Polaron properties in 2D organic molecular crystals: directional dependence of non-local electron–phonon coupling

  • Marcelo Lopes Pereira JuniorEmail author
  • Rafael Timóteo de Sousa Júnior
  • Bernhard Georg Enders Neto
  • Geraldo Magela e Silva
  • Luiz Antonio Ribeiro Junior
Original Paper
Part of the following topical collections:
  1. VII Symposium on Electronic Structure and Molecular Dynamics – VII SeedMol


In organic molecular crystals, the polaronic hopping model for the charge transport assumes that the carrier lies at one or a small number of molecules. Such a kind of localization suffers the influence of the non-local electron–phonon (e–ph) interactions associated with intermolecular lattice vibrations. Here, we developed a model Hamiltonian for numerically describing the role played by the intermolecular e–ph interactions on the stationary and dynamical properties of polarons in a two-dimensional array of molecules. We allow three types of electron hopping mechanisms and, consequently, for the nonlocal e–ph interactions: horizontal, vertical, and diagonal. Remarkably, our findings show that the stable polarons are not formed for isotropic arrangements of the intermolecular transfer integrals, regardless of the strengths of the e–ph interactions. Interestingly, the diagonal channel for the e–ph interactions changes the transport mechanism by sharing the polaronic charge between parallel molecular lines in a breather-like mode.


Holstein–Peierls model Polaron Electron–phonon coupling Charge transport Organic semiconductors 



The authors gratefully acknowledge the financial support from Brazilian Research Councils CNPq, CAPES, and FAP-DF and CENAPAD-SP for providing the computational facilities. This research work has the support of the Brazilian Ministry of Planning, Development and Management (Grants 005/2016 DIPLA – Planning and Management Directorate, and 11/2016 SEST – State-owned Federal Companies Secretariat) and the DPGU – Brazilian Union Public Defender (Grant 066/2016). L.A.R.J. and G.M.S. gratefully acknowledge the financial support from FAP-DF grants 0193.001.511/2017 and 0193.001.766/2017, respectively.


  1. 1.
    Coropceanu V, Cornil J, da Silva Filho DA, Olivier Y, Silbey R, Brédas JL (2007) . Chem Rev 107:926. CrossRefGoogle Scholar
  2. 2.
    Li Y, Coropceanu V, Brédas JL (2013) . J Chem Phys 138:204713. CrossRefGoogle Scholar
  3. 3.
    Li Y, Yi Y, Coropceanu V, Brédas JL (2012) . Phys Rev B 85:245201. CrossRefGoogle Scholar
  4. 4.
    Stafström S (2010) . Chem Soc Rev 39:2484. CrossRefGoogle Scholar
  5. 5.
    Troisi A (2011) . Chem Soc Rev 40:2347. CrossRefGoogle Scholar
  6. 6.
    Nelson SF, Lin YY, Gundlach DJ, Jackson TN (1998) . Appl Phys Lett 72:1854. CrossRefGoogle Scholar
  7. 7.
    Castet F, Aurel P, Fritsch A, Ducasse L, Liotard D, Linares M, Cornil J, Beljonne D (2008) . Phys Rev B 77:115210. CrossRefGoogle Scholar
  8. 8.
    Podzorov V, Gershenson ME, Kloc C, Bucher E (2004) . Appl Phys Lett 84:3301. CrossRefGoogle Scholar
  9. 9.
    Sanchez-Carrera RS, Paramonov P, Day GM, Coropceanu V, Brédas JL (2010) . J Amer Chem Soc 132:14437. CrossRefGoogle Scholar
  10. 10.
    Sanchez-Carrera RS, Coropceanu V, da Silva Filho DA, Friedlein R, Osikowicz W, Murdey R, Suess C, Salaneck WR, Brédas JL (2006) . J Phys Chem B 110:18904. CrossRefGoogle Scholar
  11. 11.
    Riedmiller M, Braun H (1993) . Proc IEEE Inte Conf Neural Netw 1:586. CrossRefGoogle Scholar
  12. 12.
    da Cunha WF, Junior LAR, Gargano R, e Silva GM (2014) . Phys Chem Chem Phys 16:1707. CrossRefGoogle Scholar
  13. 13.
  14. 14.
  15. 15.
    Gruhn NE, da Silva Filho DA, Bill TG, Malagoli M, Coropceanu V, Kahn A, Brédas JL (2001) . J Amer Chem Soc 124:7918. CrossRefGoogle Scholar
  16. 16.
    Pereira Junior ML, de Sousa Junior RT, e Silva GM, Ribeiro Junior LA (2019) . Phys Chem Chem Phys 21:2727. CrossRefGoogle Scholar
  17. 17.
    Junior LAR, Stafström S (2015) Phys. Chem Chem Phys 17:8973. CrossRefGoogle Scholar
  18. 18.
    Junior LAR, Stafström S (2016) . Phys Chem Chem Phys 18:1386. CrossRefGoogle Scholar
  19. 19.
    Mozafari E, Stafström S (2013) . J Chem Phys 138:184104. CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute of PhysicsUniversity of BrasíliaBrasíliaBrazil
  2. 2.Department of Electrical EngineeringUniversity of BrasíliaBrasíliaBrazil
  3. 3.University of Brasília, PPG-CIMA, Campus PlanaltinaBrasíliaBrazil
  4. 4.International Center for Condensed Matter PhysicsUniversity of BrasíliaBrasíliaBrazil

Personalised recommendations