Polarons in a one-dimensional quasiperiodic model

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Abstract
We considered the coupled motion of an electron described by a one-dimensional (1D) tight-binding Hamiltonian, whose diagonal matrix elements have a spatial variation incommensurate with the lattice, and a harmonic 1D lattice. The coupling was taken to be of the deformation-potential type. We studied numerically the time evolution of the coupled system starting with the lattice in its classical ground state and the electron in various initial states. Depending on the initial energy of the electron, on how close to the mobility edge it is and the strength of electron-lattice coupling, we found different types of localized and apparently extended (large) polarons. Near the mobility edge even a very weak coupling suffices to create a localized polaron even for high initial electronic energies. In many instances and even for very long times the electron does not seem to transfer much of its energy to the lattice.