mirror of https://github.com/abinit/abinit.git
90 lines
4.4 KiB
Markdown
90 lines
4.4 KiB
Markdown
---
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description: To to calculate the temperature dependence of the electronic structure
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authors: SP
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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 calculate the temperature dependence of the electronic structure with the ABINIT package.
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## Introduction
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The electronic structure changes with temperature. In most materials, such
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changes are mainly driven by the electron-phonon interaction, which is also
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present at zero Kelvin, inducing the so-called zero-point motion
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renormalization (ZPR) of the eigenvalues. These effects can be computed thanks
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to the Allen-Heine-Cardona (AHC) theory [[cite:Allen1976]],
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[[cite:Allen1981]], [[cite:Allen1983]], which is based on diagrammatic method
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of many-body perturbation theory. An extension to the standard AHC theory also
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gives access to the electronic lifetime and decay rates. These physical
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properties are available from ABINIT since v7.10.4.
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The AHC formalism and the implemented equations can be found in
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[[cite:Ponce2014a]]. An extended verification and validation study (also
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versus other first-principle codes) of the ABINIT implementation can be found
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in [[cite:Ponce2014]]. The AHC implementation can be used with any XC
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functional working with the response-function (RF) part of the code, and
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requires the use of norm-conserving pseudopotentials. NetCDF support is
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mandatory.
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The AHC implementation in ABINIT is still 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.
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We do not describe the Frohlich model computations.
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In the oldest, well-established, AHC implementation in ABINIT,
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the sum over highly energetic bands appearing in the AHC
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equations [[cite:Gonze2011]] is efficiently
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computed. Such behavior is controlled by the input variable [[ieig2rf]].
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The **k** -point convergence can be strongly improved by restoring the charge
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neutrality through the reading of the Born effective charge and dielectric
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tensor (controlled by the input variable [[getddb]]). More information on the
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importance of charge neutrality fulfillment can be found in
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[[cite:Ponce2015]]. The value of [[elph2_imagden]] sets the imaginary shifts
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used to smooth numerical instabilities in the denominator of the sum-over-
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states expression.
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We have checked that the implementation correctly holds for arbitrarily small
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[[elph2_imagden]] parameters, [[cite:Ponce2015]]. The input variable
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[[smdelta]] triggers the calculation of the electronic lifetime and the value
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of the smearing delta function can be specified through [[esmear]].
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A double grid can be used to speed-up the calculations with [[getwfkfine]] or
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[[irdwfkfine]]. The variable [[getgam_eig2nkq]] gives the contribution at Γ so
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that the Debye-Waller term can be computed. This variable is only relevant for
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calculations of AHC using the abinit program only. It is nonetheless
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recommended to use the provided python post-processing script
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temperature_para.py with its module rf_mods.py in the directory
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scripts/post_processing/ to allow for more flexibility. The python scripts
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support multi-threading.
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The following steps are required to perform an AHC calculation:
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* Perform a response function calculation at **q** =Γ with electric field perturbation.
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* Perform phonon calculations and produce the EPC for a large set of wavevectors **q** , reading the Born effective charge and dielectric tensor with [[getddb]].
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* Gather and compute the impact of the electron-phonon coupling on the electronic eigenenergies using the temperature_para.py python script.
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The outputs of the script are provided in text and NetCDF format to allow for
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later reading inside ABINIT. This could be used in the future developments of
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ABINIT to compute temperature-dependent optical properties for example.
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For the temperature dependence of the Fermi energy, see [[topic:ElPhonTransport]].
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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 procedure) A tutorial is available at [[tutorial:eph_tdep_legacy|the temperature dependence of the electronic structure]]:.
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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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[[tutorial:eph4zpr|Zero-point renormalization of the band gap and temperature-dependent band gaps]]:.
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