Nonlinear transport by solitons in nanofibers of the polyacethylene at high magnetic fields.

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

3. Vanishing magnetoresistance in high electric and magnetic fields • 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

4. New helicoidal polyacethelene PA (K. Akagi) - multi-scale material: cells -> spirals -> threads -> crystalline fibers -> polymer chains -> p-electrons -> Peierls-SSH dimerization -> solitons -> confinement Single fiber: l10mm;  <100 nm Inside:  103 chains of the (CH)x

5. 1% Doped PA – (I-V) and magnetoresistance (H,T) E  1.7x104 V/cm Nonlinear I-V at E>104V/cm Saturation by T=10K -> quantum tunneling ! Transverse ○ and longitudinal □ magnetoresistance Terra incognita – spin MR in nonlinear, particularly quantum, regime Spin, not an orbital origin

6. Why the MR is so high at E>20kV/cm? Why the MR vanishes at E>23kV/cm ? T=1.5 K – quantum nonlinear regime

7. Polyaniline (PANI) Nanofibers NHMFL/FSU, Tallahassee, FL

8. Solitons and polarons at an isolated (CH)x chain Split-off intra-gap bound states at levels ±Eb D Spontaneous symmetry breaking gives rise to solitons – kinks between domains of opposite dimerizations. In PA - identified by spectroscopy and ESR. -D specific Eb=0 Spinless solitons would be favorite charge carries for an unperturbed chain. Non-specific D D 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

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

10. 3D reality: interchain interactions - confinement force F≈2×105V/cm D D Neutral phase of trapped polarons P ξ -D -D -D -D Neutral phase of trapped deconfined solitons DS ξ L Ionic phase: deconfined bi-solitons (q=2e) occupy half of the dopants - CS x D D D

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

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

13. Conduction by tunneling deconfinement of solitons tunneling deconfinement confined G>e2/ξL e2/L2 < G < e2/L deconfined tunneling I-V G<e2/L2

14. G=F-E

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. Otherpolymers– non degeneratedground state, confinement is at least 10 times higher, electricfields in experiments are not enough.