Many-body Green's function approaches to the doped Fröhlich solid: Exact solutions and anomalous mass enhancement

Kandolf, Nikolaus; Verdi, Carla; Giustino, Feliciano

doi:10.1103/physrevb.105.085148

Title: Many-body Green's function approaches to the doped Fröhlich solid: Exact solutions and anomalous mass enhancement

Journal Article · Fri Feb 25 00:00:00 EST 2022 · Physical Review. B

DOI:https://doi.org/10.1103/physrevb.105.085148· OSTI ID:1903346

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Univ. of Texas, Austin, TX (United States); Univ. of Oxford (United Kingdom)
Univ. Wien (Austria)
Univ. of Texas, Austin, TX (United States)

In polar semiconductors and insulators, the Fröhlich interaction between electrons and long-wavelength longitudinal optical phonons induces a many-body renormalization of the carrier effective masses and the appearance of characteristic phonon sidebands in the spectral function, commonly dubbed “polaron satellites.” The simplest model that captures these effects is the Fröhlich model, whereby electrons in a parabolic band interact with a dispersionless longitudinal optical phonon. The Fröhlich model has been employed in a number of seminal papers, from early perturbation-theory approaches to modern diagrammatic Monte Carlo calculations. One limitation of this model is that it focuses on undoped systems, thus ignoring carrier screening and Pauli blocking effects that are present in real experiments on doped samples. Here, to overcome this limitation, we extend the Fröhlich model to the case of doped systems, and we provide exact solutions for the electron spectral function, mass enhancement, and polaron satellites. We perform the analysis using two approaches, namely, Dyson’s equation with the Fan-Migdal self-energy, and the second-order cumulant expansion. We find that these two approaches provide qualitatively different results. In particular, Dyson’s approach yields better quasiparticle masses and worse satellites, while the cumulant approach provides better satellite structures, at the price of worse quasiparticle masses. Both approaches yield an anomalous enhancement of the electron effective mass at finite doping levels, which in turn leads to a breakdown of the quasiparticle picture in a significant portion of the phase diagram.

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Research Organization:: Univ. of Texas, Austin, TX (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES); National Science Foundation (NSF)

Grant/Contract Number:: SC0020129; DMR21002; ERCAP0016747

OSTI ID:: 1903346

Journal Information:: Physical Review. B, Vol. 105, Issue 8; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (66)

