Bloch Oscillations in Fibonacci lattices: polaron formation

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.