Serguei Brazovskii and Natasha Kirova Natal 2012 Physics of synthetic conductors as low dimensional correlated electro

1. SergueiBrazovskii and Natasha Kirova Natal 2012 Physics of synthetic conductors as low dimensional correlated electronic systems. Lecture 5, part 2 Solitons, experimental manifestations

3. Polyacetylene - Traditional plastic : Polyethylene Ethylene - Conjugated polymer : Trans-polyacetylene Acetylene Line of milestones:S. Shirakawa; A. Mac Diarmid, A. Heeger, Y.W. Park, S. Etemad, V. Vardeny,

4. Films of undoped PA: Spaghetti of fibrils D~50nm. Can be oriented by stretching. What is inside? Polycrystals of chains, Structure is known for the pristine material. Under doping,the structure is modified into a high-symmetryhexagonal form.Columns of ions intercalatethizig-zags of chains. Trans -PA : the stable form. But: The PA is always obtained in the metastableCis form. Transformed under heat or doping.

5. H H H C C C C C H H E E F -kF kF -kF kF Dream Reality Peierls effect - one dimentional chain of equidistant atoms is unstable with respect to the dimerisation: Spontaneus symmetry braking results in the dielectric state, the gap is open. Wexp(- Holes dopinggives conduction

6. W  Topologicaldefects on the polyacethylenechains Ideal chain Δ0 Δ0 0 0 -Δ0 -Δ0 Q=+e Charge solitons q=e, s=0 Δ0 Q=-e 0 -Δ0 Spin soliton, q=0, s=1/2 0 tanh [x/0], Wtot = (2/)0 Eel =0

7. 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

8. Measurements of the magnetic susceptibility χ χ through the "Knight shift of the NMR-Nuclear Magnetic Resonance - an important test for homogeneity and directly (Faraday balance) conductivity s A major puzzle: spins appear at much higher dopingthan the metallic conductivity: the whole interval of conduction byspinless – unlike electrons -- particles

9. Metallization under doping Low doping: gap is preserved, Mid-Gap and IR activity appear Larger doping: No more gap seen, all absorption goes to IR Metallization in Si, etc.: n=1018/cm3 – x=10-6/per Si,distance 100 units Metallization in (CH)x starts at x=1% of dopping, end up at 10% - enormous concentration, distance 101/3 ~2-3 units,effect of one-dimensionality! Only the impurity along the chain is seen for hopping.

10. Linear and non linear optics Linear optics (LO): Pump: change the light energy, observe the absorption/emission spectra Pump PL Nonlinear optics (NLO): pumpe – probe experiment. Photoinduced absorption (PA) Pump - Light 1 : fixed energy through the gap E>Eg, creation of the excited states Probe – Light 2: test excitations of the earlier excited states by changing the probe light energy Stimulated emission (SE) Pumpe - Light 1 : fixed energy through the gap E>Eg, creation of the excited states Probe – Light 2: provoke recombination of the excited states with the emission of the optical photons. Time resolved NLO: Measurements as a function of time delay between pump and probe. PA Pump SE

11. Optics and Electron-Phonon Coupling: Adiabaticalprinciple (Frank-Condon, Born-Oppengeimer) Excitation E Figure: energy of an electronic excitation as a function of a lattice deformation q. Light is absorbed in a time ~ћ/Eg~10-15sec Compare with relaxation time of a heavy lattice ~ћ/ωph~10-13sec : -- Absorption goes from the relaxed ground state GS the unrelaxed excited one. -- Emission – luminescence goes from the relaxed excited sate to the unrelaxed ground state. -- Indirect (minimum to minimum ) transitions require the quantum overlap of the lattice zero-point vibrations, hence the reduced probability ~exp(-ΔEmin/ћωp) LES Relaxation effects Absorption Emission GS q

12. Optical absorption spectra of (CH)x Δ0 Δ0 0 0 -Δ0 -Δ0 Doping

13. Photo-current, hence the photo-conductivity, comes only from excited unbound pairs at E>EgAbsorption – also from bound excitons, hence expect a lower threshold at Eex<Eg as it is normally observed. Figure shows the photocurrent Iphoffsetwhich starts below the absorption ! Resolution: Iph is much more sensitive,it recovers adiabatically forbidden creationof relaxed configurations – here pares of solitons. Their threshold is, theoretically, 30% lower. In favor of that: exponential growth of Iph.

