drag), whereas standard EPW transport often uses frozen phonons or RTA.
• vs. BoltzTraP: BoltzTraP uses constant relaxation time (CRTA); elphbolt calculates fully energy- and momentum-dependent lifetimes from first principles.
• vs. Perturbo: Perturbo is similar (BTE solver) but elphbolt has a strong historical focus on the coupled drag effects.

Application Areas

• Thermoelectrics: Optimization of $zT$ by engineering phonon drag contributions.
• Hydrodynamic Electron Flow: Regimes where electron-electron or electron-phonon scattering conserves momentum.
• Low-Temperature Transport: Analyzing the "phonon peak" in thermal conductivity.

Community and Support

• Development: Developed by Nakib Protik (Harvard / MIT / now industry).
• Source: GitHub.
• Citations: Protik et al., Phys. Rev. B 102, 064302 (2020).

Verification & Sources

• Repository: https://github.com/nakib/elphbolt
• Primary Publication: N. H. Protik, B. Kozinsky, et al.
• Verification status: ✅ VERIFIED
  • Active research code.
  • Verified against experimental data for Silicon and other standards.