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 7 Ferroelectricityin carbon based materials. From realities of organic conductors to perspectives of conjugated polymers and the graphene

2. Requests: Light-weight, plastic, processible ferroelectric materials. • Working example: Structural ferroelectricity in a saturated polymer. • R&D: Neutral-to-Ionic transitions in insulating organic crystals • Electronic ferroelectrics: Mott-Hubbardphase and the • polar charge ordering in organic conductors. • Predictions: ferroelectricity in electronically and optically active conjugated polyenes. • Hypothesis: Spontaneous polarization of zigzag edges in graphenenanoribbons.

3. E E E Electron Cloud Electron Cloud - - + + - - + + + + Electronic polarization, occurs in all insulators Molecular polarization, occurs in all insulating molecules; oils, polymers, H2O… - - - - - - + + + + + + Ionic polarization occurs in all ionic solids: NaCl, MgO… Polarization in Insulators Positively charged species in insulators shift/rotate/align toward the negative electrode and negatively charged species shift/rotate/align towards the positive electrode; creating dipoles. The dipole moment density is called the Polarization(P) .

4. Basic types of polarizeable media : Polarization P in applied field E DielectricParaelectricFerroelectricPyroelectric Spontaneous polarization in the absence applied electrical field. Strong variation in polarization with temperature Ferroelectric materials show piezoelectric and pyroelectric effects High strain response to applied electrical field  piezoelectricity

5. Polarization P in theoretical physics: A most fundamental law – the conservation of the charge The most general solution: There is such a vector P that the local density n and the local current j are given as - Jump in P gives the surface charge density

6. W W P P Landau theory for the ferroelectric phase transition, order parameter – polarization P : T>Tc T<Tc Soliton (FE domain wall): Critical relaxation:

7. PZT - Pb(ZrxTi1-x)O3(Tc~370°C)SBT – SrBi2Ta2(Tc~570°C) Traditional Ferroelectrics: Dielectric oxides of transition metals. Origin: particular generally unpredictable energy gains from homogeneous ions’ displacements Slight Ionic asymmetry (from cubic to tetragonal) - Ferroelectrics Why the hysteresis: P is retarded with respect to E. Q. Finite backward Et is necessary to switch the sign of E ? A.Pinning of domain walls by lattice defects!

8. Ferroelectricity is a rising demand in fundamental and applied solid state physics. • R&D include: • Active gate materials and electric RAM in microelectronics, • Capacitors in portable WiFi communicators, • Electro-Optical-Acoustic modulators, • Electro-Mechanical actuators • Transducers and Sensors in medical imaging. Ferroelectrics are available mostly in the inorganic world. Pb(ZrxTi1-x)O3 ,SrBi2Ta2O9 ,PbNb2O6 , Bi4Ti3O12 ,PbBi2Nb2O9, LiNbTaO3 Special need: plastic ferroelectrics in medical echography - low weight , compatibility of acoustic impedances with biological tissues. Today, the demand is satisfied by rather inefficient composite materials like PTZ powders dispersed in a plastic matrix.

9. Can we have organic-only, particularly polymer-only ferroelectric ? • One ferroelectric saturated polymer does exist - Poly(vinylideneflouride) PVDF : • ferroelectric and pyroelectric, • efficient piezoelectric if poled – quenched under a high voltage. • Light, flexible, non-toxic, cheap • Helps in very costly applications : • ultrasonic transducers, sonar equipment • unique as long stretching actuator. PVDF structural unit Driving force behind the FE ordering: preference of trance- (versus cis-) conformation But: ε~10 – modest efficiency (compare to ε~500 for inorganic FE) FE β-phase (trans-polymer) Can we go wider, diversely, and may be better with conjugated polymers? Can we mobilize their fast p-electrons to make a better job than common ions?

