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Temperature effects on the electronic band structure of PbTe from first principles
Materials Science · Submitted 7 Sep 2018
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We find that both thermal expansion and electron-phonon interaction have a considerable effect on these temperature variations.
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We report a fully {\it ab-initio} calculation of the temperature dependence of the electronic band structure of PbTe. We address two main features relevant for the thermoelectric figure of merit: the temperature variations of the direct gap and the difference in energies of the two topmost valence band maxima located at L and $\Sigma$. We account for the energy shift of the electronic states due to thermal expansion, as well as electron-phonon interaction computed using the non-adiabatic Allen-Heine-Cardona formalism within density functional perturbation theory and the local density approximation. We capture the increase of the direct gap with temperature in very good agreement with experiment. We also predict that the valence band maxima at L and $\Sigma$ become aligned at $\sim 600-700$ K. We find that both thermal expansion and electron-phonon interaction have a considerable effect on these temperature variations. The Fan-Migdal and Debye-Waller terms are of almost equal magnitude but have an opposite sign, and the delicate balance of these terms gives the correct band shifts. The electron-phonon induced renormalization of the direct gap is produced mostly by high-frequency optical phonons, while acoustic phonons are also responsible for the alignment of the valence band maxima at L and $\Sigma$.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We report a fully {\it ab-initio} calculation of the temperature dependence of the electronic band structure of PbTe. | contribution 1.00 | 0.96 | 0.07 | asserted 0.97 |
| s1 | We address two main features relevant for the thermoelectric figure of merit: the temperature variations of the direct gap and the difference in energies of the two topmost valence band maxima located at L and $\Sigma$. | contribution 0.91 | 0.56 | 0.07 | asserted 0.66 |
| s2 | We account for the energy shift of the electronic states due to thermal expansion, as well as electron-phonon interaction computed using the non-adiabatic Allen-Heine-Cardona formalism within density functional perturbation theory and the local density approximation. | method 0.99 | 0.94 | 0.06 | asserted 1.00 |
| s3 | We capture the increase of the direct gap with temperature in very good agreement with experiment. | result 1.00 | 0.95 | 0.25 | asserted 1.00 |
| s4 | We also predict that the valence band maxima at L and $\Sigma$ become aligned at $\sim 600-700$ K. | result 1.00 | 0.95 | 0.27 | asserted 0.70 |
| s5 | We find that both thermal expansion and electron-phonon interaction have a considerable effect on these temperature variations. | result 0.85 | 0.96 | 0.21 | asserted 1.00 |
| s6 | The Fan-Migdal and Debye-Waller terms are of almost equal magnitude but have an opposite sign, and the delicate balance of these terms gives the correct band shifts. | interpretation 0.64 | 0.92 | 0.12 | asserted 1.00 |
| s7 | The electron-phonon induced renormalization of the direct gap is produced mostly by high-frequency optical phonons, while acoustic phonons are also responsible for the alignment of the valence band maxima at L and $\Sigma$. | interpretation 0.60 | 0.93 | 0.16 | asserted 1.00 |
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Original abstract
We report a fully {\it ab-initio} calculation of the temperature dependence of the electronic band structure of PbTe. We address two main features relevant for the thermoelectric figure of merit: the temperature variations of the direct gap and the difference in energies of the two topmost valence band maxima located at L and $\Sigma$. We account for the energy shift of the electronic states due to thermal expansion, as well as electron-phonon interaction computed using the non-adiabatic Allen-Heine-Cardona formalism within density functional perturbation theory and the local density approximation. We capture the increase of the direct gap with temperature in very good agreement with experiment. We also predict that the valence band maxima at L and $\Sigma$ become aligned at $\sim 600-700$ K. We find that both thermal expansion and electron-phonon interaction have a considerable effect on these temperature variations. The Fan-Migdal and Debye-Waller terms are of almost equal magnitude but have an opposite sign, and the delicate balance of these terms gives the correct band shifts. The electron-phonon induced renormalization of the direct gap is produced mostly by high-frequency optical phonons, while acoustic phonons are also responsible for the alignment of the valence band maxima at L and $\Sigma$.
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2 arXiv papers cite this in 2 sentences
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Uses its method or tool 1 paper
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We computed the temperature dependence of $E_g$ accounting both for the contributions of thermal expansion and e-ph coupling [ref] , where the latter effect was computed using the Allen-Heine-Cardona approach [ref] and DFPT [ref] .
Dominant electron-phonon scattering mechanisms in $n$-type PbTe from first principles · Electronic band structure · 0.96
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