Erratum: Fröhlich polaron effective mass and localization length in cubic materials: Degenerate and anisotropic electronic bands [Phys. Rev. B 
<b>104</b>
, 235123 (2021)]

Guster, Bogdan; Melo, Pedro; Martin, Bradley A. A.; Brousseau-Couture, Véronique; Abreu, Joao; Miglio, Anna; Giantomassi, Matteo; Côté, Michel; Frost, Jarvist M.; Verstraete, Matthieu J.; Gonze, Xavier

doi:10.1103/physrevb.105.119902

Cited by 5 publications

(5 citation statements)

References 6 publications

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“…See Ref. [58] for a thorough discussion of the different phase conventions in the literature. The unitary matrix s nm ( k) describes the directiondependent overlap between the electronic states at the band extrema located at Γ and states along the k direction, in the k → 0 limit, computed from the periodic part of the wavefunction (indicated by the subscript P ):…”

Section: Generalized Fröhlich Modelmentioning

confidence: 99%

Effect of spin-orbit coupling on the zero-point renormalization of the electronic band gap in cubic materials: First-principles calculations and generalized Fröhlich model

2023

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The electronic structure of semiconductors and insulators is affected by ionic motion through electron-phonon interaction, yielding temperature-dependent band gap energies and zero-point renormalization (ZPR) at absolute zero temperature. For polar materials, the most significant contribution to the band gap ZPR can be understood in terms of the Fröhlich model, which focuses on the non-adiabatic interaction between an electron and the macroscopic electrical polarization created by a long-wavelength optical longitudinal phonon mode. On the other hand, spin-orbit interaction (SOC) modifies the bare electronic structure, which will, in turn, affect the electron-phonon interaction and the ZPR. We present a comparative investigation of the effect of SOC on the band gap ZPR of twenty semiconductors and insulators with cubic symmetry using first-principles calculations. We observe a SOC-induced decrease of the ZPR, up to 30%, driven by the valence band edge, which almost entirely originates from the modification of the bare electronic eigenenergies and the decrease of the hole effective masses near the Γ point. We also incorporate SOC into a generalized Fröhlich model, addressing the Dresselhaus splitting which occurs in non-centrosymmetric materials, and confirm that the predominance of non-adiabatic effects on the band gap ZPR of polar materials is unchanged when including SOC. Our generalized Fröhlich model with SOC provides a reliable estimate of the SOC-induced decrease of the polaron formation energy obtained from first principles and brings to light some fundamental subtleties in the numerical evaluation of the effective masses with SOC for non-centrosymmetric materials. We finally warn about a possible breakdown of the parabolic approximation, one of the most fundamental assumptions of the Fröhlich model, within the physically relevant energy range of the Fröhlich interaction for materials with high phonon frequencies treated with SOC. This is a post-peer-review version of the article published in Physical Review B, which includes the Supplemental Material in the main file.

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Section: Generalized Fröhlich Modelmentioning

confidence: 99%

Effect of spin-orbit coupling on the zero-point renormalization of the electronic band gap in cubic materials: First-principles calculations and generalized Fröhlich model

2023

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“…The choice of convention affects the form of some relations in Section II B, see Ref. 48. In later sections dealing with the Fröhlich model, we will use Born and Huang convention.…”

Section: Background a First-principles Modeling Of A Polaronmentioning

confidence: 99%

“…( 20) and (21), we have followed the Born and Huang choice of phase, as explained in Appendix A, and in Ref. 48. Here * is the effective permittivity due only to the ionic movements, defined from the difference of inverse high-frequency and static permittivities ∞ and 0 :…”

Section: B Fröhlich Modelmentioning

confidence: 99%

“…( 20) and ( 21) for a primitive unit cell, since N p is already present in the prefactor of Eq. (48).…”

Section: B Variational Anisotropic Fröhlich Modelmentioning

confidence: 99%

“…Keeping in mind the aforementioned cutoff procedure and combining Eqs. ( 43), ( 47) an (48), we arrive at the variational polaron expression applied to the Fröhlich model:…”

Section: B Variational Anisotropic Fröhlich Modelmentioning

confidence: 99%

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Variational Polaron Equations Applied to the Anisotropic Fröhlich Model

Vasilchenko,

Zhugayevych,

Gonze

2022

Preprint

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Starting from recent advances in the first-principles modeling of polarons, variational polaron equations in the strong-coupling adiabatic approximation are formulated in Bloch space. In this framework, polaron formation energy as well as individual electron, phonon and electron-phonon contributions are obtained. We suggest an efficient gradient-based optimization algorithm and apply these equations to the generalized Fröhlich model with anisotropic non-degenerate electronic bands, both in two-and three-dimensional cases. The effect of the divergence of Fröhlich electronphonon matrix elements at Γ-point is treated analytically, improving the convergence with respect to the sampling in reciprocal space. The whole methodology is validated by obtaining the known asymptotic solution of the standard Fröhlich model in isotropic scenario and also by comparing our results with the Gaussian ansatz approach, showing the difference between the numerically exact and Gaussian trial wavefunctions. Additionally, decomposition of the energy into individual terms allows one to recover the Pekar's 1:2:3:4 theorem, which is shown to be valid even in the anisotropic case. We expect that the improvements in the formalism and numerical implementation will be applicable beyond the large polaron hypothesis inherent to Fröhlich model.

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High-throughput analysis of Fröhlich-type polaron models

de Melo,

de Abreu,

Guster

et al. 2023

npj Comput Mater

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The electron–phonon interaction is central to condensed matter, e.g. through electrical resistance, superconductivity or the formation of polarons, and has a strong impact on observables such as band gaps or optical spectra. The most common framework for band energy corrections is the Fröhlich model, which often agrees qualitatively with experiments in polar materials, but has limits for complex cases. A generalized version includes anisotropic and degenerate electron bands, and multiple phonons. In this work, we identify trends and outliers for the Fröhlich models on 1260 materials. We test the limits of the Fröhlich models and their perturbative treatment, in particular the large polaron hypothesis. Among our extended dataset most materials host perturbative large polarons, but there are many instances that are non-perturbative and/or localize on distances of a few bond lengths. We find a variety of behaviors, and analyze extreme cases with huge zero-point renormalization using the first-principles Allen-Heine-Cardona approach.

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Erratum: Fröhlich polaron effective mass and localization length in cubic materials: Degenerate and anisotropic electronic bands [Phys. Rev. B 104 , 235123 (2021)]

Cited by 5 publications

References 6 publications

Effect of spin-orbit coupling on the zero-point renormalization of the electronic band gap in cubic materials: First-principles calculations and generalized Fröhlich model

Effect of spin-orbit coupling on the zero-point renormalization of the electronic band gap in cubic materials: First-principles calculations and generalized Fröhlich model

Variational Polaron Equations Applied to the Anisotropic Fröhlich Model

High-throughput analysis of Fröhlich-type polaron models

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