Defect-Free Carbon Nanotube CoilsNitzan Shadmi,† Anna Kremen,‡ Yiftach Frenkel,‡ Zachary J. Lapin,§ Leonardo D. Machado,⊥

Sergio B. Legoas,∥ Ora Bitton,# Katya Rechav,# Ronit Popovitz-Biro,# Douglas S. Galvao,⊥ Ado Jorio,▽

Lukas Novotny,§ Beena Kalisky,‡ and Ernesto Joselevich*,†

†Department of Materials and Interfaces and #Chemical Research Support, Weizmann Institute of Science, Rehovot, 76100, Israel‡Department of Physics, Nano-magnetism Research Center, Institute of Nanotechnology and Advanced Materials,Bar-Ilan University, Ramat-Gan, 52900, Israel§ETH Zurich, Photonics Laboratory, Zurich, 8093, Switzerland⊥Instituto de Física “Gleb Wataghin”, Universidade Estadual de Campinas, C. P. 6165, 13083-970 Campinas, Sao Paulo, Brazil∥Departamento de Fisica, CCT, Universidade Federal de Roraima, 69304-000 Boa Vista, Roraima, Brazil▽Departamento de Física, Universidade Federal de Minas Gerais, Belo Horizonte, MG 31270-901, Brazil

*S Supporting Information

ABSTRACT: Carbon nanotubes are promising building blocks for variousnanoelectronic components. A highly desirable geometry for such applicationsis a coil. However, coiled nanotube structures reported so far were inherentlydefective or had no free ends accessible for contacting. Here we demonstratethe spontaneous self-coiling of single-wall carbon nanotubes into defect-freecoils of up to more than 70 turns with identical diameter and chirality, and freeends. We characterize the structure, formation mechanism, and electrical pro-perties of these coils by different microscopies, molecular dynamics simula-tions, Raman spectroscopy, and electrical and magnetic measurements. Thecoils are highly conductive, as expected for defect-free carbon nanotubes, butadjacent nanotube segments in the coil are more highly coupled than inregular bundles of single-wall carbon nanotubes, owing to their perfect crystalmomentum matching, which enables tunneling between the turns. Althoughthis behavior does not yet enable the performance of these nanotube coils asinductive devices, it does point a clear path for their realization. Hence, this study represents a major step toward the productionof many different nanotube coil devices, including inductors, electromagnets, transformers, and dynamos.KEYWORDS: CNT, SWNT, guided growth, horizontal CNTs

Extensive research has been devoted to exploring thepotential of carbon nanotubes for the assembly of various

nanoelectronic components, including transistors,1 diodes,2

resistors,3 capacitors4 and interconnects.5 One importantcomponent yet to be demonstrated is a coil. Carbon nanotubecoiled structures reported so far were based on periodic defects,which induce curvature,6,7 but also scattering and high resis-tance,8,9 or had no free ends available for electrical contact-ing.10,11 In order to produce carbon nanotube coils that aresuitable for electronic applications, we investigate the coiling ofdefect-free carbon nanotubes and the properties of the resultingnanotube coils.Coiling is a general phenomenon that can be observed at very

different scales in falling flexible rods,12 such as cables, ropes, andspaghetti, as well as in viscous jets,13 such as when pouring honeyor shampoo. In these macroscopic cases, coiling is usuallydriven by gravity, while self-affinity plays a secondary role. Inmicroscopic systems, coiling is often driven by self-affinity, forinstance by the addition of a condensing agent such asspermidine to DNA plasmids,14 or by dipolar interactions in

ZnO nanobelts, leading to their epitaxial self-coiling into single-crystal rings.15 In the case of carbon nanotubes, coiled structureswere previously obtained by the formation of periodic struc-tural defects in the gas phase,6 or by the aggregation of manynanotubes into toroidal bundles.10,11,16 Incidental observation ofcoiling at the end of individual single-wall carbon nanotubeswas also reported17 and believed to take place in free space priorto landing on a substrate, but no focused studies on this pheno-menon have been reported. Overall, none of these coiled struc-tures were suitable for electronic applications, either because oftheir large defect-induced resistance or because their ends werenot well-separated from the bundle to facilitate their selectiveconnection to electrodes.Here we report for the first time the self-coiling of single-wall

carbon nanotubes into defect-free coils with fully accessible ends.This configuration allowed us to connect the two ends of each

Received: August 25, 2015Revised: December 25, 2015Published: December 27, 2015

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© 2015 American Chemical Society 2152 DOI: 10.1021/acs.nanolett.5b03417Nano Lett. 2016, 16, 2152−2158

coil to electrodes and thus to characterize its electrical properties(Figure 1a,b). As opposed to previous coiled structures, wherecoiling takes place in the gas phase or in liquid suspension, ourself-coiling process takes place on regular silicon substrates,making the coils ready for integration into a series of potentialdevices. Another unique feature of these structures is that all theparallel nanotube segments in the coil have the same diameterand chirality and are thus hexagonally packed as a single crystal.Long-sought single-crystals of single-wall carbon nanotubes wereinitially reported, but later found to be artifact.18 Our optical andelectronic characterization of true single-crystals of single-wallcarbon nanotubes reveals a higher coupling than in regular ropesof single-wall carbon nanotubes with different chiralities.The single-wall carbon nanotubes were grown on Si/SiO2

