One-dimensional transport in polymer nanowires A. N. Aleshin 1,2, H. J. Lee 2, K. Akagi 3, Y. W. Park 2 1 A. F. Ioffe Physical-Technical Institute, Russian Academy of Sciences, St. Petersburg, Russia 2 School of Physics and Nano Systems Institute - National Core Research Center, Seoul National University, Seoul, Korea 3 Institute of Materials Science and Tsukuba Research Center for Interdisciplinary Materials Science, University of Tsukuba, Tsukuba, Ibaraki, Japan Nano and Giga Challenges in Microelectronics Cracow, September 13-17, 2004

Introduction - Recent advances on transport in 1D conductors - Nanofibers made of conjugated polymers Results - Helical polyacetylene nanofibers preparation - Transport in R-helical PA nanofibers: G(T), I(V) at low T - Results for other polymer fibers and tubes Discussion - Are the doped polymer fibers a Lattinger liquid ? - … or a Wigner crystal ? - Tunneling between the ends of LL with intramolecular junctions Conclusions Outline

Transport in 1D conductors The progress in carbon nanotube and semiconductor nanowire technology reveals the problem of transport in 1D conductors The feature of 1D systems - the power-law shape of the tunneling density of states near the Fermi level g(E) ~ E  resulting in the power-laws in temperature dependencies of the conductance, G(T) and the current-voltage characteristics, I(V) G(T)  T , at low V I(V)  V , at high V Electron-electron interactions (EEI) are affecting the transport in 1D systems by leading to phases different from Fermi liquid The repulsive short-range EEI result in Luttinger liquids (LL), while long-range Coulomb interactions cause a Wigner crystal (WC)

Recent results on transport in 1D conductors The power-law for G(T) & I(V) has observed in 1D inorganic conductors: - single wall (SWNT) carbon nanotubes [M. Bockrath, et al., Nature, 1999] - multi-wall (MWNT) carbon nanotubes [A. Bachtold, et al., PRL 2001] - doped semiconductor nanowires (InSb, NbSe 3 ) [S.V.Zaitsev-Zotov et al., J.P.C 2000] - in fractional quantum Hall edge states (GaAs) [A.M.Chang et al., 1996] The LL, WC or Environmental Coulomb blockade (ECB) models are involved to explain these transport features in 1D inorganic conductors For a clean LL the theory implies that both tunneling along LLs through impurity barriers and tunneling between the chains with LLs provides the conduction of a set of coupled LLs with: G(T)  T  (eV >k B T), with  =  + 1 I-V curves at different T should be fitted by general equation: I = I 0 T  +1 sinh (eV/k B T)  (1 +  /2 + i eV/  k B T)  2 where  - Gamma function, I 0 - constant

LL behavior in carbon nanotubes MWCN A. Bachtold, et al., PRL 87 (2001) SWCN M. Bockrath, et al., Nature 397 (1999) 598  ~ 0.36 LL state is characterized by the LL interaction parameter - g.  bulk =(g + 1/g – 2)/8 For the strong repulsive EEI, g << 1 For the non-interacting electrons, g = 1 For tunneling into a SWCN from a metal electrode, g ~ 0.22

InSb - set of parallel nanowires ( D ~ 50 A, L ~ mm) S.V.Zaitsev-Zotov, et al., J.Phys. C 12, L303(2000)  ~ 2-7,  ~ 2-6 LL-like behavior in semiconductor nanowires NbSe 3 (D ~ nm, L ~ 2-20  m)  ~ 1-3,  ~ E. Slot, et al., cond/mat

Nanofibers & tubes made of conjugated polymers Polyethylene dioxythiophene (PEDOT) tubes [J.L.Duvail et al., Synth.Met. 131 (2002) 123] Polyacetylene (PA) fibers [J. G. Park, et al., Synth.Met.119 (2001) 53] Conjugated polymers are an example of initially quasi-1D conductors

Nanotubes made of conjugated polymers Polyaniline (PANI-CSA) tubes [Y. Long et al., Appl. Phys. Lett. 83 (2003) 1863] Polypyrrole (PPy) tubes [J. G. Park, et al., Appl. Phys. Lett. 81 (2002) 4625] The progress in polymer nanostructures synthesis is very fast ! However transport experiments are still rare

Doped helical PA films demonstrate typical semiconductor behavior [D.S.Suh,et al,J.Chem.Phys.114(2001)7222] No data available on the transport in a helical PA fibers Helical polyacetylene nanofibers R-PA bundle We analyze the transport in conjugated polymer nanostructures such as R-helical PA fibers doped with iodine and polypyrrole tubes to find out the correlation with theoretical models for 1D conductors S-PA bundle The goals Polyacetylene (PA) nanofibers, E g ~ 1.5 eV, (CH) n - unique structure, good ability of doping Single PA fibers doped with iodine are well studied [J.G.Park,et al.,Syn.Met.119 (2001) 53; ibid 469; TSF 393 (2001) 161] H elical PA (hel-PA) is a new, advanced form of PA first synthesized by K. Akagi et al., [Science 282 (1998) 1683]

