1. Nonlinear transport by solitons in nanofibers of the polyacethylene at high magnetic fields. N. Kirova Laboratoire de Physique des Solides CNRS & Université Paris-Sud, Orsay France

2. 2 Materials:K. Akagi groupKyoto, Japan Experiment:Y. W. Park group J. S. Brooks A.N. Aleshin, Seoul, South Korea NHMFL, US St. Petersbourg, Russia Theory :N. Kirova & S. BrazovskiiOrsay, France

3. The high magnetic field HMF is not responsible for the effects to be reported. This is the high electric field which makes the job. But : the HMF made the events visible and brought the challenge to understand them. The synergy typical for "synthetic metals":  New synthesis of a conducting polymer,  New way to split nano-scale fibers,  High electric field transforming the electronic state,  High magnetic field separating spin- versus spinless carriers,  Theory of solitons and of their confinement - deconfinement adapting from 1D models to 3D reality Vanishing magnetoresistance in high electric and magnetic fields

4. Single fiber: l  10  m;  <100 nm Inside:  10 3 chains of the (CH)x New helicoidal polyacethelene PA (K. Akagi) - multi-scale material: cells -> spirals -> threads -> crystalline fibers -> polymer chains ->  -electrons -> Peierls-SSH dimerization -> solitons -> confinement

5. 1% Doped PA – (I-V) and magnetoresistance (H,T) E  1.7x10 4 V/cm Transverse ○ and longitudinal □ magnetoresistance 5 Spin, not an orbital origin Nonlinear I-V at E>10 4 V/cm Saturation by T=10K -> quantum tunneling ! Terra incognita – spin MR in nonlinear, particularly quantum, regime

6. 6 T=1.5 K – quantum nonlinear regime Why the MR is so high at E>20kV/cm? Why the MR vanishes at E>23kV/cm ? E ( V/cm) A 2.00 × 10 4 B 2.35 × 10 4 C 2.50 × 10 4 D 2.80 × 10 4 E 3.05 × 10 4

7. Polyaniline (PANI) Nanofibers NHMFL/FSU, Tallahassee, FL E (V/cm) A1.25x10 5 B1.50x10 5 C1.75x10 5 D2.00x10 5

8. 8 Solitons and polarons at an isolated (CH) x chain E b =0    Split-off intra-gap bound states at levels ±E b Spinless solitons would be favorite charge carries for an unperturbed chain. The higher energy Polarons (charge e, spin ½) enter the game thanks to Coulomb attraction from charged dopants. Only they bring the spin and the magnetoresistance Spontaneous symmetry breaking gives rise to solitons – kinks between domains of opposite dimerizations. In PA - identified by spectroscopy and ESR. specific Non-specific

9. In-phase Out of phase Crystal of interacting chains brings confinement of solitons into pairs. In-between the kinks, the interchain correlation is broken, hence the confinement energy W cnf = F|x|; For one soliton, the confinement force F>0 is additive to the electric field E, hence erasable :W cnf + W E = F|x|-Ex, F -> G=F-E Solitons aggregated into domain walls in spin-polarized CDWs and spin-Peierls chains – successes of HMFs in NHMFL and Grenoble. (CH)x – 3D phase

10. 3D reality: interchain interactions - confinement force F≈2×10 5 V/cm 10 Neutral phase of trapped polarons P Ionic phase: deconfined bi-solitons (q=2e) occupy half of the dopants - CS Neutral phase of trapped deconfined solitons DS   L  x  ξ ξ

11. P DS E W W DS WPWP W CS Possible ground states P CS DS W E W DS W CS WPWP Deconfined solitons : Soliton at the dopant:

12. Tunneling conduction by polaron -> bisoliton transformations 12 Two trapped polarons. Transfer of the bound electron at E b <  -EL gain against repulsion U cost. E Emptified polaron shall vanishes leaving the nude dopant Overcharged polaron shall evolves into divergent solitons creating the CS complex at one dopant. The energy gain by evolving the intragap energy from E b =0.7  for polaron to E b -> 0 for solitons compensates for the e-e repulsion cost facilitating the tunneling. Kinetic, against equilibrium local transformation from P to CS phase.

13. confined deconfined tunneling deconfinement tunneling I-V G<e 2 /L 2 G>e 2 /ξL e 2 /L 2 < G < e 2 /L  13 Conduction by tunneling deconfinement of solitons

14. 14 E ( V/cm) A 2.00 × 10 4 B 2.35 × 10 4 C 2.50 × 10 4 D 2.80 × 10 4 E 3.05 × 10 4 E (V/cm) A1.25x10 5 B1.50x10 5 C1.75x10 5 D2.00x10 5 G=F-E

15. 15 Conclusion In the lightly doped conducting PA, three phases are possible: neutral polaronic phase, neutral solitonic phase, ionic bi-solitonic phase. Electric field erases the confinement force providing the crossover between different phases. At low electric field, charge carriers are polarons, giving rise the magnetoresistance. At high electric field – the crossover from polaronic phase to the deconfined solitons, (possibility via confined ionic phase), hence vanishing magnetoresistance. Tunneling deconfinement gives the nonlinear I-V in the spinless regime. Tunneling conversion of polarons into confined pair of solitons gives the nonlinear I-V in the spinful regime of the nonlinear magnetoresistance. Other polymers – non degenerated ground state, confinement is at least 10 times higher, electric fields in experiments are not enough.