Official Resources
- Repository: https://github.com/michaelschueler/dynamics-w90
- License: GNU General Public License v3.0
Overview
dynamics-w90 is a sophisticated Fortran package designed to simulate non-equilibrium electron dynamics in solids using realistic tight-binding Hamiltonians derived from Wannier90. It focuses on light-matter interactions, enabling the study of ultrafast phenomena such as high-harmonic generation (HHG), time-resolved photoemission (tr-ARPES), and transient band structure engineering. The code distinguishes itself by implementing a gauge-invariant formulation for coupling electromagnetic fields to the Wannier basis, ensuring physical accuracy even in truncated basis sets.
Scientific domain: Ultrafast Spectroscopy, Non-linear Optics, Quantum Materials
Target user community: Theorists and experimentalists working on pump-probe spectroscopy and attosecond physics
Theoretical Methods
- Time-Dependent Schrödinger Equation (TDSE): Propagates the electronic wavefunction or density matrix in time under external fields.
- Peierls Substitution + Corrections: Implements a rigorous gauge-invariant coupling of the vector potential $\mathbf{A}(t)$ to the tight-binding Hamiltonian, including non-local terms.
- Orbital Angular Momentum (OAM): Includes modern position operator corrections to calculating OAM and magnetic dichroism.
- Berry Physics: Evaluates topological quantities like Berry curvature and spin texture continuously in k-space.
Capabilities
- Spectroscopy Simulation:
- High-Harmonic Generation (HHG): Calculates the time-dependent current $J(t)$ and its spectrum.
- Linear/Non-linear Optics: Optical conductivity and higher-order susceptibilities.
- tr-ARPES: Simulates time-resolved angle-resolved photoemission spectra (planned/beta).
- Analysis:
- Spin/Orbital Texture: Maps spin and OAM on the Fermi surface.
- Population Dynamics: Tracks excitation and relaxation of carriers.
- System Types: Bulk crystals, 2D materials (TMDs, Graphene), Topological Insulators.
Key Strengths
- Realism: Uses DFT-derived parameters ($ab initio$ accuracy) rather than toy models.
- Gauge Invariance: Solves the long-standing problem of unphysical gauge-dependence in truncated basis simulations of optical response.
- Efficiency: Highly optimized Fortran 2008 core for time-propagation.
- Modern Features: Support for non-collinear spin and Spin-Orbit Coupling (SOC).
Inputs & Outputs
- Inputs:
_tb.dat or _hr.dat: Wannier90 Hamiltonian.params.nml: Namelist controlling the laser pulse (field strength, frequency, envelope) and time-stepping.
- Outputs:
current.dat: Time-dependent current (for HHG).populations.dat: Time-dependent band populations.snapshots: Wavefunction/Density matrix at specific times.
Interfaces & Ecosystem
- Upstream: Wannier90 (v2.x/v3.x compatible).
- Helper Scripts: Python scripts included for generating inputs and plotting results.
Performance Characteristics
- Computational Cost: Scales linearly with the number of k-points and time steps; much cheaper than TD-DFT.
- Parallelization: MPI parallelization over k-points allows scaling to clusters.
Limitations & Known Constraints
- Correlations: Currently primarily a mean-field / independent particle picture (with dephasing models). Full many-body scattering (Boltzmann/GKBA) is in development.
- Basis Size: Limited by the number of Wannier functions; extremely large bases (100+ bands) become expensive for time-propagation.
Comparison with Other Codes
- vs. TD-DFT (Octopus, Salmonella): dynamics-w90 is a "model" approach using fixed basis functions, allowing for much longer time scales and larger systems than full real-space TD-DFT.
- vs. Python TB codes (Kwant): dynamics-w90 is specialized for optical driving and gauge-invariant field coupling, which is non-trivial in general TB codes.
- vs. SBE codes: Similar to Semiconductor Bloch Equation solvers but handles arbitrary multi-band structures from DFT.
Application Areas
- Valleytronics: Selective valley excitation in TMDs.
- Floquet Engineering: Modifying topological properties with periodic driving.
- Petahertz Electronics: Analyzing current generation on sub-cycle time scales.
Community and Support
- Development: Maintained by the group of Michael Schüler (PSI / University of Fribourg).
- Source: GitHub.
Verification & Sources