R-helical PA fibers preparation Bulk helical PA is synthesized using chiral nematic liquid crystal as a solvent of Ziegler-Natta catalyst by K. Akagi et al.. Helical PA can be obtained either R-(counterclockwise) or S-(clockwise) type with the opposite helicity. H. J. Lee et al., ICSM 2004 Conf. Proc. (2004) The cross-section of a single helical PA fiber is ~ nm (vert.), ~ nm (horiz.) The length is ~ 10  m R-helical PA fibers are deposited onto the Si substrates with SiO 2 layer and thermally evaporated gold or platinum electrodes with a 2  m gap C 12 E 6 -Hexaethylene Glycol Mono-n-dodecyl in DMF-N,N-Dimethylformamide

Structural studies of R-helical PA fibers X- ray diffraction pattern of R- and S-hel PA films gave a broad reflection indicating that films are polycrystalline, and corresponding to a spacing of 3.68 A characteristic to trans-PA [G. Piao, K. Akagi et al, Curr. Appl. Phys. 1 (2001) 121] XRD of hel PA fibers in DMF solution Polycrystalline rings are from hel-PA fibers Diffuseness is from DMF solution

R-helical PA fibers doping Helical PA fibers were doped with iodine from vapor phase up to the saturation level (several wt %) H. J. Lee et al., ICSM 2004 Conf. Proc. (2004) ~ 870 K  The I-V are measured in the 2-probe geometry in vacuum ~ 10 –5 Torr with displex-osp cryogenic system and Keithley 6517A electrometer R(T) at each T is estimated from the Ohmic regime of the I-V The values of R(300 K) obtained by 4-probe and 2-probe technique are of the same order of magnitude

Transport in R-helical PA fibers For all samples G(T)  T  with  ~ 2.2 – 7.2 depends on the fiber geometry,  increases as D or cross section decreases Temperature dependence of the conductance

Transport in R-helical PA fibers I-V characteristics I(V)  V ,  ~ 2.5 at eV >> k B T I-V at different T collapsed into one scaling curve: I/T  +1 vs. eV/k B T in agreement with the LL model

Results for other polymer fibers and tubes R-hel PA, Sample 2  ~ 5.5,  ~ 4.8 PA single fiber  ~ 5.6,  ~ 2.0 PPy tubes (J.G.Park,Ph.D Tesis)  ~ 5.0,  ~ 2.1 Power laws in G(T)  ~ 2.2 – 7.2 and I(V)  ~ 2.0 – 5.7 are a general feature of transport in polymer fibers and tubes These data are close to those found for InSb 1D wires:  ~ 2-7,  ~ 2-6

What about the crossed R-hel PA fibers? We considered a bundle of 4-5 R-hel PA fibers, Sample 7  ~ 3.7,  ~ 2.3 Surprisingly, the power-law behavior is valid even for several crossed R-hel PA fibers, similar to that in crossed SWNT [B. Gao et al.,PRL 92 (2004) ]

Summary of parameters for all polymer samples The behavior: G(T)  T  at eV > k B T is general for all polymer fibers and tubes under consideration The exponents are close to those for truly 1D semiconductor nanowires

The models for the power law in G(T) and I(V) Some other 1D transport models should be involved It is evident that polymer fibers differ from truly 1D inorganic nanowires However are they a Luttinger liquid? …or a Wigner crystal? 1D Variable Range Hopping model G(T)  exp[-(T 0 /T) p ] with p ~ [M.Fogler et al., PRB 69 (2004) ] - too strong to obtain the power law in G(T) Critical regime of the metal-insulator transition in a 3D systems  (T)  (e 2 p F /ћ 2 )(k B T/E F ) - 1/   T - , p F - Fermi momentum, 1 <  < 3, i.e <  < 1 [D. E. Khmelnitskii et al, Sol.St.Comm. 39 (1981) 1069] For all 1D polymer fibers  > 1 - the model doesn't work Space-charge limited current (SCLC) model for transport in semiconductors predict I(V)  V ,with  ~ 2 [K.C.Kao&W.Hwang, Electrical Transport in Solids, 1981] In all R-hel PA fibers and PPy tubes  > 2 that rules out the SCLC case Fluctuation-induced tunneling (FIT) model [P. Sheng PRB 21 (1980) 2180] FIT model reveals an unreasonable fitting parameters to get the power law