Tailoring the nature and strength of electron–phonon interactions in the SrTiO3(001) 2D electron liquid Wang, Z.; McKeown Walker, S.; Tamai, A. Nature Materials, Vol. 15, Issue 8 https://doi.org/10.1038/nmat4623	journal	April 2016
Critical Doping for the Onset of a Two-Band Superconducting Ground State in ${SrTiO}_{3 - δ}$ Lin, Xiao; Bridoux, German; Gourgout, Adrien Physical Review Letters, Vol. 112, Issue 20 https://doi.org/10.1103/PhysRevLett.112.207002	journal	May 2014
Observation of a two-dimensional liquid of Fröhlich polarons at the bare SrTiO3 surface Chen, Chaoyu; Avila, José; Frantzeskakis, Emmanouil Nature Communications, Vol. 6, Issue 1 https://doi.org/10.1038/ncomms9585	journal	October 2015
A new variational ansatz in the polaron theory Röseler, J. Physica Status Solidi (b), Vol. 25, Issue 1 https://doi.org/10.1002/pssb.19680250129	journal	January 1968
Diagrams in the polaron model Smondyrev, M. A. Theoretical and Mathematical Physics, Vol. 68, Issue 1 https://doi.org/10.1007/BF01017794	journal	July 1986
Many-Body Effects on the Zero-Point Renormalization of the Band Structure Antonius, G.; Poncé, S.; Boulanger, P. Physical Review Letters, Vol. 112, Issue 21 https://doi.org/10.1103/PhysRevLett.112.215501	journal	May 2014
Spectral fingerprints of electron-plasmon coupling Caruso, Fabio; Giustino, Feliciano Physical Review B, Vol. 92, Issue 4 https://doi.org/10.1103/PhysRevB.92.045123	journal	July 2015
Dependence of the Superconducting Transition Temperature on Carrier Concentration in Semiconducting SrTi $O_{3}$ Schooley, J. F.; Hosler, W. R.; Ambler, E. Physical Review Letters, Vol. 14, Issue 9 https://doi.org/10.1103/PhysRevLett.14.305	journal	March 1965
Electron-Phonon Renormalization of the Direct Band Gap of Diamond Giustino, Feliciano; Louie, Steven G.; Cohen, Marvin L. Physical Review Letters, Vol. 105, Issue 26 https://doi.org/10.1103/PhysRevLett.105.265501	journal	December 2010
Fröhlich polaron and bipolaron: recent developments Devreese, Jozef T.; Alexandrov, Alexandre S. Reports on Progress in Physics, Vol. 72, Issue 6 https://doi.org/10.1088/0034-4885/72/6/066501	journal	May 2009
Physical Origin of Satellites in Photoemission of Doped Graphene: An Ab Initio $G W$ Plus Cumulant Study Lischner, Johannes; Vigil-Fowler, Derek; Louie, Steven G. Physical Review Letters, Vol. 110, Issue 14 https://doi.org/10.1103/PhysRevLett.110.146801	journal	April 2013
Satellite structures in the spectral functions of the two-dimensional electron gas in semiconductor quantum wells: A $G W$ plus cumulant study Lischner, Johannes; Vigil-Fowler, Derek; Louie, Steven G. Physical Review B, Vol. 89, Issue 12 https://doi.org/10.1103/PhysRevB.89.125430	journal	March 2014
Long-range quadrupole electron-phonon interaction from first principles Park, Jinsoo; Zhou, Jin-Jian; Jhalani, Vatsal A. Physical Review B, Vol. 102, Issue 12 https://doi.org/10.1103/PhysRevB.102.125203	journal	September 2020
Satellite band structure in silicon caused by electron-plasmon coupling Lischner, Johannes; Pálsson, G. K.; Vigil-Fowler, Derek Physical Review B, Vol. 91, Issue 20 https://doi.org/10.1103/PhysRevB.91.205113	journal	May 2015
Band Structures of Plasmonic Polarons Caruso, Fabio; Lambert, Henry; Giustino, Feliciano Physical Review Letters, Vol. 114, Issue 14 https://doi.org/10.1103/PhysRevLett.114.146404	journal	April 2015
Ab Initio Finite-Temperature Excitons Marini, Andrea Physical Review Letters, Vol. 101, Issue 10 https://doi.org/10.1103/PhysRevLett.101.106405	journal	September 2008
Cumulant Green's function calculations of plasmon satellites in bulk sodium: Influence of screening and the crystal environment Zhou, Jianqiang Sky; Gatti, Matteo; Kas, J. J. Physical Review B, Vol. 97, Issue 3 https://doi.org/10.1103/PhysRevB.97.035137	journal	January 2018
Dispersion and line shape of plasmon satellites in one, two, and three dimensions Vigil-Fowler, Derek; Louie, Steven G.; Lischner, Johannes Physical Review B, Vol. 93, Issue 23 https://doi.org/10.1103/PhysRevB.93.235446	journal	June 2016
XX. Properties of slow electrons in polar materials Fröhlich, H.; Pelzer, H.; Zienau, S. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Vol. 41, Issue 314 https://doi.org/10.1080/14786445008521794	journal	March 1950
Wannier interpolation of the electron-phonon matrix elements in polar semiconductors: Polar-optical coupling in GaAs Sjakste, J.; Vast, N.; Calandra, M. Physical Review B, Vol. 92, Issue 5 https://doi.org/10.1103/PhysRevB.92.054307	journal	August 2015
The Motion of Slow Electrons in Polar Crystals Lee, Tsung-Dao; Pines, David Physical Review, Vol. 88, Issue 4 https://doi.org/10.1103/PhysRev.88.960	journal	November 1952
Carrier Lifetimes and Polaronic Mass Enhancement in the Hybrid Halide Perovskite ${CH}_{3} {NH}_{3} {PbI}_{3}$ from Multiphonon Fröhlich Coupling Schlipf, Martin; Poncé, Samuel; Giustino, Feliciano Physical Review Letters, Vol. 121, Issue 8 https://doi.org/10.1103/PhysRevLett.121.086402	journal	August 2018
Crossover from lattice to plasmonic polarons of a spin-polarised electron gas in ferromagnetic EuO Riley, J. M.; Caruso, F.; Verdi, C. Nature Communications, Vol. 9, Issue 1 https://doi.org/10.1038/s41467-018-04749-w	journal	June 2018
Phonon-dressed two-dimensional carriers on the ZnO surface Yukawa, R.; Ozawa, K.; Yamamoto, S. Physical Review B, Vol. 94, Issue 16 https://doi.org/10.1103/PhysRevB.94.165313	journal	October 2016
Fröhlich Electron-Phonon Vertex from First Principles Verdi, Carla; Giustino, Feliciano Physical Review Letters, Vol. 115, Issue 17 https://doi.org/10.1103/PhysRevLett.115.176401	journal	October 2015
Interfacial mode coupling as the origin of the enhancement of Tc in FeSe films on SrTiO3 Lee, J. J.; Schmitt, F. T.; Moore, R. G. Nature, Vol. 515, Issue 7526 https://doi.org/10.1038/nature13894	journal	November 2014
Superconductivity in Semiconducting SrTi $O_{3}$ Schooley, J. F.; Hosler, W. R.; Cohen, Marvin L. Physical Review Letters, Vol. 12, Issue 17 https://doi.org/10.1103/PhysRevLett.12.474	journal	April 1964
Ab Initio Electron-Phonon Interactions in Correlated Electron Systems Zhou, Jin-Jian; Park, Jinsoo; Timrov, Iurii Physical Review Letters, Vol. 127, Issue 12 https://doi.org/10.1103/PhysRevLett.127.126404	journal	September 2021
Electron-phonon interactions from first principles Giustino, Feliciano Reviews of Modern Physics, Vol. 89, Issue 1 https://doi.org/10.1103/RevModPhys.89.015003	journal	February 2017
A Difficulty in Fröhlich's Theory of Superconductivity Kohn, W. Physical Review, Vol. 83, Issue 2 https://doi.org/10.1103/PhysRev.83.462	journal	July 1951
Two-dimensional electron gas with universal subbands at the surface of SrTiO₃ Santander-Syro, A. F.; Copie, O.; Kondo, T. Nature, Vol. 469, Issue 7329, p. 189-193 https://doi.org/10.1038/nature09720	journal	January 2011
Angle-resolved photoemission studies of the cuprate superconductors Damascelli, Andrea; Hussain, Zahid; Shen, Zhi-Xun Reviews of Modern Physics, Vol. 75, Issue 2 https://doi.org/10.1103/RevModPhys.75.473	journal	April 2003
Phonon-induced renormalization of electron wave functions Lihm, Jae-Mo; Park, Cheol-Hwan Physical Review B, Vol. 101, Issue 12 https://doi.org/10.1103/PhysRevB.101.121102	journal	March 2020
