Subsonic and supersonic polarons in one-electron model of polyacetylene
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THE EUROPEAN PHYSICAL JOURNAL B
Regular Article
Subsonic and supersonic polarons in one-electron model of polyacetylene Tatiana Astakhova a and George Vinogradov Emanuel Institute of Biochemical Physics RAS, Moscow, Russia
Received 5 March 2020 / Received in final form 28 April 2020 Published online 6 July 2020 c EDP Sciences / Societ`
a Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 2020 Abstract. Free-moving polarons are investigated in the framework of new one-electron model of conjugated polymers. It is shown that on a dimerized lattice there exist free (in the absence of an external force like an electric field) stationary polarons, both subsonic and supersonic. Subsonic free polarons are observed in the velocity range from 0 to the speed of sound. Supersonic free polarons are observed in a limited range of velocities. There is a range of forbidden velocities between subsonic and supersonic free polarons. An analytical expression for the free polaron shape at different velocities is derived and confirmed in molecular dynamics simulations. The dynamics of subsonic and supersonic polarons in an electric field is different. It is shown that the subsonic polaron motion is not stationary and the velocity oscillations are associated with the periodic emission of tensile impulses in front of the polaron, taking away the energy received from the electric field. The supersonic polaron motion is stationary and the energy gained from the electric field is permanently transformed into oscillations behind the polaron.
1 Introduction There is a large family of polymers with conjugated single and double bonds. The most famous example is polyacetylene (PA) with the structural formula (−CH = CH−)n . PA plays an important role in both practical applications and especially in the theory of one-dimensional manyelectron systems. Of greatest interest was the discovery of the transition of PA from a wide-gap semiconductor (∆E ≈ 2.4 eV) to a conducting state with a specific conductivity comparable to the conductivity of metals under doping [1–3]. This discovery has generated great interest to the theory of many-electron systems and the reasons for the increase in conductivity by ∼10 orders of magnitude upon doping. Since that time, a large number of organic conducting polymers have been obtained, such as polypyrrole, polythiophene, polyanilines, etc. They are of great potential application and have been used as organic light emitting diodes, field-effect transistors, solar cells [4]. Also they have been used in various biomedical devices [5]. This progress stimulated a large number of studies both in the theory of charge transport in organic conducting polymers and in material science. Currently, the polaron model of charge transfer in conductive polymers is a dominant paradigm. Polarons are formed as a result of doping, when an acceptor or donor, a
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receives or gives an additional electron to the polymer chain. As a result of the electron-phonon interaction, the la
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