Are the doped polymer fibers a Lattinger liquid? This reflects strong Coulomb interactions among the electrons Evidences in favor to LL model: 1. G(T)  T  with  ~ 2.2 – 7.2 at eV << k B T at T = K 2. I(V)  V  with  ~ 2.0 – 5.7 at eV >> k B T at low T 3. All I-V at different T collapsed into one scaling curve: I/T  +1 vs eV/k B T Restrictions: LL implies almost purely 1D transport, the interchain hopping (predominant at low T in polymers) destroys the LL state Thus LL state in conjugated polymers is possible at rather high T only in agreement with our results for polymer nanofibers Arguments against the LL model: 1.For all polymer fibers    + 1,  << , (similar to inorganic nanowires), which is not consistent with LL and ECB theories 2.LL interaction parameter g estimated from  bulk =(g +1/g – 2)/4 - g ~ too small even for the most conductive R-hel PA << g ~ 0.2 for SWNT

Evidences in favor to WC model: PA nanofibers are initially quasi-1D disordered conductors with low electronic density, where WC may occur. PA chain consists of alternating single and double bounds, which results in the Peierls distortion, and the potential wells where the electrons may be get trapped Is the polymer fiber a Wigner crystal? The conditions for WC: WC occurs in low dimensional systems with low electronic densities with a presence of repulsive LRCI The periodic Peierls distortion of the lattice creates potential wells where electrons can get trapped in and hence form the Wigner crystal WC occurs if r s = a/ 2a B is large, a - distance between electrons, a B - Bohr radius, or r s = E C /E F, E C - Coulomb energy > E F - kinetic energy WC transition is taking place at r s ~ 36 [B.Tanatar et al., PRB 39(1989) 5005] A pinned WC is close to classical charge density wave - CDW systems

The arguments pro et contra WC model For WC the tunneling density of states follows a power law with exponents ~ 3-6 [G.S.Jeon et al., PRB 54 (1996) R8341] similar to G(T) for polymer fibers The power-law in G(T) is valid up to 300 K. Are the polymer nanofibers a WC up to room temperature?. I3-I3- I3-I3- a Other arguments in favor to WC model: PA chain length L ~ n x 10 nm, a ~ 10 nm r s is large enough to get WC in the PA fiber. The arguments against WC model: The impurities in doped conjugated polymers located outside of the polymer chains and thus they only supply carriers without strong pinning (the polymer chain either not pinned or weakly pinned by conjugated defects) For a classical 1D WC pinned by impurities one should expect the VRH regime at low T with an exponential G(T) [B. Shklovskii, Phys.Stat.Sol.(c) 1 (2004) 46] The absence of effective pinning and the high resistance in polymer fibers prevents the observation of VRH at least at T>30 K.(One can expect the transition to VRH for more conductive PA fibers)

Tunneling between the ends of LL?.. T hus VRH, LL, ECB and WC models can not describe precisely the power -law variations observed in G(T) and I(V) for polymer nanofibers and tubes We suggest that the real transport mechanism is ether the superposition of these models or the tunneling between parts of metallic polymer nanofibers obeyed the LL-like behavior -separated by intramolecular junctions Tunneling between the ends of two LLs in SWNT results in more strong G(T) across the kink [Z. Yao, et al, Nature 402 (1999) 273]  ~ 0.35  ~ 2.2 G(T)  T  Calculated value  end-end = (1/g-1) ~ 1.8 at g ~ 0.22

Tunneling between the ends of LL in polymer fiber? Each kink in the polymer fiber acts as the tunneling junction between the ends of two LLs It is known that any polymer fibers contain kinks at a distance between electrodes ~ several  m This effect results in more strong G(T) and I(V) power-law variations in polymer nanofibers with respect to a clean LL, which causes the above- mentioned contradictions with a pure LL model The obvious kink on the hel-PA fiber Sample 1 - G(T)  T   ~ The similar strong G(T) and I(V) power-law variations observed for the 4-5 crossed hel-PA fibers speaks for this model

Conclusions There is a disagreement between our results and the theories for tunneling in 1D systems; the tunneling between the ends of LL is more reasonable approach We analyzed t he conductance and I-V for different polymer fibers and tubes including R-helical PA and PPy The conductance at T = 30 – 300 K follows the power law: G(T)  T  with  ~ 2.2 – 7.2 (the fiber geometry dependent) The I-V at low T follow the power law: I(V)  V  with  ~ 2 – 5.7 The power-law behavior is general for the polymer nanofibers and tubes characteristic of 1D systems, such as Luttinger liquid or Wigner crystal Further experimental and theoretical studies are necessary to explain the power laws in G(T) and I(V) in polymeric and inorganic 1D systems

Acknowledgments The authors are grateful to B. Shklovskii and S. Brazovskii for valuable comments and fruitful discussion This work was supported by the Nano Systems Institute - National Core Research Center (NSI-NCRC) program of KOSEF, Korea Support from the Brain Pool Program of Korean Federation of Science and Technology Societies for A. N. A. is gratefully acknowledged