10. Ferroelectric transition : polarizationagainst long range Coulomb energy Why? Displacement transitions – generallyunknownreasons Traditionalinorganicferroelectrics, BaTiO3, Pb(ZrxTi1-x)O3 et al Global conformations in polymers : PVDF cis vers trans. (preferable angles for molecular bonds) Local molecular conformations of bigmolecules : organicferroelectrics

11. Instructions of the FE design: Combined symmetry breaking. More secure : symmetry defined approach, particularly when driven by electronic correlations • Lift the inversion symmetry, remove the mirror symmetry, • do not leave a glide plane. • Keepthe double degeneracy to get a ferroelectric. Chain withboth bond and site dimerizations Bonds are polar because of site dimerizationDipoles are not compensated if bonds are also dimerized.

12. Bothdimerizations are built must bepyroelectric, no way to change polarization Any one of twodimerizationisspontaneous. Direction of polarizationcanbechanged - ferroelectric Bonds – built in, sites – spontaneous: organiccrystals Charge orderingendorsed by energy gain fromMottinsulator Sites – built in, bonds – spontaneous: Peierlsdimerization: conjugated polymers of the (AB)x type: modified polyacetylene (CRCR’)x Spin- Peierlsdimerization: organic quantum magnets Bothdimerizations of sites and bonds spontaneous: Neutral-Ionic transitions NIT in organic charge transfersalts

13. The world of organic crystalline conductors.The most orderly and still most diverse part of the universe of p-conjugated carbon based system (TMTTF)2PF6

14. The ever richest phase diagram of electronic phases. (TMTCF)2X SC- superconductivity AF- AFM = SDW SP- Spin-Peierls LL- Luttinger liquid MI- Mott insulator CO= charge ordering + Ferroelectricity H

15. (TMTCF)2X, 1980-2002 SC- superconductivity AF- AFM = SDW SP- Spin-Peierls LL- Luttinger liquid MI- Mott insulator Red line T0 - 2000 revolution: Structurlesstransitions = Ferroelectricity = Charge disproportionation structurlesstransitions : Huge anomaly of dielectric susceptibility Charge ordering from the NMR

16. ORGANIC CRYSTALS Perfect Curie law, Landau theory AsF6 SbF6 ReO4 PF6 Real part of dielectric constant of (TMTTF)2X Second order phase transition with the Curie-Landau law ’= 1/T-TCO, above Tc and ’= 1/2T-TCO below Tc width 30K ! FERROELECTRICITY How to prove direct? X-ray does not work (“structureless transitions” ) Hysteresis loop is not seen – effects of conduction?

17. Direct proof for the FE state: Second harmonic generation , α-(ET)2I3 K. Yamamoto et al. (2008-11) Second harmonic generation λ(ω)=1400nm Identification of the frozen polarization: through anomalous optical activity - lack of inversion symmetry E2 is allowed only if the inversion symmetry is lifted.

19. conterion = dopant X Molecule TMTTF or TMTSF Built-in: dimerization of bonds (the counter-ions X are placed against each second pair of molecules ) Arrows:collinear– FE Alternating – AFE Spontaneous: displacements of ions X stabilize the electronic charge ordering signify the dimerization of sites, it lifts last mirror symmetries, hence the ferroelectricity. Major polarization comes from redistribution of electronic density,amplification of polarizability by a factor of (ωp/∆)2~102even a background  ~103

20. Diverse and advanced experimental techniques: Angle Resolved Photoemission - ARPES It sees the dispersion, delocalization, and the band structure of conducting organic stacks Here, for the double-stackedorganic crystal TTF-TCNQ

21. S. Kagoshima et al. (1976) 4Kf lines exist since the RT but never condense 2Kf appear at lower T but condense into true Braggs. 4KfCDW = Wigner crystal ever coexists with both metallic and CDW phases.

