# ElPhonTransport

This page gives hints on how to compute transport properties that are determined by the electron-phonon interaction (electrical resistivity, superconductivity, thermal conductivity) with the ABINIT package.

## Introduction¶

Warning : this topic concerns metals only.

The calculation of bulk transport quantities (electrical and thermal resistivities - the part that is determined by the electron-phonon interaction) is possible using anaddb. Analogous quantities are obtained from the conducti post-processor, but due to electron-electron scattering, instead of electron-phonon.

A preliminary calculation of the derivatives of the wavefunctions with respect to k-vector must be carried out. After generating a GKK file (see topic_ElPhonInt), the Electron-Phonon Coupling (EPC) analysis is performed in anaddb, setting elphflag variable to 1. Most of the procedure is automatic, but can be lengthy if a large number of k-points is being used.

While the legacy implementation of the transport properties in ABINIT is quite stable, there is a new implementation under heavy development. Most of the present information relates to the legacy implementation, although some also relates to the most recent procedure that relies on optdriver=7. The documentation of the new procedure is given mostly by the related tutorials (introduction and mobility), see below. Another tutorial for the new procedure for superconductivity calculations is still under development.

For the superconductivity calculations (legacy implementation), The electron-phonon interaction is interpolated in reciprocal space, then integrated over the Fermi surface to give the Eliashberg function. Several quadrature methods are available. The default (telphint=1) is to use Gaussian weighting, with a width elphsmear. Another option is the improved tetrahedron [Bloechl1994a] (telphint=0). Finally (telphint=2), one can integrate a given set of electron bands, between ep_b_max and ep_b_min. The resulting integrated quantities are the Eliashberg function (in a file suffixed _A2F), and the EPC strength λ which is printed in the main output file.

The transport calculation is turned on by setting ifltransport to 1 in anaddb. The transport quantities depend on the Fermi velocity for each band, and the electronic band-dependence of the matrix elements must be preserved before integration, by setting ep_keepbands to 1. This increases the memory used, by the square of the number of bands crossing EF. The results are the transport Eliashberg function (in file _A2F_TR), the electrical resistivity (in file _RHO), and the thermal conductivity (in file _WTH).

It is also possible to consider the temperature dependence of the Fermi energy: cubic spline interpolation (ep_nspline) enables to linearly interpolate the transport arrays and reduce the memory usage. Besides setting the Fermi level with elph_fermie (in Hartree), it is also possible to specify the extra electrons per unit cell, (i.e., the doping concentration often expressed in cm-3) with ep_extrael.

Some details about the calculation of electron-phonon quantities in ABINIT and ANADDB can be found here.

compulsory:

basic:

useful:

expert:

v5:

v6:

v7: