User menu

Accès à distance ? S'identifier sur le proxy UCLouvain

Many-body perturbation theory approach to the electron-phonon interaction with density-functional theory as a starting point

Primary tabs

Marini, Andrea [Istituto di Struttura della Materia of the National Research Council, Monterotondo Stazione, Italy] Poncé, Samuel [UCL] Gonze, Xavier [UCL]

The electron–phonon interaction plays a crucial role in many fields of physics and chemistry. Nevertheless, its actual calculation by means of modern many–body perturbation theory is weakened by the use of model Hamiltonians that are based on parameters difficult to extract from the experiments. Such shortcoming can be bypassed by using density–functional theory to evaluate the electron–phonon scattering amplitudes, phonon frequencies and electronic bare energies. In this work, we discuss how a consistent many–body diagrammatic expansion can be constructed on top of density–functional theory. In that context, the role played by screening and self–consistency when all the components of the electron–nucleus and nucleus–nucleus interactions are taken into account is paramount. A way to avoid overscreening is notably presented. Finally, we derive cancellations rules as well as internal consistency constraints in order to draw a clear, sound and practical scheme to merge many–body perturbation and density–functional theory.

Document type Article de périodique (Journal article) – Article de recherche
Access type Accès restreint
Publication date 2015
Language Anglais
Journal information "Physical review. B, Condensed matter and materials physics" - Vol. 91, no.22, p. 224310 (2015)
Peer reviewed yes
Publisher American institute of physics
issn 1098-0121
e-issn 1550-235X
Publication status Publié
Affiliation UCL - SST/IMCN/NAPS - Nanoscopic Physics
Links
  1. J. Ziman, Electrons and Phonons: The Theory of Transport Phenomena in Solids (1960)
  2. Mitsuhashi Ryoji, Suzuki Yuta, Yamanari Yusuke, Mitamura Hiroki, Kambe Takashi, Ikeda Naoshi, Okamoto Hideki, Fujiwara Akihiko, Yamaji Minoru, Kawasaki Naoko, Maniwa Yutaka, Kubozono Yoshihiro, Superconductivity in alkali-metal-doped picene, 10.1038/nature08859
  3. Allen P. B., Cardona M., Temperature dependence of the direct gap of Si and Ge, 10.1103/physrevb.27.4760
  4. Gosar P., Choi Sang-il, Linear-Response Theory of the Electron Mobility in Molecular Crystals, 10.1103/physrev.150.529
  5. Tamura Hiroyuki, Ramon John G. S., Bittner Eric R., Burghardt Irene, Phonon-Driven Ultrafast Exciton Dissociation at Donor-Acceptor Polymer Heterojunctions, 10.1103/physrevlett.100.107402
  6. Adachi Hiroto, Uchida Ken-ichi, Saitoh Eiji, Maekawa Sadamichi, Theory of the spin Seebeck effect, 10.1088/0034-4885/76/3/036501
  7. Bernardi Marco, Vigil-Fowler Derek, Lischner Johannes, Neaton Jeffrey B., Louie Steven G., Ab InitioStudy of Hot Carriers in the First Picosecond after Sunlight Absorption in Silicon, 10.1103/physrevlett.112.257402
  8. Sangalli D., Marini A., Ultra-fast carriers relaxation in bulk silicon following photo-excitation with a short and polarized laser pulse, 10.1209/0295-5075/110/47004
  9. Moser S., Moreschini L., Jaćimović J., Barišić O. S., Berger H., Magrez A., Chang Y. J., Kim K. S., Bostwick A., Rotenberg E., Forró L., Grioni M., Tunable Polaronic Conduction in AnataseTiO2, 10.1103/physrevlett.110.196403
  10. Cannuccia Elena, Marini Andrea, Effect of the Quantum Zero-Point Atomic Motion on the Optical and Electronic Properties of Diamond and Trans-Polyacetylene, 10.1103/physrevlett.107.255501
  11. Cannuccia E., Marini A., Zero point motion effect on the electronic properties of diamond, trans-polyacetylene and polyethylene, 10.1140/epjb/e2012-30105-4