Creation and control of a two-dimensional electron liquid at the bare SrTiO3 surface Meevasana, W.; King, P. D. C.; He, R. H. Nature Materials, Vol. 10, Issue 2 https://doi.org/10.1038/nmat2943	journal	January 2011
Phase Transition and Padé Approximants for Fröhlich Polarons Selyugin, O. V.; Smondyrev, M. A. physica status solidi (b), Vol. 155, Issue 1 https://doi.org/10.1002/pssb.2221550114	journal	September 1989
Singularities in the X-Ray Spectra of Metals Langreth, David C. Physical Review B, Vol. 1, Issue 2 https://doi.org/10.1103/PhysRevB.1.471	journal	January 1970
On the combined use of GW approximation and cumulant expansion in the calculations of quasiparticle spectra: The paradigm of Si valence bands Gumhalter, Branko; Kovač, Vjekoslav; Caruso, Fabio Physical Review B, Vol. 94, Issue 3 https://doi.org/10.1103/PhysRevB.94.035103	journal	July 2016
Dynamical effects in electron spectroscopy Zhou, Jianqiang Sky; Kas, J. J.; Sponza, Lorenzo The Journal of Chemical Physics, Vol. 143, Issue 18 https://doi.org/10.1063/1.4934965	journal	November 2015
High Mobility in ${LaAlO}_{3} / {SrTiO}_{3}$ Heterostructures: Origin, Dimensionality, and Perspectives Herranz, G.; Basletić, M.; Bibes, M. Physical Review Letters, Vol. 98, Issue 21, Article No. 216803 https://doi.org/10.1103/PhysRevLett.98.216803	journal	May 2007
Slow Electrons in a Polar Crystal Feynman, R. P. Physical Review, Vol. 97, Issue 3 https://doi.org/10.1103/PhysRev.97.660	journal	February 1955
The GW plus cumulant method and plasmonic polarons: application to the homogeneous electron gas* Caruso, Fabio; Giustino, Feliciano The European Physical Journal B, Vol. 89, Issue 11 https://doi.org/10.1140/epjb/e2016-70028-4	journal	November 2016
Solids with thermal or static disorder. I. One-electron properties Allen, P. B. Physical Review B, Vol. 18, Issue 10 https://doi.org/10.1103/PhysRevB.18.5217	journal	November 1978
Polarons in materials Franchini, Cesare; Reticcioli, Michele; Setvin, Martin Nature Reviews Materials, Vol. 6, Issue 7 https://doi.org/10.1038/s41578-021-00289-w	journal	March 2021
Fermi Surface and Some Simple Equilibrium Properties of a System of Interacting Fermions Luttinger, J. M. Physical Review, Vol. 119, Issue 4 https://doi.org/10.1103/PhysRev.119.1153	journal	August 1960
Origin of the crossover from polarons to Fermi liquids in transition metal oxides Verdi, Carla; Caruso, Fabio; Giustino, Feliciano Nature Communications, Vol. 8, Issue 1 https://doi.org/10.1038/ncomms15769	journal	June 2017
Polaron spectral properties in doped ZnO and ${SrTiO}_{3}$ from first principles Antonius, Gabriel; Chan, Yang-Hao; Louie, Steven G. Physical Review Research, Vol. 2, Issue 4 https://doi.org/10.1103/PhysRevResearch.2.043296	journal	December 2020
Electron-Phonon beyond Fröhlich: Dynamical Quadrupoles in Polar and Covalent Solids Brunin, Guillaume; Miranda, Henrique Pereira Coutada; Giantomassi, Matteo Physical Review Letters, Vol. 125, Issue 13 https://doi.org/10.1103/PhysRevLett.125.136601	journal	September 2020
Tunable Polaronic Conduction in Anatase ${TiO}_{2}$ Moser, S.; Moreschini, L.; Jaćimović, J. Physical Review Letters, Vol. 110, Issue 19 https://doi.org/10.1103/PhysRevLett.110.196403	journal	May 2013
Theory of Superconductivity Bardeen, J.; Cooper, L. N.; Schrieffer, J. R. Physical Review, Vol. 108, Issue 5 https://doi.org/10.1103/PhysRev.108.1175	journal	December 1957
Cumulant expansion for phonon contributions to the electron spectral function Story, S. M.; Kas, J. J.; Vila, F. D. Physical Review B, Vol. 90, Issue 19 https://doi.org/10.1103/PhysRevB.90.195135	journal	November 2014