22. Charge Transfer Change at High Pressure D. Jerome 1978 Collective nature of on-chain transportversussingle-particle nature of inter-chain transport 1:3 commensurability locking and its consequences. On-chain conductivity drops at the 3:1 lock-in Inter-chain conductivity does not feel the lock-in

23. COMBINED MOTT - HUBBARD STATE2 types of dimerization  Site dimerization :HUs=-Us cos 2 (spontaneous) Bond dimerization:HUb=-Ub sin 2 (built-in) HU= -Uscos 2 -Ubsin 2 = -Ucos (2-2) Us00  shifts from  =0 to  =  - the gigantic FE polarization. From the single stack to a crystal: Macroscopic FerroElectric ground state: the same  for all stacks Anti-FE state: the sign of  alternates

24. φ=-  φ=  Spontaneous Us can change sign between different FE domains. Domain boundary Us-Us - the phase soliton Δφ=-2 non integer charge q=-2/ per chain. alpha- solitons - walls between domains of opposite FE polarizations On-chain conducting particles above TFE. Macroscopic walls below TFE do not conduct, but determine the FE depolarization dynamics.

25. AsF6 SbF6 ReO4 PF6 SCN Ferroelectricity or antiferroeletriity in the bulk ? Dielectric anomaly (T) in (TMTTF)2X, after Nad & Monceau Anti-FE case of SCN shows only a kink as it should be.

26. What does conduct in these “narrow gap semiconductors” ? NOT the electrons, even in the polaronic version ! PF6 AsF6 SbF6 Conductance G , normalized to RT - Ahrenius plot Log G(1/T). Gaps cfor thermal activation of conductance range within 500-2000K. c~exp(-Ds/T) , Ds~75K Contrarily to normal semiconductors -NO GAP, or a very small gap Ds, in spin susceptibility χ(T). Clearlest example for conduction by charged spinless solitons - holons. Spin gaps are the order of magnitude smaller than the charge gaps.

27. exciton=breather = two-kinks bound state Eg=2 - unbound pair of kinks Drude peaks Optical excitation of sin-Gordon solitons’ pairs within the coexisting metal – Mott insulator state.

28. HYSTERESIS ? Go to low T, introduce the defects D~300 K Polarizations inclined  normal component of electric field E  surface charge. Unusually, it is screened by current carriers, no field goes out of the sample  no need for a domain structure. Mono-domain state  gigantic ’andc2 (global symmetry breaking) ac current Domain walls sweep in the course of re-polarization by ac current. Jump of the longitudinal polarization makes the wall charged. Hence the accompanying cloud of normal carriers which resistance gives rise to the observed activated damping at low T. v. v. : domain wall concentrates carriers, effecting || & ┴ conduction

29. Dow we see the motion of FE solitons - walls ? Yes at T<Tc frequency f dependence of imaginary part ε" ε′′(f) curves at two temperatures around Tc=102K, above - 105K and below - 97K. Low frequency shoulder – only at T<Tc : pinning of FE domain walls i.e. hidden hysteresis ? t(T) =1/fm

30. Relaxation time t(T) in a wide temperature range. t(T) =1/fm is given by the maximum position fm of e"(f) • Perfect low T activation law. • Activation energy Dt=322Kwell correlates with the conductivity activation Ds≈350K  ferroelectric polarizationdissipates via charge carriers • spinlessssolitons (holons). • Proof for the FE and I-V interference critical relaxation

31. 5 5.5x10 5 5.0x10 5 4.5x10 10-6 5 4.0x10 5 3.5x10 5 3.0x10 5 2.5x10 5 2.0x10 5 1.5x10 f f 5 1.0x10 5 6 7 10 10 10 100000 1000000 1E7 Advantage of using the inverse complex function: e=e'+ie" → 1/e=m= m'+im" e" m' m"~fn n=0.86 m" • Log-Log plots ofe" and m',m'' above Tc : T=105K • Hump in e"straight line form"over the whole interval of f.The power law m" ~fnwith n=0.86±0.01. The exponent0.86 is not 1 as in mean field theory of critical relaxation- unexpected access to the profound dynamical scaling at the criticality.

