nakib / elphbolt

A solver for the coupled and decoupled electron and phonon Boltzmann transport equations.

elphbolt + superconda

elphbolt (short for electron-phonon Boltzmann transport) is a modern Fortran (2018 standard) suite of transport codes. It provides a solver for both the coupled and decoupled electron and phonon Boltzmann transport equations (BTEs). You can read about the methodology and implementation here: https://www.nature.com/articles/s41524-022-00710-0. In addition, you get the superconda app for solving the phonon-mediated superconducting properties within the Eliashberg formalism.

Using ab initio electron-phonon and 3- and 4-phonon interactions and a fully wave vector and electron band/phonon branch resolved formulation of the BTEs, the elphbolt app gives you the

• phonon and electronic thermal conductivities;
• electronic conductivity;
• phonon and electronic contributions to the thermopower; and
• effect of the mutual electron-phonon drag on the transport coefficients listed above.

Using ab initio electron-phonon and a fully wave vector and electron band/phonon branch resolved, Eliashberg formulation of superconductivity, the superconda app gives you the

• anisotropic and isotropic Eliashberg spectral function and
• phonon-mediated superconducting transition temperature.

To date (January 10, 2024), elphbolt / superconda has been used in the following works:

material(s)	physics probed	publication
Si, BAs, LiF, & GaN	new models of phonon-isotope interaction and temperature dependent 3+4ph limited thermal conductivity	arXiv:2401.04473
GaN	3+4 phonons and thin-film scattering limited thermal conductivity	Phys. Rev. B 108, 235313
GaN & AlN	drag	Phys. Rev. B 107, 245202
MgB2	superconductivity enhancement	Phys. Rev. B 107, 184518
BAs	drag	Phys. Rev. B 107, L081202
Diamond	drag	Mat. Tod. Phys 27, 100740
Si	drag	npj Comp. Mat. 8, 28

Stylistically, elphbolt is designed to be simple, small, fast, and extensible. It uses an object-based procedural style, which allows fast development, while resulting in a rather compact source (~ 10k lines of code, generated using David A. Wheeler’s SLOCCount). The symmetries of the crystal are fully exploited and the transport active Fermi window is used to allow the sampling of extremely fine wave vector meshes needed for accurate solutions of the BTEs and Eliashberg equations. Parallelism is achieved through modern Fortran’s intrinsic coarrays feature that is fully supported by recent versions of both the gcc and intel compilers.

elphbolt currently works with the Quantum Espresso (https://www.quantum-espresso.org/) suite and its core module EPW (https://epw-code.org/) for the phonon quantities and the Wannier space information, respectively. An interface with all-electron exciting (https://exciting-code.org/) code is currently under construction.

elphbolt is a “free as in freedom” code distributed under the GNU General Public License (GPL) version 3. You can read more about the philosophy of software freedom here: https://www.gnu.org/philosophy/free-sw.en.html.

elphbolt is for all of the transport physics community. Feel free to fork and contribute. Create a pull request to incorporate your changes to this project. Tailor it to your own liking/needs and please pay it forward in the spirit of free software and open science. Let me know of bugs, suggestions for improvement, feature requests, criticism, and praises. You may use the Discussions section of this repository for this purpose. There is also a discord server for informal discussions about theory, set up, usage, extensions, maintenance, possible collaborations, etc. You might find me hanging out there from time to time. I’d love to have a coffee with you and talk physics there in the office-hour voice channel.

Documentation

The source is heavily commented and can be auto-documented with FORD (https://github.com/cmacmackin/ford). For installation of FORD, consult https://forddocs.readthedocs.io/en/latest/. To generate the documentation and the call graphs (you need graphviz for the latter), say ford projectfile.md. Then read ./documentation/index.html with your browser.

Install on HPC systems with gcc

1. Get spglib

elphbolt uses the spglib (https://spglib.github.io/spglib/) library for crystal symmetry analysis. Currently, versions 1.6.0 and 1.14.1 have been tried and tested. A lot of HPCs provide this library as a module, so check before building from source.

2. Get OpenCoarrays

OpenCoarrays (http://www.opencoarrays.org) is an implementation of the coarrays functionalities. Some HPC systems include it (for example, MareNostrum4 (BSC) and LaPalma (IAC)). In that case, load it. If not, you can build it from source.