Theory of the temperature dependence of electronic band structures Allen, P. B.; Heine, V. Journal of Physics C: Solid State Physics, Vol. 9, Issue 12 https://doi.org/10.1088/0022-3719/9/12/013	journal	June 1976
Predicting charge transport in the presence of polarons: The beyond-quasiparticle regime in ${SrTiO}_{3}$ Zhou, Jin-Jian; Bernardi, Marco Physical Review Research, Vol. 1, Issue 3 https://doi.org/10.1103/PhysRevResearch.1.033138	journal	December 2019
Diagrammatic quantum Monte Carlo study of the Fröhlich polaron Mishchenko, A.; Prokof’ev, N.; Sakamoto, A. Physical Review B, Vol. 62, Issue 10 https://doi.org/10.1103/PhysRevB.62.6317	journal	September 2000
Electron-plasmon and electron-phonon satellites in the angle-resolved photoelectron spectra of $n$ -doped anatase ${TiO}_{2}$ Caruso, Fabio; Verdi, Carla; Poncé, Samuel Physical Review B, Vol. 97, Issue 16 https://doi.org/10.1103/PhysRevB.97.165113	journal	April 2018
Polaron Problem by Diagrammatic Quantum Monte Carlo Prokof'ev, Nikolai V.; Svistunov, Boris V. Physical Review Letters, Vol. 81, Issue 12 https://doi.org/10.1103/PhysRevLett.81.2514	journal	September 1998
Unraveling intrinsic correlation effects with angle-resolved photoemission spectroscopy Zhou, Jianqiang Sky; Reining, Lucia; Nicolaou, Alessandro Proceedings of the National Academy of Sciences, Vol. 117, Issue 46 https://doi.org/10.1073/pnas.2012625117	journal	October 2020
A high-mobility electron gas at the LaAlO3/SrTiO3 heterointerface Ohtomo, A.; Hwang, H. Y. Nature, Vol. 427, Issue 6973 https://doi.org/10.1038/nature02308	journal	January 2004
Theory of the Superconducting State. I. The Ground State at the Absolute Zero of Temperature Fröhlich, H. Physical Review, Vol. 79, Issue 5 https://doi.org/10.1103/PhysRev.79.845	journal	September 1950
Many-body large polaron optical conductivity in ${SrTi}_{1 - x} {Nb}_{x} O_{3}$ Devreese, J. T.; Klimin, S. N.; van Mechelen, J. L. M. Physical Review B, Vol. 81, Issue 12 https://doi.org/10.1103/PhysRevB.81.125119	journal	March 2010
Predominance of non-adiabatic effects in zero-point renormalization of the electronic band gap Miglio, Anna; Brousseau-Couture, Véronique; Godbout, Emile npj Computational Materials, Vol. 6, Issue 1 https://doi.org/10.1038/s41524-020-00434-z	journal	November 2020
Theory of electron-plasmon coupling in semiconductors Caruso, Fabio; Giustino, Feliciano Physical Review B, Vol. 94, Issue 11 https://doi.org/10.1103/PhysRevB.94.115208	journal	September 2016
Polaronic metal state at the LaAlO3/SrTiO3 interface Cancellieri, C.; Mishchenko, A. S.; Aschauer, U. Nature Communications, Vol. 7, Issue 1 https://doi.org/10.1038/ncomms10386	journal	January 2016
Effects of Recoil on Shake-Up Spectra in Metals Hedin, Lars Physica Scripta, Vol. 21, Issue 3-4 https://doi.org/10.1088/0031-8949/21/3-4/039	journal	January 1980
Electron-polaron dichotomy of charge carriers in perovskite oxides Husanu, M. -A.; Vistoli, L.; Verdi, C. Communications Physics, Vol. 3, Issue 1 https://doi.org/10.1038/s42005-020-0330-6	journal	April 2020
Nonlinear response in the cumulant expansion for core-level photoemission Tzavala, Marilena; Kas, J. J.; Reining, Lucia Physical Review Research, Vol. 2, Issue 3 https://doi.org/10.1103/PhysRevResearch.2.033147	journal	July 2020
Quasiparticles and phonon satellites in spectral functions of semiconductors and insulators: Cumulants applied to the full first-principles theory and the Fröhlich polaron Nery, Jean Paul; Allen, Philip B.; Antonius, Gabriel Physical Review B, Vol. 97, Issue 11 https://doi.org/10.1103/PhysRevB.97.115145	journal	March 2018

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