Solve the Non-Equillibrium Green's Functions (NEGF) transport on examples for educational purposes. Limited to a 1D linear chain for now. See the documentation website.
pip install fuNEGF
If you find this package useful, please cite L. Vojáček, Multiscale Modeling of Spin-Orbitronic Phenomena at Metal, Oxide, and 2D Material Interfaces for Spintronic Devices, PhD thesis, Université Grenoble Alpes (2024).
- the
LinearChain
class including the NEGF routines resides insrc/fuNEGF/models.py
- a Jupyter notebook
examples/one-dimensional_channel.ipynb
contains the linear chain case study with the underlying physics explained - a Jupyter notebok
examples/time_complexity.ipynb
contains a time complexity study of constructing the model$\mathcal{O}(N)$ and calculating the transmission coefficient$\mathcal{O}(N^2)$
A linear chain with a single or multiple on-site potential impurities will present a chemical potential (occupation) drop, which may not be apparent unless a phase relaxation is included, as shown below.
An additional momentum relaxation will cause a non-zero chemical potential slope in between the impurity regions.
The complete description and calculation are provided in the examples/one-dimensional_channel.ipynb
notebook.
- documentation website
- object-oriented
- PEP8-compliant
The retarded Green's function
is a function of energy
Along with the advanced Green's function
they provide the spectral function
and are used to solve for the "electron occupation" Green's function
which gives the density matrix
The in-scattering term
Both, the self-energy
NOTE: We use the (physically expressive) notation of S. Datta, where the self-energies and Green's functions in relation to the standard notation (on the right) are defined as
For the LinearChain
model, the Hamiltonian
Impurity potential
The self-energies
with the broadening functions
where
The in-scattering terms
where
The self-energies describing the phase and phase-momentum relaxation are defined in terms of the Green's functions themselves. Their strength is defined via the (scalar) coefficients
which is used for an element-wise multiplication
Since the Green's functions enter the definition of the self-energy, a self-consistent loop is performed, where