3. Build

Use one of the following two methods:

Using fpm [v>=0.7]

Standard method (no gpu)

For a cpu-only build and test with Fortran Package Manager (https://fpm.fortran-lang.org/), say

	source fpm_config_caf.sh; yes | fpm clean; fpm build; fpm install
	fpm test test_misc
	fpm test test_autodiff
	fpm test bte_regression --runner="sh test/3C-SiC/fpm_run_bte_caf.sh"

The elphbolt and superconda apps will be available in your /.local/bin directory. They should both be directly callable from your shell.

Modify the fpm manifest file, fpm.toml, to suit your system. I’d appreciate any feedback.

Experimental method (with gpu)

For a cpu+gpu build with OpenACC (https://www.openacc.org/), say

	source fpm_config_caf_openacc.sh; yes | fpm clean; fpm build; fpm install
	fpm test test_misc
	fpm test test_autodiff
	fpm test bte_regression --runner="sh test/3C-SiC/fpm_run_bte_caf.sh"

For this build, you will need a recent version of gcc build with nvptx. You can have it on your HPC system using, for example, spack (https://spack.io/):

spack install gcc@12.3.0+nvptx

and adding the relevant <path to spack build of gcc>/bin directory to your PATH.

Using cmake

Issue the following command to build and run tests: mkdir build; cd build; cmake ..; make; ctest. If all goes well, the exectuable will be available as build/bin/{elphbolt, superconda}.

Docker

To build a docker image, say

docker build - < Dockerfile

The docker build uses cmake internally.

Examples

A full example for cubic silicon is provided. More examples will be added over time.

Workflow

This is a transport code. And it comes after doing some DFT, DFPT, and Wannier calculations. Users of the popular ShengBTE (https://bitbucket.org/sousaw/shengbte/src/master/) code will find that just one extra step (an EPW calculation) on top of the ShengBTE workflow is needed to obtain all the input files necessary for a coupled BTEs calculation with elphbolt. You can, however, calculate just a decoupled phonon or electron BTE, or Eliashberg equations if you so choose. For these, only a subset of the input files will be needed. For example, if you want to calculate just a decoupled electron BTE or Eliashberg equations, then you do not need to provide the third order force constants. Similarly, if you are interested in just a phonon BTE without the phonon-electron interactions, then the Wannier parameters are not required.

Following is the full set of input files:

Input file

The input file - input.nml - contains the information about the crystal and the various parameters of the calculation. A full description of all the input parameters is given in the next section. Also take a look at the input.nml file for the cubic silicon example.

Second order interatomic force constants

This comes out of the usual ph.x and q2r.x calculation from Quantum Espresso. This file is needed to calculate phonon quantities and must be named espresso.ifc2.

Third order interatomic force constants

This code supports the thirdorder.py, dense d3q, and the sparse d3q formats of the third order force constants file. For the d3q interface, the sparse format is strongly recommended. Check out https://bitbucket.org/sousaw/thirdorder/src/master and https://anharmonic.github.io/d3q/ to learn more.

If you seek a solution of the decoupled phonon BTE or the coupled electron-phonon BTEs, at least one of these files, named FORCE_CONSTANTS_3RD, mat3R, or mat3R.sparse for the three supported formats, respectively, must be provided.

4-phonon scattering rates

These are the 4-phonon scattering rates out of the code FourPhonon (https://github.com/FourPhonon/FourPhonon). You must pass these to elphbolt if you want to include 4-phonon scattering in the calculation. To turn on the 4-phonon functionality, look up the keys fourph and fourph_mesh_ref in the Namelist numerics below. Take special care when generating the 4-phonon scattering rates in the FourPhonon code for use in elphbolt. First off, you must choose the wave vector mesh in FourPhonon such that it scales to the phonon wave vector mesh (qmesh) of elphbolt by a non-zero integer. Secondly, you must pass the irreducible 4-phonon scattering rates data file to elphbolt as FourPhonon_BTE.w_4ph_T<temperature>. For example, for a $920$ K calculation, the file name should be FourPhonon_BTE.w_4ph_T0.920E+03. Additionally, you must prepend at the top of the file the total number of vectors in the irreducible Brillouin zone (IBZ) of the FourPhonon calculation. Thirdly, you must provide the file FourPhonon_BTE.qpoint_full. Prepend the total number of wave vectors in the full Brillouin zone (FBZ) of the FourPhonon calculation. Internally, elphbolt will interpolate the scattering rates calculated by FourPhonon on a coarse, say $10× 10× 10$, mesh on to a fine qmesh, say $60× 60× 60$ for a fourph_mesh_ref value of $6$. It is always a good idea to plot the interpolated fine mesh scattering rates, ph.W_rta_4ph, to compare against the coarse mesh ones from FourPhonon. It is also good to remember that this is a rather crude way to approximate the effect of the 4-phonon scattering because of the (in general tri-)linear interpolation method used and the fact that the corresponding 4-phonon in-scattering correction is not accounted for in the iterative solver.

