High-throughput analysis of Fröhlich-type polaron models

Band energy; Condensed matter; Degenerate electrons; Electrical resistances; Electron bands; Energy correction; High-throughput analysis; Optical spectrum; Polar materials; Polaron models; Modeling and Simulation; Materials Science (all); Mechanics of Materials; Computer Science Applications; General Materials Science

Abstract :

[en] 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.

Research Center/Unit :

CESAM - Complex and Entangled Systems from Atoms to Materials - ULiège

Disciplines :

Physics

Author, co-author :

de Melo, Pedro Miguel M. C. ; Chemistry Department, Debye Institute for Nanomaterials Science and European Theoretical Spectroscopy Facility, Condensed Matter and Interfaces, Utrecht University, Utrecht, Netherlands ; Nanomat/Q-MAT/CESAM and European Theoretical Spectroscopy Facility, Université de Liège, Liège, Belgium

de Abreu, Joao C. ; Nanomat/Q-MAT/CESAM and European Theoretical Spectroscopy Facility, Université de Liège, Liège, Belgium

Guster, Bogdan ; UCLouvain, Institute of Condensed Matter and Nanosciences (IMCN), Louvain-la-Neuve, Belgium

Giantomassi, Matteo ; UCLouvain, Institute of Condensed Matter and Nanosciences (IMCN), Louvain-la-Neuve, Belgium

Zanolli, Zeila ; Université de Liège - ULiège > Département de physique > Physique des matériaux et nanostructures ; Chemistry Department, Debye Institute for Nanomaterials Science and European Theoretical Spectroscopy Facility, Condensed Matter and Interfaces, Utrecht University, Utrecht, Netherlands

Gonze, Xavier ; UCLouvain, Institute of Condensed Matter and Nanosciences (IMCN), Louvain-la-Neuve, Belgium

Verstraete, Matthieu ; Université de Liège - ULiège > Département de physique > Physique des matériaux et nanostructures

Language :

English

Title :

High-throughput analysis of Fröhlich-type polaron models

Publication date :

December 2023

Journal title :

npj Computational Materials

eISSN :

2057-3960

Publisher :

Nature Research

Volume :

Issue :

Peer reviewed :

Peer Reviewed verified by ORBi

Tags :

CÉCI : Consortium des Équipements de Calcul Intensif
Tier-1 supercomputer

Additional URL :

https://www.nature.com/articles/s41524-023-01083-8.pdf

Funding text :

This work has been supported by the Fonds de la Recherche Scientifique (FRS-FNRS Belgium) through the PdR Grant No. T.0103.19 - ALPS, and by the Federal government of Belgium through the EoS Project ID 40007525. ZZ and PMMCM acknowledge financial support by the Netherlands Sector Plan program 2019-2023 and the research program “Materials for the Quantum Age” (QuMAt, registration number 024.005.006), part of the Gravitation program of the Dutch Ministry of Education, Culture and Science (OCW). This project has received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement No. 951786 - NOMAD CoE. Computational resources have been provided by the CISM/UCLouvain and the CECI funded by the FRS-FNRS Belgium under Grant No. 2.5020.11, as well as the Tier-1 supercomputer of the Fédération Wallonie-Bruxelles, funded by the Walloon Region under grant agreement No. 1117545. We acknowledge a PRACE award granting access to MareNostrum4 at Barcelona Supercomputing Center (BSC), Spain (OptoSpin project id. 2020225411). Moreover, we also acknowledge a PRACE Tier-1 award in the DECI-16 call for project REM-EPI on Archer and Archer2 EPCC in Edinburgh. This work was sponsored by NWO-Domain Science for the use of supercomputer facilities.

