mirror of https://github.com/abinit/abinit.git
79 lines
4.0 KiB
Markdown
79 lines
4.0 KiB
Markdown
---
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description: How to compute transport properties that are determined by the electron-phonon interaction (electrical resistivity, superconductivity, thermal conductivity)
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authors: MV
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---
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<!--- This is the source file for this topics. Can be edited. -->
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This page gives hints on how to compute transport properties that are determined by the electron-phonon
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interaction (electrical resistivity, superconductivity, thermal conductivity) with the ABINIT package.
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## Introduction
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Warning : this topic concerns metals only.
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The calculation of bulk transport quantities (electrical and thermal
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resistivities - the part that is determined by the electron-phonon
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interaction) is possible using anaddb. Analogous quantities are obtained from
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the conducti post-processor, but due to electron-electron scattering, instead
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of electron-phonon.
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A preliminary calculation of the derivatives of the wavefunctions with respect
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to k-vector must be carried out. After generating a GKK file (see
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[[topic:ElPhonInt]]), the Electron-Phonon Coupling (EPC) analysis is performed
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in anaddb, setting [[anaddb:elphflag]] variable to 1. Most of the procedure is
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automatic, but can be lengthy if a large number of k-points is being used.
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While the legacy implementation of the transport properties in ABINIT is quite stable,
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there is a new implementation under heavy development.
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Most of the present information relates to the legacy implementation,
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although some also relates to the
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most recent procedure that relies on [[optdriver]]=7. The documentation
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of the new procedure is given mostly by the related tutorials (introduction and mobility), see below.
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Another tutorial for the new procedure for superconductivity calculations is still under development.
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For the superconductivity calculations (legacy implementation), The electron-phonon interaction is
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interpolated in reciprocal space, then integrated over the Fermi surface to
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give the Eliashberg function. Several quadrature methods are available. The
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default ([[anaddb:telphint]]=1) is to use Gaussian weighting, with a width
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[[anaddb:elphsmear]]. Another option is the improved tetrahedron
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[[cite:Bloechl1994a]] ([[anaddb:telphint]]=0). Finally
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([[anaddb:telphint]]=2), one can integrate a given set of electron bands,
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between [[anaddb:ep_b_max]] and [[anaddb:ep_b_min]]. The resulting integrated
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quantities are the Eliashberg function (in a file suffixed `_A2F`), and the EPC
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strength λ which is printed in the main output file.
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The transport calculation is turned on by setting [[anaddb:ifltransport]] to 1
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in anaddb. The transport quantities depend on the Fermi velocity for each
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band, and the electronic band-dependence of the matrix elements must be
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preserved before integration, by setting [[anaddb:ep_keepbands]] to 1. This
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increases the memory used, by the square of the number of bands crossing EF.
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The results are the transport Eliashberg function (in file `_A2F_TR`), the
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electrical resistivity (in file `_RHO`), and the thermal conductivity (in file `_WTH`).
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It is also possible to consider the temperature dependence of the Fermi
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energy: cubic spline interpolation ([[anaddb:ep_nspline]]) enables to linearly
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interpolate the transport arrays and reduce the memory usage. Besides setting
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the Fermi level with [[anaddb:elph_fermie]] (in Hartree), it is also possible
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to specify the extra electrons per unit cell, (i.e., the doping concentration
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often expressed in cm-3) with [[anaddb:ep_extrael]].
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Some details about the calculation of electron-phonon quantities in ABINIT and
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ANADDB can be found [[pdf:elphon_manual|here]].
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## Related Input Variables
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{{ related_variables }}
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## Selected Input Files
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{{ selected_input_files }}
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## Tutorials
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* (Legacy approach) [[tutorial:eph_legacy|The legacy 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).
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* (New procedure) Two tutorials are available at [[tutorial:eph_intro|an overview of the EPH code]], and
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at [[tutorial:eph4mob|Phonon-limited mobility]]:.
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