Wannier space information

These are required if you want to solve a decoupled electron BTE, include phonon-electron interaction in the decoupled phonon BTE, Eliashberg equations for the phonon-mediated superconducting properties, or the coupled electron-phonon BTEs. You have the option of choosing between two external Wannier calculators.

epw

These include the files rcells_k, rcells_q, rcells_g, wsdeg_k, wsdeg_q, and wsdeg_g which must be printed out of an EPW calculation. We will also need the files epmatwp1 and epwdata.fmt, both of which are outputted by EPW after the Bloch -> Wannier calculation step. The first contains the Wannier space electron-phonon matrix elements and the second contains the Wannier space dynamical matrix and Hamiltonian. A couple of modified source files can be found in EPW/src/ directory which are needed to correctly print these quantities out during EPW’s Bloch -> Wannier calculation step. The user must recompile their EPW code following the replacement with these modified source codes. At this time, EPW v5.3.1 (shipped with Quantum Espresso v6.7MaX_Release) must be used for this purpose.

Note that elphbolt can only read the epwdata.fmt file only if the EPW calculation is performed with the flag lifc set to .false.. I thank Gui-Lin Zhu for pointing this out. In any case, I strongly recommend that the user generates the relevant quantites from elphbolt along high-symmetry paths and compares directly against EPW (see next section).

exciting

[I will list here the input files from exciting soon.]

High symmetry electron and phonon wave vector path and initial electron wave vector

These are required if you want to plot the electronic bands, phonon dispersions, and the electron-phonon matrix elements along high symmetry paths in the Brillouin zone.

You need to provide a wave vector path file named highsympath.txt (to be used as both the electron and phonon wave vectors) and an initial electron wave vector file named initialk.txt if you want the electron bands, phonon dispersions, and electron-phonon matrix elements calculated along the path. The first line of highsympath.txt must be an integer equaling the number of wave vectors in the path. This should be followed by the same number of rows of wave vectors expressed in crystal coordinates (fractions of the reciprocal lattice vectors). The initialk.txt file must simply contain one wave vector in crystal coordinates.

Bespoke screening for the isotropic Eliashberg spectral function

If needed (see flag use_external_eps below), the isotropic Eliashberg spectral function can be screened with a bespoke dielectric function. In this case, a file named eps_squared must be placed into the run directory. This will contain a single column of data, giving the modulus-square of the dielectric function at each point in the equidistant phonon energy mesh (see flag domega below).

Description of input.nml

For the elphbolt app, there are 5 Namelists in the input.nml file: allocations, crystal_info, electrons, numerics, and wannier. For the superconda app, there is an additional Namelist – superconductivity. Users of the ShengBTE code will find the format of this file familiar. Below the keys for each Namelist are described.

allocations

key	Type	Default	Description
numelements	Integer	0	Number of types of basis atoms.
numatoms	Integer	0	Number of basis atoms.