14. Effect upon kinks: global lifting of symmetry - confinement. Ideal chain Bipolaron -twoconfined solitons Nature present -- cis-isomer of (CH)x : build-in slight inequivalence of bondshence lifting of ground state degeneracy, hence confinement of solitons Cis-(CH)x : Nonsymmetric dependenceof GS energy on dimerisation Confinement – the linear growth of the attraction energy while the particle diverge. Confinement of kinks pair into 2e charged (bipolaron) or neutral (exciton) compex. Symmetry determined picture of optical differences for trans- and cis- isomers S. B. and N. K., 1981 Photoconductivity trans-(CH)x versus photoluminescence cis-(CH)xalso new optical features due to hybridization of mid-gap states

15. Energy difference per unit lengthis a constant confinement force F. The confinement energy is F|x|. Cis-(CH)c – photoluminescence, no photoconductivity, Trans-(CH)x – free solitons, no photoluminescence, but the photoconductivity

16. Neglecting Coulomb repulsion (suppose two donors sit nearby as counter-ions)the two bound solitons are always more favorable than two electrons and even two polarons. • It can be: • exciton – in case of light pumping (bound e-h pair, two charged solitons with opposite charges) • Bipolaron (BP) – in case of doping (bound pair of two solitons with the same charge) • N.B. taking the bipolarons away from the donors (attempt to make conduction by BPs) turns on the Coulomb repulsion between the two electrons. • Confinement scenario :the BP is a string between the two kinks at a distance x: • the BP energy, with respect to two bare electrons is • dWbp=Wbp(x)-2D=-(2D-2Ws)+F|x|+e2/(e|x|) • - always an optimal x: dWbp=-0.6D+2(Fe2/e)1/2 • – favorable for small enough confinement force F.

17. Luminescence of cis-(CH)x and trans- (CH)x Right: same -- cleaned from phonons Left – a broad line covered by multiple phonons repetitions- vibrations of the lattice dressing of the selft-traped state - additional proof of the selftrapping. trans-PA, T=7K, pumping at 2.54eV Remnant luminescence is 50 times less then that of cis-PA

18. Time resolved photoconductivity from the old pico-second epoch: After a short pump, the photocurrent decays with a characteristic time ~100ps - result of recombination of carriers. Resolving the shorter time, one finds a fast initial recombination of geminate carriers –the e-h pairs created by the same photon. This is why in applications we need a fast capturing of one kind of carriers.

19. How do we identify bipolarons? In optics by specific lines appearing under doping or even (?) pumping. Doing ESRunder low-to-moderate doping to detect no spins- especially clear in polytheophene. Clear evidences that BPs function as the main reservoir for charge storage- generalize to junctions, to field-effect transistor! (N.K and S.B. for theory) No clear proof that BPs can conduct as individual 2e particles – would be a step towards the superconductivity –activation into polarons may be necessary.

20. Energy schemes for a) 2-holes bi-polaron – 2 transitionsb) 1-hole polaron – 3 transitions. Both split inside the gap a symmetric pair of levels- viewed as splitting of the zero-energy state in PA Experimental identification of bipolarons by the double-shape structure of the absorption. -- proved to be WRONG ! One of transitions is optically forbidden, hence expect 1 transition for BPs and 2 transitions for Ps

21. How do we identify polarons? In optics by specific lines appearing under doping and pumping –proving their similarity. Doing ESR under low-to-moderate doping to detect the spins. Doing combined experiments for ESR under optical pumping (V. Vardeny et al). In kinetics, beyond the internal optical transitions, the polarons are like electrons or holes,just ~100 times more heavy, hence reduced mobility, enhanced binding to dopants, impurities. Why they may not exist? Theoretically, the polaron energy is 0.9Δ – only 10% gain with respect to a free electron :In spite of strongly split-off intarband levels (E0=± 0.7Δ), the energy gain 0.3Δ is almost compensatedby the cost to form the self-consistent potential well. Perturbation like the interchain coupling can level out the small net gain 0.1Δ to leave electrons free from selftraping

22. Combination of the techniques of the photoinduced absorption (PA) and of the PA-detected magnetic resonance (PADMR). Photo-absorption spectra of (a) regular and (b) improved Polytheophene films. Inset: schematic diagrams of negative (a) polarons and (b) bipolaronsand their optical transitions. Two spin 1/2 polarons will produce pairs with spins either parallel (sp) or antiparallel (sap). For non-geminate e-h pairs, both sp and sap pairs will form initially, but the recombination rate of sap pairs is higher, leading to steady state populations with sp. MW-induced spin flips convert sp pairs into sap pairs, increasing the recombination rate of oppositely charged pairs to the ground state and reducing polaron populations – to be detected by the photoinduced absorption . Magnetic resonance will also enhance bipolaron formationfrom like-charged pairs.

23. 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