The Linear Response Transport Centre (LinReTraCe) is a package for the simulation of transport properties driven by carriers with finite lifetimes. The underlying theory, described in PRB:105.085139 (arxiv:2112.07604), establishes a comprehensive and thermodynamically consistent phenomenology capable of reproducing qualitatively correct full temperature profiles in metals as well as semiconductors. A comprehensive code documentation including implementation details, benchmarks, and test cases is described in SciPostPhysCodeb.16 and a step-by-step installation guide is available in the tutorial.

The code package provides several interfaces to common electronic structure codes, including Wien2K, VASP, as well as maximally localized Wannier functions from Wannier90. The DFT input can also be supplied with the band interpolation scheme of BoltzTraP2.

Moreover, we provide an interface to create general tight-binding models, as well as a Python3 interface where source-agnostic data can be supplied via specifically shaped arrays.

At its core, LinReTraCe is a highly efficient and scalable MPI parallalized Fortran code for the calculation of accurate, artefact-free transport coefficients of, both, realistic electronic structures as well as models and with high precision down to lowest temperatures. All the surrounding interfaces and tools are written in modern Python3. In order to obtain all required and optional packages for the running of the pre- and postprocessing at its full functionality, simply install the dependencies via pip. To avoid package incompatibilities with global installations, we highly recommend the usage of local environments. In the root folder of linretrace use

python -m venv pylrtc

source pylrtc/bin/activate

pip install -e .

If you want to include the BoltzTraP2 features also use

pip install cmake packaging pyfftw boltztrap2

To return to your standard environment, simply use

deactivate

The Fortran part of LinReTraCe requires a full HDF5 installation (version >=1.12.1) whose underlying HDF5 library calls are handled with an HDF5 wrapper written by one of us. At the wrapper's page, an installation guide and test code for the HDF5 library is provided, if needed (Please note that one needs to register at the HDF5 site to download the tar ball). To maximize the scalabilty of the code, we recommend making use of the MPI implementation.

To obtain the LinReTraCe source, clone this repository:

git clone https://github.com/linretrace/linretrace

To compile the code, a special make_include file needs to be saved in the main linretrace folder. An examplary configuration that enables MPI looks as follows

FC       = mpiifort       # Main Fortran compiler
FCDG     = ifort          # Fortran Compiler for the Special functions
FFLAGS   = -O3
FPPFLAGS = -DMPI
HDF5     = -I/opt/hdf5-1.13.1_icc/include
HDF5    += -L/opt/hdf5-1.13.1_icc/lib -lhdf5_fortran -lhdf5hl_fortran

A single core configuration looks as

FC       = gfortran
FCDG     = gfortran
FFLAGS   = -O3
HDF5     = -I/opt/hdf5-1.13.1_gcc/include
HDF5    += -L/opt/hdf5-1.13.1_gcc/lib -lhdf5_fortran -lhdf5hl_fortran

The configuration can be checked via make validate and the compilation is done with make linretrace, creating the bin subfolder in which the binary linretrace will be moved into. An overview of validation, compilation, and testsuite is displayed via make.

The center point of LinReTraCe's input is the energy file, where all the necessary band energies as well as optical elements (among other auxiliary data) are stored. In order to prepare this file one of the following interfaces can be used:

WIEN2k and VASP are interfaced with ldft:

ldft <wien2k folder> --optic --output wien2k_structure.hdf5

ldft <vasp folder> --interp --output vasp_structure.hdf5

In the WIEN2k example we make use of the dipole matrix elements from the optic subpackage (x optic) whereas in the VASP example we interface the BoltzTraP2 band interpolation scheme via --interp. There the Peierls approximation is used based on optical elements consisting of band velocities and curvatures. For a full description, see the code publication and ldft --help.

Wannier90 is interfaced with lwann:

lwann <wannier90 folder> --output wannier90_structure.hdf5

Please note that we provide the possibility to expand the reducible grid with --kmesh nkx nky nkz as well as sub-interface generic WIEN2k momemtum grids if the required case.struct and case.klist files are provided: lwann <wannier90 folder> --wien2k --output wannier90_wien2k.hdf5

General tight-binding models are created with ltb. Simply provide a text file with the corresponding hopping parameters, atomic positions and lattice vectors and execute:

ltb tb_file nkx nky nkz charge --output model.hdf5

The tight binding file has a Wannier90 inspired format:

begin hopping
#  a1 a2 a3    orb1 orb2  hopping.real [hopping.imag]
   0  0  0     1    1     0.3  # on site energy
  +1  0  0     1    1     1.0  # nearest neighbor hopping
   0 +1  0     1    1     1.0
  -1  0  0     1    1     1.0
   0 -1  0     1    1     1.0
end hopping

begin atoms
#  sort rx ry rz
   1    0  0  0     # fractional lattice vector coordinates
end atoms

begin real_lattice
#  x   y   z
   5   0   0       # a1 lattice vector in units of Angstroem
   0   5   0       # a2
   0   0   1       # a3
end real_lattice

Please note that we use the convention employed by the strongly correlated electron systems community, where a positive hopping leads a reduction of the energy, i.e.

$$ H(\mathbf{k}) = -\sum_\mathbf{R} e^{i\mathbf{k}\cdot\mathbf{R}} (1-2\delta_{\mathbf{R},\mathbf{0}}\delta_{l,l'}) H_{ll'}(\mathbf{R}) $$

If instead one wants to provide energies and optical elements that cannot be created with the above tools we provide a generic interface linterface that contains the class StructureFromArrays that supports the load-in of the necessary data (multiplicity, energies, optical elements, ...).

Arbitrary (momentum, band, and spin dependent) scattering rates (quasi particle weights and energy shifts) are supported through a custom HDF5 scattering file. The workflow to create a custom file follows

• Copy lscat_template from the installation folder into your working direction.
• Insert the linretrace folder into the system path.
• Reference to correct energy file.
• Define calculation axis ($\mu$ or $T$-scan).
• Define scattering rates as numpy array. Optionally: Define quasi particle weights and/or band shifts.
• Execute script to generate LRTC scattering file.

Simplistic temperature dependencies (polynomial) on the other hand can be generated via the config file.

LinReTraCe itself is configured via a free format configuration file. lconfig provides a minimal starting point through interactive questioning. Its main purpose is to define which quantities should be calculated at which precision in addition to mode-specific sub configurations. The temperature mode, e.g. further supports impurity levels, impurity bands, and homogeneous doping. For a full description see documentation/configspec.

Running your LinReTraCe installation is done either via mpirun -np <cores> bin/linretrace config.lrtc or bin/linretrace config.lrtc where config.lrtc is the config file from the previous subsection.

The generated output is an HDF5 file, whose tree structure is documented in [paper]. To interface this file in an effortless way we provide lprint, capable of plotting/printing all the available transport coefficients.

lprint <LRTCoutput file> list lists all the available datasets, which then can be retrieved by providing the corresponding key and, optionally, directional arguments:

lprint -p <LRTCoutput file> s-intra xx yy plots, e.g., the xx and yy components of the intra-band Seebeck tensor

lprint -p <LRTCoutput file> rh-intra xyz plots the Hall coefficient in the xy-plane (magnetic-field in z-direction)

This project is licensed under the GNU General Public License v3 which can be found in LICENSE.

Matthias Pickem*, Emanuele Maggio, Jan M. Tomczak*

* Corresponding authors:

matthias [dot] pickem [at] gmail [dot] com

tomczak [dot] jm [at] gmail [dot] com

LinReTraCe was funded by the Austrian Science Fund (FWF) through project P 30213.