crystal_info

key	Type	Default	Description
name	String	“Crystal”	Name of material.
elements	String array of size numelements	‘X’	Elements in the basis.
atomtypes	Integer array of size numatoms	0	Integer tagging unique elements in the basis.
masses	Real array of size numelements	-1.0	Masses of the basis atoms in amu. If masses are not provided, set VCA or DIB to .True..
VCA	Logical	.False.	Use isotopic mix for basis atom masses?
DIB	Logical	.False.	Use dominant isotope mass for basis atom masses
lattvecs	3 x 3 real array	0.0	Lattice vectors in Cartesian coordinates in units of nm. If twod is .True., the crystal must be positioned on the x-y plane and the third lattice vector must be of the form (0 0 layer thickness).
basis	3 x numatoms real array	0.0	Atomic basis vectors in crystal coordinates (i.e. fraction of lattvecs).
polar	Logical	.False.	Is the system polar?
born	3 x 3 x numatoms rank-3 real tensor	0.0	Born effective charge tensor (from phonon calculation).
epsilon	3 x 3 rank-2 real tensor	0.0	High-frequency dielectric tensor (from phonon calculation).
read_epsiloninf	Real	.False.	Read high-frequency dielectric constant from input?
epsiloninf	Real	0.0	High-frequency scalar dielectric constant. If read_epsiloninf is .True. (.False.), this is read from the input (set equal to the trace-average of epsilon). Currently this quantity is not used in any calculation.
epsilon0	Real	0.0	Static scalar dielectric constant. Used for screening electron-charged impurity interaction, if included. Look up elchimp under the Namelist numerics. For the default value of epsilon0, the electron-charged interaction blows up.
T	Real	-1.0_dp	Crystal temperature in K.
twod	Logical	.False.	Is the system (quasi)-2-dimensional? See description of lattvecs also.
subs_masses	Real array of size numelements	0.0	Masses of substitution atoms in amu. This is needed if phsubs is .True. See table of keys for Namelist numerics.
subs_conc	Real array of size numelements	0.0	Concentration of the substitutional atoms in cm-3 (or cm-2 if twod is .True.). This is needed if phsubs is .True. See table of keys for Namelist numerics.
bound_length	Real	1e12 mm	Characteristic sample length for boundary scattering. This is needed if phbound or elbound is .True. See table of keys for Namelist numerics.

electrons

key	Type	Default	Description
spindeg	Integer	2	Spin degeneracy of the bands.
enref	Real	-999999.99999	Electron referenc energy in eV. This is the center of the transport active window. Also see description for fsthick. See table of keys for Namelist ‘numerics’.
chempot	Real	-999999.99999	Chemical potential in eV.
metallic	Logical	.False.	Is the system metallic?
numbands	Integer	0	Total number of electronic Wannier bands.
indlowband	Integer	0	Lowest transport band index.
indhighband	Integer	0	Highest transport band index.
indlowconduction	Integer	0	Lowest conduction band index. For metallic .False., this or indhighvalence must be provided.
indhighvalence	Integer	0	Highest valence band index. For metallic .False., this or indlowconduction must be provided.
dopingtype	Character	‘x’	Type of doping (‘n’ or ‘p’). This is needed for runlevel 0 only. See table of keys for Namelist ‘numerics’.
scissor	Real	0.0	Scissor operator for conduction bands in eV.
numconc	Integer	100	Number of carrier concentration points. This is needed for runlevel 0 only. See table of keys for Namelist ‘numerics’.
conclist	Real array of size numconc	0.0	List carrier concentrations in cm-3 (or cm-2 if twod is .True.). This is needed for runlevel 0 only. See table of keys for Namelist ‘numerics’.
numT	Integer	100	Number of temperature points. This is needed for runlevel 0 only. See table of keys for Namelist ‘numerics’.
Tlist	Real array of size numT	100	List of temperatures in K. This is needed for runlevel 0 only. See table of keys for Namelist ‘numerics’.
Zn	Real	0.0	Ionization number of donor impurities. This is needed only when elchimp is .True. and metallic is .False. See table of keys for Namelist ‘numerics’.
Zp	Real	0.0	Ionization number of acceptor impurities. This is needed only when elchimp is .True. and metallic is .False. See table of keys for Namelist ‘numerics’.