  12. Dreizler Reiner M., Gross Eberhard K. U., Density Functional Theory, ISBN:9783642861079, 10.1007/978-3-642-86105-5
  13. Onida Giovanni, Reining Lucia, Rubio Angel, Electronic excitations: density-functional versus many-body Green’s-function approaches, 10.1103/revmodphys.74.601
  14. Baroni Stefano, Giannozzi Paolo, Testa Andrea, Green’s-function approach to linear response in solids, 10.1103/physrevlett.58.1861
  15. Gonze Xavier, First-principles responses of solids to atomic displacements and homogeneous electric fields: Implementation of a conjugate-gradient algorithm, 10.1103/physrevb.55.10337
  16. Baroni Stefano, de Gironcoli Stefano, Dal Corso Andrea, Giannozzi Paolo, Phonons and related crystal properties from density-functional perturbation theory, 10.1103/revmodphys.73.515
  17. van Schilfgaarde M., Kotani Takao, Faleev S., Quasiparticle Self-ConsistentGWTheory, 10.1103/physrevlett.96.226402
  18. Grüning Myrta, Marini Andrea, Rubio Angel, Effect of spatial nonlocality on the density functional band gap, 10.1103/physrevb.74.161103
  19. Niquet Y. M., Gonze X., Band-gap energy in the random-phase approximation to density-functional theory, 10.1103/physrevb.70.245115
  20. Cardona M., Lastras-Martínez L. F., Aspnes D. E., Comment on “Ab InitioCalculation of Excitonic Effects in the Optical Spectra of Semiconductors”, 10.1103/physrevlett.83.3970
  21. Gonze X., Boulanger P., Côté M., Theoretical approaches to the temperature and zero-point motion effects on the electronic band structure, 10.1002/andp.201000100
  22. Giustino Feliciano, Louie Steven G., Cohen Marvin L., Electron-Phonon Renormalization of the Direct Band Gap of Diamond, 10.1103/physrevlett.105.265501
  23. Poncé S., Antonius G., Boulanger P., Cannuccia E., Marini A., Côté M., Gonze X., Verification of first-principles codes: Comparison of total energies, phonon frequencies, electron–phonon coupling and zero-point motion correction to the gap between ABINIT and QE/Yambo, 10.1016/j.commatsci.2013.11.031
  24. Antonius G., Poncé S., Boulanger P., Côté M., Gonze X., Many-Body Effects on the Zero-Point Renormalization of the Band Structure, 10.1103/physrevlett.112.215501
  25. Miller Daniel R., The Chromium Isotope of Mass 55, 10.1103/physrev.78.808
  26. Fan H. Y., Temperature Dependence of the Energy Gap in Semiconductors, 10.1103/physrev.82.900
  27. E. Antoncík, Cechoslovackij Fiziceskij Zurnal, 5, 449 (1955)
  28. Keffer Charles, Hayes Timothy M., Bienenstock Arthur, PbTe Debye-Waller Factors and Band-Gap Temperature Dependence, 10.1103/physrevlett.21.1676
  29. Walter John P., Zucca Ricardo R. L., Cohen Marvin L., Shen Y. R., Temperature Dependence of the Wavelength-Modulation Spectra of GaAs, 10.1103/physrevlett.24.102
  30. Kasowski R. V., Band Structure of NiS as Calculated Using a Simplified Linear-Combination-of-Muffin-Tin-Orbitals Method, 10.1103/physrevb.8.1378
  31. Allen P B, Heine V, Theory of the temperature dependence of electronic band structures, 10.1088/0022-3719/9/12/013
  32. Allen P. B., Cardona M., Theory of the temperature dependence of the direct gap of germanium, 10.1103/physrevb.23.1495
  33. Lautenschlager P., Allen P. B., Cardona M., Temperature dependence of band gaps in Si and Ge, 10.1103/physrevb.31.2163
  34. Zollner Stefan, Cardona Manuel, Gopalan Sudha, Isotope and temperature shifts of direct and indirect band gaps in diamond-type semiconductors, 10.1103/physrevb.45.3376
  35. King-Smith R. D, Needs R. J, Heine V, Hodgson M. J, A First-Principle Calculation of the Temperature Dependence of the Indirect Band Gap of Silicon, 10.1209/0295-5075/10/6/011
  36. Franceschetti A., First-principles calculations of the temperature dependence of the band gap of Si nanocrystals, 10.1103/physrevb.76.161301
