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
electrical resistivity (in file
_RHO), and the thermal conductivity (in file
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.
Related Input Variables¶
- elphflag ELectron-PHonon FLAG
- ep_keepbands Electron-Phonon KEEP dependence on electron BANDS
- ifltransport IFLag for TRANSPORT
- kptrlatt K PoinT Reciprocal LATTice
- telphint Technique for ELectron-PHonon INTegration
- a2fsmear Alpha2F SMEARing factor
- elph_fermie ELectron-PHonon FERMI Energy
- elphsmear ELectron-PHonon SMEARing factor
- ep_b_max Electron Phonon integration Band MAXimum
- ep_b_min Electron Phonon integration Band MINimum
- ep_extrael Electron-Phonon EXTRA ELectrons
- ep_nspline Electron Phonon Number for SPLINE interpolation
- mustar MU STAR
- prtfsurf PRinT the Fermi SURFace
- prtvol PRinT VOLume
- band_gap BAND GAP
- ep_nqpt Electron Phonon Number of Q PoinTs
- kptrlatt_fine K PoinT Reciprocal LATTice for FINE grid
Selected Input Files¶
- The tutorial on the electron-phonon interaction presents the use of the utility MRGKK and ANADDB to examine the electron-phonon interaction and the subsequent calculation of superconductivity temperature (for bulk systems).