numerics

key	Type	Default	Description
qmesh	Integer array of size 3	1 1 1	Phonon wave vector mesh (q).
mesh_ref	Integer	1	Electron wave vector mesh (k) refinement factor with respect to the phonon mesh.
fsthick	Real	0.0	Fermi surface thickness in eV.
datadumpdir	String	”./”	Runtime data dump directory.
read_gq2	Logical	.False.	Read electron-phonon (irreducible wedge q) vertices from disk?
read_gk2	Logical	.False.	Read electron-phonon (irreducible wedge k) vertices from disk?
read_V	Logical	.False.	Read phonon-phonon (irreducible wedge q) vertices from disk?
read_W	Logical	.False.	Read phonon-phonon (irreducible wedge q) transition probabilities from disk?
tetrahedra	Logical	.False.	Use the analytic tetrahedron method instead of the triangular method for 3d delta function evaluation?
fourph	Logical	.False.	Include 4-ph scattering at the RTA level?
fourph_mesh_ref	Integer	1	Mesh refinement factor of elphbolt’s phonon wavectors with respect to external (FourPhonon code) 4-ph calculation.
phe	Logical	.False.	Include phonon-electron interaction in phonon BTE?
phiso	Logical	.False.	Include phonon-isotope interaction in phonon BTE?
phiso_1b_theory	String	‘DIB-1B’	Choose between ‘Tamura’ (1st Born on top of virtual crystal approximation) or ‘DIB-1B’ (1st Born on top of dominant isotope background).
phsubs	Logical	.False.	Include phonon-substitution interaction in phonon BTE? If .True., look up subs_masses and subs_conc under the Namelist crystal_info.
phbound	Logical	.False.	Include phonon-boundary interaction in phonon BTE? If .True., look up bound_length under the Namelist crystal_info.
onlyphbte	Logical	.False.	Calculate phonon BTE without electron drag?
elchimp	Logical	.False.	Include electron-charged impurity scattering in electron BTE? If .True., look up epsilon0 under Namelist crystal_info and Zn and Zp under Namelist electrons.
elbound	Logical	.False.	Include electron-boundary interaction in electron BTE? If .True., look up bound_length under the Namelist crystal_info.
onlyebte	Logical	.False.	Calculate electron BTE without phonon drag?
drag	Logical	.True.	Include electron and phonon drag term in the phonon and electron BTE, respectively.
maxiter	Intger	50	Maximum number of iteration steps for the BTE(s).
conv_thres	Real	1e-4	Relative convergence threshold for the BTE(s).
runlevel	Integer	1	Control for the type of calculation. 0: Calculate table of chemical potentials for a given doping type, temperature range, and carrier concentrations. Look up dopingtype, numconc, conclist, numT, and Tlist under Namelist electrons. 1: Transport calculation(s). 2: Post-processing results to calculate the spectral transport coefficients. 3: Superconductivity calculation, look up keys of the Namelist superconductivity.
plot_along_path	Logical	.False.	Plot Wannier interpolated quantities along high symmetry wave vectors?
ph_en_min	Real	0.0	Lower bound of equidistant phonon energy mesh in eV. Only needed for runlevel 2.
ph_en_max	Real	1.0	Upper bound of equidistant phonon energy mesh in eV. Only needed for runlevel 2.
ph_en_num	Integer	100	Number of equidistant phonon energy mesh points. Only needed for runlevel 2.
el_en_min	Real	-10.0	Lower bound of equidistant electron energy mesh in eV. Only needed for runlevel 2.
el_en_max	Real	10.0	Upper bound of equidistant electron energy mesh in eV. Only needed for runlevel 2.
el_en_num	Integer	100	Number of equidistant electron energy mesh points. Only needed for runlevel 2.
use_Wannier_ifc2s	Logical	.False.	Use 2nd order force constants from the Wannierized data?

wannier

key	Type	Default	Description
coarse_qmesh	Integer array of size 3	0 0 0	Coarse phonon wave vector mesh employed in the Wannier calculation. This must match the q-mesh in the Quantum Espresso second order force constants file.
Wannier_engine_name	String	‘epw’	Choose external code (‘epw’ or ‘exciting’) for Wannierized quantities.

superconductivity

key	Type	Default	Description
mustar	Real	0.0	Dimensionless Coulomb pseudopotential parameter.
domega	Real	0.0 eV	Equidistant phonon energy mesh spacing.
matsubara_cutoff	Integer	0	Matsubara energy cutoff as a factor of the highest phonon energy.
qp_cutoff	Integer	0	Quasiparticle energy cutoff as factor of the highest phonon energy.
isotropic	Logical	.False.	Use the isotropic (fast!) version of the Eliashberg theory?
use_external_eps	Logical	.False.	Use user generated modulus-squared dielectric function to screen the Eliashberg spectral function. For now, only works for the isotropic theory.
Tstart	Real	0.0 K	Starting point of the temperature sweep.
Tend	Real	0.0 K	End point of the temperature sweep.
dT	Real	0.0 K	Temperature difference used in temperature sweep.