  37. Kamisaka Hideyuki, Kilina Svetlana V., Yamashita Koichi, Prezhdo Oleg V., Ab Initio Study of Temperature and Pressure Dependence of Energy and Phonon-Induced Dephasing of Electronic Excitations in CdSe and PbSe Quantum Dots†, 10.1021/jp710435q
  38. Ibrahim Z. A., Shkrebtii A. I., Lee M. J. G., Vynck K., Teatro T., Richter W., Trepk T., Zettler T., Temperature dependence of the optical response: Application to bulk GaAs using first-principles molecular dynamics simulations, 10.1103/physrevb.77.125218
  39. Ramírez Rafael, Herrero Carlos P., Hernández Eduardo R., Path-integral molecular dynamics simulation of diamond, 10.1103/physrevb.73.245202
  40. Ramírez Rafael, Herrero Carlos P., Hernández Eduardo R., Cardona Manuel, Path-integral molecular dynamics simulation of3C−SiC, 10.1103/physrevb.77.045210
  41. Monserrat Bartomeu, Drummond N. D., Needs R. J., Anharmonic vibrational properties in periodic systems: energy, electron-phonon coupling, and stress, 10.1103/physrevb.87.144302
  42. Capaz Rodrigo B., Spataru Catalin D., Tangney Paul, Cohen Marvin L., Louie Steven G., Temperature Dependence of the Band Gap of Semiconducting Carbon Nanotubes, 10.1103/physrevlett.94.036801
  43. Patrick Christopher E., Giustino Feliciano, Quantum nuclear dynamics in the photophysics of diamondoids, 10.1038/ncomms3006
  44. Han Peng, Bester Gabriel, Large nuclear zero-point motion effect in semiconductor nanoclusters, 10.1103/physrevb.88.165311
  45. Poncé S., Antonius G., Gillet Y., Boulanger P., Laflamme Janssen J., Marini A., Côté M., Gonze X., Temperature dependence of electronic eigenenergies in the adiabatic harmonic approximation, 10.1103/physrevb.90.214304
  46. Kawai Hiroki, Yamashita Koichi, Cannuccia Elena, Marini Andrea, Electron-electron and electron-phonon correlation effects on the finite-temperature electronic and optical properties of zinc-blende GaN, 10.1103/physrevb.89.085202
  47. Marini Andrea, Ab InitioFinite-Temperature Excitons, 10.1103/physrevlett.101.106405
  48. R. Mattuck, A Guide to Feynman Diagrams in the Many-Body Problem (1976)
  49. A. L. Fetter, Quantum Theory of Many-Particles Systems (1971)
  50. Mahan Gerald D., Many-Particle Physics, ISBN:9781441933393, 10.1007/978-1-4757-5714-9
  51. Allen P. B., Solids with thermal or static disorder. I. One-electron properties, 10.1103/physrevb.18.5217
  52. van Leeuwen Robert, First-principles approach to the electron-phonon interaction, 10.1103/physrevb.69.115110
  53. L. Hedin, Solid State Physics (1969)
  54. Aryasetiawan F, Gunnarsson O, TheGWmethod, 10.1088/0034-4885/61/3/002
  55. Ceperley D. M., Alder B. J., Ground State of the Electron Gas by a Stochastic Method, 10.1103/physrevlett.45.566
  56. Perdew J. P., Zunger Alex, Self-interaction correction to density-functional approximations for many-electron systems, 10.1103/physrevb.23.5048
  57. Gonze Xavier, Adiabatic density-functional perturbation theory, 10.1103/physreva.52.1096
  58. Strinati G., Application of the Green’s functions method to the study of the optical properties of semiconductors, 10.1007/bf02725962
  59. Hybertsen Mark S., Louie Steven G., Ab initiostatic dielectric matrices from the density-functional approach. I. Formulation and application to semiconductors and insulators, 10.1103/physrevb.35.5585
  60. Ghosez Ph., Gonze X., Godby R. W., Long-wavelength behavior of the exchange-correlation kernel in the Kohn-Sham theory of periodic systems, 10.1103/physrevb.56.12811
Bibliographic reference Marini, Andrea ; Poncé, Samuel ; Gonze, Xavier. Many-body perturbation theory approach to the electron-phonon interaction with density-functional theory as a starting point. In: Physical review. B, Condensed matter and materials physics, Vol. 91, no.22, p. 224310 (2015)
Permanent URL http://hdl.handle.net/2078.1/167906