Available on ORBi :

since 01 October 2023

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Bibliography

Cardona, M. & Thewalt, M. Isotope effects on the optical spectra of semiconductors. Rev. Mod. Phys. 77, 1173–1224 (2005).
Shishkin, M., Marsman, M. & Kresse, G. Accurate quasiparticle spectra from self-consistent GW calculations with vertex corrections. Phys. Rev. Lett. 99, 246403 (2007).
Marini, A. Ab-initio finite temperature excitons. Phys. Rev. Lett. 101, 106405 (2008).
Giustino, F., Louie, S. & Cohen, M. Electron-phonon renormalization of the direct band gap of diamond. Phys. Rev. Lett. 105, 265501 (2010).
Moser, S. et al. Tunable polaronic conduction in anatase TiO2. Phys. Rev. Lett. 110, 196403 (2013).
Antonius, G., Poncé, S., Boulanger, P., Côté, M. & Gonze, X. Many-body effects on the zero-point renormalization of the band structure. Phys. Rev. Lett. 112, 215501 (2014).
Poncé, S. et al. Temperature dependence of the electronic structure of semiconductors and insulators. J. Chem. Phys. 143, 102813 (2015).
Verdi, C., Caruso, F. & Giustino, F. Origin of the crossover from polarons to Fermi liquids in transition metal oxides. Nat. Commun. 8, 15769 (2017).
Miglio, A. et al. Predominance of non-adiabatic effects in zero-point renormalization of the electronic band gap. Npj Comput. Mater. 6, 167 (2020).
Hohenberg, P. & Kohn, W. Inhomogeneous electron gas. Phys. Rev. 136, B864–B871 (1964).
Kohn, W. & Sham, L. J. Self-consistent equations including exchange and correlation effects. Phys. Rev. 140, A1133–A1138 (1965).
Martin, R. M. Electronic structure. Theory and practical methods. (Cambridge University Press, Cambridge, United Kingdom, 2004).
Hedin, L. New method for calculating the one-particle green’s function with application to the electron-gas problem. Phys. Rev. B 139, A 796 (1965).
Martin, R. M., Reining, L. & Ceperley, D. M. Interacting Electrons. Theory and Computational Approaches (Cambridge University Press, Cambridge, United Kingdom, 2016).
Fröhlich, H. Interaction of electrons with lattice vibrations. Proc. R. Soc. A: Math 215, 291–298 (1952).
Allen, P. B. & Heine, V. Theory of the temperature dependence of electronic band structures. J. Phys. C 9, 2305–2312 (1976).
Allen, P. B. & Cardona, M. Theory of the temperature dependence of the direct gap of germanium. Phys. Rev. B 23, 1495–1505 (1981).
Allen, P. & Cardona, M. Temperature dependence of the direct gap of Si and Ge. Phys. Rev. B 27, 4760 (1983).
Verdi, C. & Giustino, F. Fröhlich electron-phonon vertex from first principles. Phys. Rev. Lett. 115, 176401 (2015).
Giustino, F. Electron-phonon interactions from first principles. Rev. Mod. Phys. 89, 015003 (2017).
Sio, W. H., Verdi, C., Poncé, S. & Giustino, F. Polarons from first principles, without supercells. Phys. Rev. Lett. 122, 246403 (2019).
Brown-Altvater, F. et al. Band gap renormalization, carrier mobilities, and the electron-phonon self-energy in crystalline naphthalene. Phys. Rev. B 101, 165102 (2020).
Brousseau-Couture, V., Godbout, E., Côté, M. & Gonze, X. Zero-point lattice expansion and band gap renormalization: Grüneisen approach versus free energy minimization. Phys. Rev. B 106, 085137 (2022).
Brousseau-Couture, V., Godbout, E., Côté, M. & Gonze, X. 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. Phys. Rev. B 107, 115173 (2023).
Devreese, J. T. Fröhlich polarons from 0D to 3D: concepts and recent developments. J. Condens. Matter Phys. 19, 255201 (2007).
Feynman, R. P. Slow electrons in a polar crystal. Phys. Rev. 97, 660–665 (1955).
Mishchenko, A., Prokof’ev, N., Sakamoto, A. & Svistunov, B. Diagrammatic quantum Monte Carlo study of the Fröhlich polaron. Phys. Rev. B 62, 6317–6336 (2000).
