# Electron-phonon interaction

### This page gives hints on how to compute the matrix elements of the electron-phonon interaction with the ABINIT package.

##### Copyright (C) 2016-2017 ABINIT group (MV)

Mentioned in topic_ElPhonTransport, topic_PhononWidth, help_features#6.

### Table of content:

- 1. Introduction.
- 2. Related lesson(s) of the tutorial.
- 3. Related input variables.
- 4. Selected input files.
- 5. References.

### 1. Introduction.

The theory and details of the implementation are described in [Gonze2009] and [Gonze2016].

Basic calculations of electron-phonon interaction in ABINIT: one performs a normal ground state, then DFPT phonon calculations (using rfphon, with added keywords prepgkk and prtgkk, which saves the matrix elements to files suffixed GKK. The main change in this respect is that prtgkk now disables the use of symmetry in reducing q-points and perturbations. This avoids ambiguities in wave function phases due to band degeneracies. The resulting GKK files are merged using the mrggkk utility, and processed by anaddb.

With the implementation of phonons in PAW DFPT, the electron phonon coupling is also available in PAW, though this has not yet been tested extensively. The input variables for electron-phonon coupling in anaddb are described in [Gonze2009] and [Gonze2016].

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

Subsequently, the GKK file is used to compute many quantities, as explained in topic_PhononWidth, topic_TDepES and topic_ElPhonTransport.

A brand new ABINIT driver, focusing on the treatment of electron-phonon interaction is under development. Most of the input variables for experts, with optdriver==7 are related to this development, that is not yet operational as of v8.5 .
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### 2. Related lesson(s) of the tutorial.

- The lesson Response-Function 1 (RF1) presents the basics of DFPT calculations within ABINIT. The example given is the study of dynamical and dielectric properties of AlAs (an insulator): phonons at Gamma, dielectric constant, Born effective charges, LO-TO splitting, phonons in the whole Brillouin zone. The creation of the "Derivative Data Base" (DDB) is presented.
- The lesson 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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### 3. Related input variables.

Compulsory input variables:

... optdriver [OPTions for the DRIVER]
... prepgkk [PREPAre GKK calculation]
... prtgkk [PRinT the GKK matrix elements file]

Useful input variables:

... get1den [GET the first-order density from _1DEN file]
... gkqwrite@anaddb [GKk for input Q grid to be WRITtEn to disk]
... irdddb [Integer that governs the ReaDing of DDB file]
... use_nonscf_gkk [USE NON-SCF calculation of GKK matrix elements (electron phonon)]

Input variables for experts:

... ddb_ngqpt [Derivative DataBase: Number of Grid points for Q-PoinTs]
... ddb_shiftq [Derivative DataBase: SHIFT of the Q-points ]
... ep_prt_yambo@anaddb [Electron Phonon PRinTout YAMBO data]
... eph_extrael [Electron-PHonon: EXTRA ELectrons]
... eph_fermie [Electron-PHonon: FERMI Energy]
... eph_fsewin [Electron-Phonon: Fermi Surface Energy WINdow]
... eph_fsmear [Electron-PHonon: Fermi surface SMEARing]
... eph_intmeth [Electron-Phonon: INTegration METHod]
... eph_mustar [Electron-PHonon : MU STAR (electron-electron interaction strength)]
... eph_ngqpt_fine [Electron-PHonon : Number of Grid Q-PoinTs in FINE grid.]
... eph_task [Electron-PHonon: Task]
... eph_transport [Electron-PHonon: TRANSPORT flag]
... getddb [GET the DDB from ...]
... prtphdos [PRinT the PHonon Density Of States]
... prtphsurf [PRinT PHonon iso-SURFace]
... symgkq@anaddb [SYMmetrize the GKk matrix elements for each Q]
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### 4. Selected input files.

WARNING : as of ABINITv8.6.x, the list of input files provided in the specific section of the topics Web pages is still to be reviewed/tuned. In some cases, it will be adequate, and in other cases, it might be incomplete, or perhaps even useless.
The user can find some related example input files in the ABINIT package in the directory /tests, or on the Web:

tests/v5/Input: t96.in t97.in t98.in

tests/v7/Input: t89.in t90.in t91.in t92.in
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### 5. References.

[Gonze2009] X. Gonze, B. Amadon, P.-M. Anglade, J.-M. Beuken, F. Bottin, P. Boulanger, F. Bruneval, D. Caliste, R. Caracas, M. Côté, T. Deutsch, L. Genovese, Ph. Ghosez, M. Giantomassi, S. Goedecker, D.R. Hamann, P. Hermet, F. Jollet, G. Jomard, S. Leroux, M. Mancini, S. Mazevet, M.J.T. Oliveira, G. Onida, Y. Pouillon, T. Rangel, G.-M. Rignanese, D. Sangalli, R. Shaltaf, M. Torrent, M.J. Verstraete, G. Zerah and J.W. Zwanziger, "ABINIT: First-Principle approach to material and nanosystem properties", Comp. Phys. Comm. 180, 2582-2615 (2009).
[Gonze2016] X. Gonze, F. Jollet, F. Abreu Araujo, D. Adams, B. Amadon, T. Applencourt, C. Audouze, J.-M. Beuken, J. Bieder, A. Bokhanchuk, E. Bousquet, F. Bruneval, D. Caliste, M. Côté, F. Dahm, F. Da Pieve, M. Delaveau, M. Di Gennaro, B. Dorado, C. Espejo, G. Geneste, L. Genovese, A. Gerossier, M. Giantomassi, Y. Gillet, D.R. Hamann, L. He, G. Jomard, J. Laflamme Janssen, S. Le Roux, A. Levitt, A. Lherbier, F. Liu, I. Lukacevic, A. Martin, C. Martins, M.J.T. Oliveira, S. Poncé, Y. Pouillon, T. Rangel, G.-M. Rignanese, A.H. Romero, B. Rousseau, O. Rubel, A.A. Shukri, M. Stankovski, M. Torrent, M.J. Van Setten, B. Van troeye, M.J. Verstraete, D. Waroquier, J. Wiktor, B. Xue, A. Zhou and J.W. Zwanziger, "Recent developments in the ABINIT software package", Computer Physics Communications 205, 106 (2016).
DOI: 10.1016/j.cpc.2016.04.003.

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