Description of output files

The code produces a large amount of data. Here, we provide a description of the various types output files.

Below I(F)BZ = irreducible (full) Brillouin zone; RTA = relaxation time approximation; ch. imp. = charged impurities; bound = boundary; subs = substitution; numbands = number of electron bands; and numbranches = number of phonon branches.

Zero temperature data

File name	Directory	Units	Description
gk2.istate*	datadumpdir/g2/	eV2	Squared e-ph (1-phonon) vertices for every IBZ electron state. Binary.
gq2.istate*	datadumpdir/g2/	eV2	Squared e-ph (1-phonon) vertices for every IBZ electron state. Binary.
Vm2.istate*	datadumpdir/V2/	eV2Å-6amu-3	Squared ph-ph (3-phonon) vertices for every IBZ phonon state. Binary.
el(ph).dos	./	eV-1	Band resolved electronic (phononic) density of states. numbands (numbranches) columns of reals.
el(ph).ens_ibz	./	eV	IBZ electronic (phononic) band energies. numbands (numbranches) columns of reals.
el.inwindow_states_ibz	./	none	IBZ electronic states (wave vector index, band index) within the transport active window. 2 columns of integers.
el(ph).vels_ibz	./	Kms-1	IBZ electronic (phononic) band (branch) velocities. In each row, there are 3 (Cartesian direction) sets of numbands (numbranches) numbers.
el(ph).wavevecs_ibz[fbz]	./	crystal	IBZ [FBZ] electronic (phononic) wave vectors. For the electrons, these are only within the transport window.
el.W_rta_elbound	./	THz	IBZ RTA el-bound scattering rates. numbands columns of reals.
ph.W_rta_phiso(bound)[subs]	./	THz	IBZ RTA ph-iso (bound) [subs] scattering rates. numbranches columns of reals.
el.ens_kpath	./	eV	Electron energies along the given k-path.
ph.ens_qpath	./	eV	Phonon energies along the given q-path.
gk_qpath	./	eV	Absolute value of the e-ph matrix elements (averaged over the degenerate bands and branches) for the given k-vector and q-path.
a2F.istate*	datadumpdir/sc/	none	Anisotropic Eliashberg spectral function for every IBZ state. Binary.
omegas	./	eV	Equidistant phonon energy mesh.
a2F_iso	./	none	Isotropic Eliashberg spectral function on the equidistant phonon energy mesh.
a2F_iso_branch_resolved	./	none	Phonon branch resolved isotropic Eliashberg spectral function on the equidistant phonon energy mesh.
cum_lambda_iso_branch_resolved	./	none	Phonon branch resolved standard, isotropic electron-phonon coupling parameter on the equidistant phonon energy mesh.
quasiparticle_ens	./	eV	Equidistant electronic quasiparticle energy mesh.

