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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.


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.

For the superconductivity calculations, 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.





Selected Input Files