32. BelowTc : T=97K 10-5 10-6 f 10-7 10MHz Log-Log scales m"~fn, n=0.78 m' m" 10kHz 100kHz • Log-Log plot still recovers a good straight line • but only at sufficiently high f. • The power law is m"~fnwith n=0.78 • – not far from n=0.86 for T=105K but beyond our accuracy 0.02. • This fit covers symmetrically both slopes of the maximum of e". Now we extrapolate and subtract the straight line, to single out the contribution of the low f shoulder in m" ande".

33. Separation of the low f feature - now it shows up sharply and can be plotted in Lin-Lin scales. FINAL RESULT : 2x10-8 f 4 5 5 5 5 5 1.0x10 1.5x10 m" Isolated low frequency contribution to the imaginary part m" of the inverse permittivity. 1x10-7 50kHz 200kHz 300kHz Presumably: pinning of sweeping domain walls, weak hysteresis.

34. Ferroelectricity in conducting polymers? • Where does the confidence come? • What may be a scale of effects ? Proved by success in organic conducting crystals.

35. Combined Peiels effect in diatomic linear chain polymer (C2RR`)x Joint effect of extrinsic ∆e and intrinsic ∆i contributions to dimerization gap ∆. ∆ecomes from the build-in site dimerization – non-equivalence of sites A and B. ∆icomes from spontaneous dimerization of bonds, the Peierls effect. R` R` R R E F Threshold effect : ∆i WILL NOT be spontaneously generated if ∆e already exceeds the wanted optimal Peierls gap. Needa small difference of ligandsR and R’ -kF kF

36. “Accidental” origin of the success to get the Peierls effect of bonds dimerization: weak difference or radicals – only by a distant side group.Small site dimerisation gap allows addingthe bond dimerizationgap.

37. How do we know that the spontaneous dimerization is present (X-rays are no good for spaghettis of polymer fibrils)? From identification of physics of solitons.

38. Diatomic (C2RR`)x chain Solitonic intra-gap states Standard (CH)x chain Δ0 +Δe 0 -Δe -Δ0 -Δe 0 0 +Δe Δ0 S=0 Q=e +Δe 0 -Δe -Δ0 Q=-e 0 +Δe -Δe Δ0 All solitons are charged, even the spin ones - they are elementary ferroelectric domain walls -Δe 0 S=1/2 -Δ0 Q=0

39. Proof for spontaneous dimerizationvia the existence of solitons Optical results : Soliton feature, Absorption, Luminescence, Dynamics Not a polaron, but spin soliton ?

40. Particular interest in developing ferroelectric π-conjugated systems “electronic ferroelectrics”: • Manipulations of charged solitons by electric field. Their spectral features arrive in optics • Gigantic ε, easy repolarization – fast response • Conductivity and/or optical activity of p-conjugated systems will add more functionality to their ferroelectric states. • Polarizability of chains can allow to manipulate morphology (existing hybrids of polymers and liquid crystals. K. Akagi - Kyoto). • High and fast nonlinearity : χ2 for the optical mixing , second harmonic generation

41. Hypothesis (AB)x polymer Graphene ? e-ph coupling λ~10-2 (Japan) λ~0.3 The Netherlands

42. LESSONS and PERSPECTIVES • p-conjugated systems can support the electronic ferroelectricity. • Effect is registered and interpreted in two families of organic crystalline conductors (quasi 1D and quasi 2D). • Mechanism is well understood as combined collective effects of Mott or Peierlstypes. • An example of a must_be_ferroelectricpolyene has been already studied . • The design is symmetrically defined and can be previewed. • Solitons will serve duties of re-polarization walls.

43. «In the beginning was the Word, … and without him was not anything made that was made» Physical Review 1964 W.A. Little Possibility of a synthesizing an organic superconductor. “Little” mystification: did he actually mean ferroelectricity?

44. Was “organic superconductivity” the only promised land? Not quite : some of the prophet's visions actually imply a spontaneous electric polarization, hence they are Pyro/Ferro-Electics. Drawing - PRB 1964- pyroelectric His later popular drawing (Sci. Am.) Questionably a superconductor, It must be a ferroelectric.