April 2014 EPL, 106 (2014) 27004 www.epljournal.org doi: 10.1209/0295-5075/106/27004 On the electron transport in polydiacetylene crystals and derivatives M. G. Velarde 1,2 , A. P. Chetverikov 1,3 , W. Ebeling 1,4 , E. G. Wilson 1,5,6 and K. J. Donovan 5 1 Instituto Pluridisciplinar, Universidad Complutense - Paseo Juan XXIII, 1, Madrid-28040, Spain 2 Fundacion Universidad Alfonso X El Sabio - Villanueva de la Canada, Madrid-28691, Spain 3 Dept. of Physics, Saratov State University - Astrakhanskaya 83, Saratov-410012, Russia 4 Institut f¨ ur Physik, Humboldt-Universit¨ at Berlin - Newtonstrasse 15, Berlin-12489, Germany 5 School of Physics and Astronomy, Queen Mary University of London - Mile End Road, London E1 4NS, UK 6 New York University in London - 6 Bedford Square, London WC1B 3RA, UK received 21 October 2013; accepted in final form 5 April 2014 published online 22 April 2014 PACS 72.80.Le – Polymers; organic compounds (including organic semiconductors) PACS 72.20.Jv – Charge carriers: generation, recombination, lifetime, and trapping PACS 63.20.Ry – Anharmonic lattice modes Abstract – We provide here a theory to account for the thirty-year-old outstanding experimental results by Donovan and Wilson on the electron transport in polydiacetylene (PDA) single crystals. Both supersonic and subsonic velocities are described. In the former case we predict that the ve- locity is field independent for several decades of the field strength in accordance with experimental results. The results offer a novel form of electron transport in addition to the previously known form in (trans)polyacetylene and other conjugated polymers. Copyright c  EPLA, 2014 In this letter we discuss the possibility of subsonic and supersonic electron surfing on acoustic lattice solitons thus providing a theory to support the experimental results obtained long ago by Donovan and Wilson on polydiacety- lene (PDA) single crystals and some derivatives [1–4]. The results offer a novel form of electron transport in addition to the Heeger discovery in (trans)polyacetylene (tPA) and other conjugated polymers [5]. PDA crystals are composed of parallel long π conjugated carbon chains spaced apart by inert side groups. The in- terchain distance is sufficiently large so that π electron transfer between chains is not possible. Thus, they form a perfect scenario for the investigation of one-dimensional (1d) electron transport (figs. 1, 2) [6]. Experiments by Wilson and collaborators in the 1980s [1–4] were on the transient photo-conduction, over 10 time decades, of cur- rents induced by light pulses, of picoseconds to seconds. The photo-generation efficiency is linear in the field, as established by the “cuts” experiments on PDATS [1] and the “electronic walls” experiment in PDADCH [4]. The velocity is independent of the applied field over several orders of magnitude of the field. The initial current in- duced by the light pulse, i.e., the photo-efficiency of the generation multiplied by the velocity, is linear in the field. The low field mobility is ultra-high, i.e., higher than in any conventional semiconductor. Wilson [7] assumed that an electron self-traps in the acoustic distortion that it cre- ates in one such π conjugated carbon chain and travels, as a localized state, along the carbon backbone. Dissipa- tion was shown to be very weak, so the smallest field gives rise to a virtually constant velocity just below the sound velocity. Below we show that replacing the harmonic in- teractions in the lattice Hamiltonian [7] by Morse interac- tions, the self-trapping (polaron) effect is overwhelmed by a soliton-assisted process thus offering supersonic as well as subsonic electron transport. Since the experiments in the 1980s [1–4] few transport experiments have been performed. There are two prob- lems. First, it was difficult, in the 1980s experiments, to inject carriers from electrodes into the PDA. Also, unlike the standard conducting polymers, PDA cannot be chem- ically doped to create carriers. Indeed, these perfect 1d chains provide the electron high mobility; but the perfec- tion does not allow for doping. Second, due to the high perfection of the crystals, a kind of “queuing” is postulated to occur. Consider an electron on a particular chain to be trapped at some defect or chain end. Electrons travel- ling on adjacent chains then queue up behind the trapped 27004-p1