Finite temperature data

File name	Directory	Units	Description
Xchimp.istate*	datadumpdir/mu*/X/	THz	Transition probability for e-ch. imp. processes for every IBZ electron state. Binary.
Xminus[plus].istate*	datadumpdir/mu*/X/	THz	Transition probability for e-ph (1-phonon) minus [plus] processes for every IBZ electron state. Binary.
Y.istate*	datadumpdir/mu*/Y/	THz	Transition probability for ph-e (1-phonon) processes for every IBZ phonon state. Binary.
Wm[p].istate*	datadumpdir/T*/W/	THz	Transition probability for ph-ph (3-phonon) minus [plus] processes for every IBZ phonon state. Binary.
el.W_rta_eph[chimp]	./T*/	THz	IBZ RTA el-ph [ch. imp.] scattering rates. numbands columns of reals. Identically zero for bands outside the transport window.
ph.W_rta_3ph(4ph)[phe]	./T*/	THz	IBZ RTA 3ph (4ph) [ph-e] scattering rates. numbranches columns of reals.
drag[nodrag]_el_sigma_*	./T*/	Ω-1m-1	Band resolved (_<integer>) and total (_tot) charge conductivity tensor at every iteration step.
drag[nodrag]_el_alphabyT_*	./T*/	Am-1K-1	Band resolved (_<integer>) and total (_tot) electronic Peltier(-ish) coefficient tensor at every iteration step.
drag[nodrag]_el_kappa0_*	./T*/	Wm-1K-1	Band resolved (_<integer>) and total (_tot) electronic thermal conductivity (zero E-field) tensor at every iteration step.
drag[nodrag]_el_sigmaS_*	./T*/	Am-1K-1	Band resolved (_<integer>) and total (_tot) electronic thermopower times conductivity tensor at every iteration step.
drag_ph_alphabyT_*	./T*/	Am-1K-1	Branch resolved (_<integer>) and total (_tot) phonon Peltier(-ish) coefficient tensor at every iteration step.
drag[nodrag]_ph_kappa_*	./T*/	Wm-1K-1	Branch resolved (_<integer>) and total (_tot) phonon thermal conductivity tensor at every iteration step.
RTA{nodrag}(partdcpl)[drag]_I0_*	./T*/	nmeVK-1	Band resolved (_<integer>) and total (_tot) electronic response function to ∇ T-field in the RTA {dragless} (partially decoupled) [drag] theory.
RTA{nodrag}(partdcpl)[drag]_J0_*	./T*/	nmC	Band resolved (_<integer>) and total (_tot) electronic response function to E-field in the RTA {dragless} (partially decoupled) [drag] theory.
RTA{nodrag}[drag]_F0_*	./T*/	nmeVK-1	Branch resolved (_<integer>) and total (_tot) phononic response function to ∇ T-field in the RTA {dragless} [fully coupled] theory.
drag_G0_*	./T*/	nmC	Branch resolved (_<integer>) and total (_tot) phononic response function to E-field in fully coupled theory.
iso_quasiparticle_DOS.T*	./	none	Scaled quasiparticle density of states on the equidistant electronic quasiparticle energy mesh.
iso_quasiparticle_Delta.T*	./	eV	Isotropic superconducting gap on the equidistant electronic quasiparticle energy mesh.

Postprocessing (runlevel 2)

File name	Directory	Units	Description
RTA{nodrag}(partdcpl)[drag]_{([iterated_el])}_sigma_spectral_*	./T*/	Ω-1m-1eV-1	Band resolved (_<integer>) and total (_tot) spectral charge conductivity tensor in the RTA {([iterated])} {dragless} (partially decoupled) [drag] theory.
RTA{nodrag}(partdcpl)[drag]_{([iterated_el])}_alphabyT_spectral_*	./T*/	Am-1K-1eV-1	Band resolved (_<integer>) and total (_tot) spectral electronic Peltier(-ish) coefficient tensor in the RTA {([iterated])} {dragless} (partially decoupled) [drag] theory.
RTA{nodrag}(partdcpl)[drag]_{([iterated_el])}_kappa0_spectral_*	./T*/	Wm-1K-1eV-1	Band resolved (_<integer>) and total (_tot) spectral electronic thermal conductivity (zero E-field) tensor in the RTA {([iterated])} {dragless} (partially decoupled) [drag] theory.
RTA{nodrag}(partdcpl)[drag]_{([iterated_el])}_sigmaS_spectral_*	./T*/	Am-1K-1eV-1	Band resolved (_<integer>) and total (_tot) spectral electronic thermopower times conductivity tensor in the RTA {([iterated])} {dragless} (partially decoupled) [drag] theory.
drag_iterated_ph_alphabyT_spectral_*	./T*/	Am-1K-1eV-1	Branch resolved (_<integer>) and total (_tot) spectral phonon Peltier(-ish) coefficient tensor in the iterated drag theory.
RTA{nodrag}[drag]_{[iterated_ph]}_kappa_spectral_*	./T*/	Wm-1K-1eV-1	Branch resolved (_<integer>) and total (_tot) spectral phonon thermal conductivity tensor in the RTA {[iterated]} {dragless} [drag] theory.
el[ph].en_grid	./	eV	Uniform electron [phonon] energy mesh for spectral coefficient calculation.