Bloch Oscillations in Fibonacci lattices: polaron formation

  • Paulo Eduardo de BritoEmail author
  • Bernhard Georg Enders
  • Luiz Antonio RibeiroJr
  • Hugo Nicolas Nazareno
Original Paper
Part of the following topical collections:
  1. VII Symposium on Electronic Structure and Molecular Dynamics – VII SeedMol


We investigated the dynamics of an electron subjected to a uniform electric field in the scope of a tight-binding electron–phonon interacting approach. We aimed at describing the transport in a one-dimensional lattice in which the on-site energies are distributed according to a Fibonacci sequence. Within this physical picture, we obtained a novel dynamical process with no counterpart in ordered lattices. Our findings showed that in low-disorder limit, the electron performs spatial Bloch oscillations, generating, in the turning points of its trajectory, composite quasi-particles—namely, polarons. When it comes to highly disordered systems, two strongly localized polarons are formed in the region where the oscillating charge is confined, thus propagating excitations that are present in the lattice.


Low-dimensional systems Electron–phonon interactions Bloch Oscillations Polarons 



The authors gratefully acknowledge the financial support from the Brazilian Research Councils CNPq, CAPES, and FINATEC. B.G.E and L.A.R.J gratefully acknowledge the financial support from the Brazilian Research Council FAPDF grants 193.001.556/2017 and 193.001.511/2017. L.A.R.J. also wish to thank the Brazilian Ministry of Planning, Budget and Management (Grant DIPLA 005/2016).


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Copyright information

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

Authors and Affiliations

  1. 1.Faculty of PlanaltinaUniversity of BrasiliaBrasiliaBrazil
  2. 2.International Center for Condensed Matter PhysicsUniversity of BrasiliaBrasiliaBrazil

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