Vasilchenko, V., Zhugayevych, A. & Gonze, X. Variational Polaron Equations Applied to the Anisotropic Fröhlich Model. Phys. Rev. B 105, 214301 (2022).
Lafuente-Bartolome, J. et al. Unified approach to polarons and phonon-induced band structure renormalization. Phys. Rev. Lett. 129 (2022).
Lafuente-Bartolome, J. et al. Ab initio self-consistent many-body theory of polarons at all couplings. Phys. Rev. B 106, 075119 (2022).
Franchini, C., Reticcioli, M., Setvin, M. & Diebold, U. Polarons in materials. Nat. Rev. Mater. 6, 560 (2021).
Holstein, T. Studies of polaron motion: Part I. the molecular-crystal model. Ann. Phys. 8, 325–342 (1959).
Holstein, T. Studies of polaron motion: Part II. The “small" polaron. Ann. Phys. 8, 343–389 (1959).
Petretto, G. et al. High-throughput density-functional perturbation theory phonons for inorganic materials. Sci. Data 5, 180065 (2018).
Hautier, G., Miglio, A., Waroquiers, D., Rignanese, G.-M. & Gonze, X. How Does Chemistry Influence Electron Effective Mass in Oxides? A High-Throughput Computational Analysis. Chem. Mater. 26, 5447 (2014).
Guster, B. et al. Fröhlich polaron effective mass and localization length in cubic materials: Degenerate and anisotropic electronic bands. Phys. Rev. B 104, 235123 (2021).
Gordy, W. New Method of Determining Electronegativity from Other Atomic Properties. Phys. Rev. 69, 604 (1946).
Nery, J. P. et al. Quasiparticles and phonon satellites in spectral functions of semiconductors and insulators: Cumulants applied to the full first-principles theory and the fröhlich polaron. Phys. Rev. B 97, 115145 (2018).
Brunin, G. et al. Phonon-limited electron mobility in Si, GaAs and GaP with exact treatment of dynamical quadrupoles. Phys. Rev. B 102, 094308 (2020).
Brunin, G. et al. Electron-phonon beyond Fröhlich: dynamical quadrupoles in polar and covalent solids. Phys. Rev. Lett. 125, 136601 (2020).
Abreu, J. C., Nery, J. P., Giantomassi, M., Gonze, X. & Verstraete, M. J. Spectroscopic signatures of nonpolarons: the case of diamond. Phys. Chem. Chem. Phys. 24, 12580–12591 (2022).
Hellwarth, R. W. & Biaggio, I. Mobility of an electron in a multimode polar lattice. Phys. Rev. B 60, 299–307 (1999).
Fröhlich, H. Electrons in lattice fields. Adv. Phys. 3, 325–361 (1954).
Mecholsky, A. N., Resca, L., Pegg, I. L. & Fornari, M. Theory of band warping and its effects on thermoelectronic transport properties. Phys. Rev. B 89, 155131 (2014).
Mahan, G. D. Many-Particle Physics. Physics of solids and liquids (Kluwer Academic, 2000), 3rd edn.
Guster, B. et al. Erratum: Fröhlich polaron effective mass and localization length in cubic materials: Degenerate and anisotropic electronic bands. Phys. Rev. B 105, 119902 (2022).
Verdi, C. First-principles Fröhlich electron-phonon coupling and polarons in oxides and polar semiconductors. PhD thesis, U. of Oxford, Oxford, UK (2017).
Gonze, X. & Lee, C. Dynamical matrices, born effective charges, dielectric permittivity tensors, and interatomic force constants from density-functional perturbation theory. Phys. Rev. B 55, 10355–10368 (1997).
Gonze, X. et al. The Abinit project: Impact, environment and recent developments. Comput. Phys. Commun. 248, 107042 (2020).
Romero, A. H. et al. ABINIT: Overview, and focus on selected capabilities. J. Chem. Phys. 152, 124102 (2020).
Janssen, J. L. et al. Precise effective masses from density functional perturbation theory. Phys. Rev. B 93, 205147 (2016).
Migdal, A. B. Interaction between electrons and lattice vibrations in a normal metal. Zh. Eksp. Teor. Fiz. 34, 1438 (1958).
Antoncik, E. On the theory of temperature shift of the absorption curve in non-polar crystals. Czechoslovak Journal of Physics 5, 449 (1955).
Fan, H. Y. Temperature dependence of the energy gap in semiconductors. Phys. Rev. 82, 900–905 (1951).