substrates from thin stripes of Fe nanoparticles patterned on asupporting layer of SiO2, known to promote suspended growthof long (>100 μm) single-wall carbon nanotubes.19 Initially, arelatively low flow rate of 70−500 sccm was used, to offerminimal perturbation of the vertical fall, although a similar yieldwas attained when using flows of up to 2000 sccm (see furtherdiscussion in Supporting Information). This procedureproduced tens to over a hundred nanotube coils per sample,which can be efficiently mapped by scanning electron micros-copy (SEM, Figure S1). The coils can be distinguished fromsimple loops by the entry and exit points of the nanotubes aroundthe closed ring part. If these points are different (Figure S1), thenthe structure is a coil with more than one turn. The diameter ofthe coils is typically 2−4 μm, although it can be as large as 10 μm,and as small as 1 μm. The coil often has a higher SEM contrastthan the individual nanotube (Figures 2a,d, S1). Atomic forcemicroscopy (AFM) is used to verify the topographic height ofeach selected coil (Figures 1c, 2f,i) relative to that of its free ends,which provides a rough estimation of the number of turns.Absolute determination of the number of turns in the coil isdone by cross-sectional transmission electron microscopy(TEM). For this, we cut a thin (50−100 nm) lamella acrossthe coil using a focused-ion beam (FIB), and observe the twocross sections at opposites regions of the coil under the TEM

(see Methods section). Each cross-section shows a denselypacked hexagonal lattice of identical nanotubes, each corre-sponding to one turn of the coil (Figures 2b,c,e,g,h,j, 4e and S2).We imaged cross sections of nine coils and accurately counted

their number of turns, which ranged from4 to 74 (Figures 2b,c,e,g,h,j,4e, and S2). Several coils had rectangular-shaped cross sections (e.g.,Figure 2g−h), similar to a nanoribbon, suggesting that there is apreference for the turns to formon one specific side of the coil. In thiscase, the state of the coil can be mixed, with part of it lying on itswide side, and another part on its narrow side (Figure 2f−h). Thecross-sectional TEM images of these parts are consistent withtheir AFM topography, and the SEM images also show alternateleft and right twists between these parts of the coil (Figure 3 andsee further discussion in Supporting Information).

Figure 1. Nanotube coils: concept and production. (a) Schematicrepresentation of the formation of a single-wall carbon nanotube coil.(b) Schematic representation of the formed coil with its two free endsconnected to electric leads. (c) AFM height image of a nanotube coil.The blue dashed line shows the position of the topographic cross-section shown in d. (d) The heights of the two sides of the coil are 22.4±0.3 nm (left) and 22.2± 0.3 nm (right), and the height of the free ends ofthe coil is 1.6 ± 0.3 nm.

Figure 2. Structural characterization of the nanotube coils. (a, d, f, and i)SEM images (a and d) and AFM height images (f and i) of coils fromwhich a lamella was cut. (b, c, e, g, h, and j) TEM images of the cross-section. Yellow lines show the location of the matching cross-section. Bycounting the turns in the corresponding TEM images (b, c, e, g, h, and j),we determine that the coils shown in a, d, f ,and i have 9.5, 13, 57, and74 turns, respectively. The inset in j shows the fast Fourier transform ofthe cross-section, which gives a lattice parameter of 2.6 ± 0.2 nm.Accounting for a van derWaals distance of 0.34 nm, this gives a diameterof 2.3 ± 0.2 nm, matching a single-wall carbon nanotube.

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The formation of defect-free carbon nanotube coils can bequalitatively rationalized in the framework of a “falling spaghetti”mechanism, initially proposed for the self-organization of nano-tube serpentines19−21 and more recently extended to othercurved structures.22 In this mechanism, the nanotube first growsup from the substrate and later falls making wiggles, which can bedirected both by the substrate and the gas flow. The fall is drivenby van der Waals interactions with the substrate while subject todynamic instabilities. Depending on the relative velocity of theforward and downward components of the nanotube motion,four different structures can be expected, including flow-aligned,serpentine, looped, and coiled geometries (Figure 4a−e). A quitesimilar macroscopic mechanism was recently proposed andtested for the coiling of elastic rods on rigid substrates.12 In thecase of a carbon nanotube, its van derWaals interaction with itselfis particularly strong,23 and predominance of the downwardmotion increases the probability of coiling of the nanotubearound itself (Figure 4b, and see further details in SupportingInformation).More quantitative insight into the mechanism of self-coiling of

single-wall carbon nanotubes on the amorphous Si/SiO2 wasobtained from atomistic molecular dynamics simulations (seeSupporting Information for detailed description and discussion),similar to those recently performed to model the formation ofnanotube serpentines on crystalline substrates.20 Our simu-lations fully reproduce the spontaneous formation of carbonnanotube coils and describe the evolution of strain, van derWaals energy and kinetic energy during the self-coiling process

(Figure 4f−i and Movies S1 and S2). These simulations indicatethat the van der Waals interaction is much stronger than thestrain energy, so the overall energy of the coil is lower than that ofa straight nanotube. Hence, once the first turn is formed, the self-coiling proceeds steadily, until disturbed by a sufficiently strongfluctuation.The structural perfection of our carbon nanotube coils was

evaluated by Raman spectroscopy (Figures 5a and S3 as well asSupporting Information). The narrow Raman lines (FWHMbelow13 cm−1)24 and the negligible intensity of the disorder-inducedD-band (∼1350 cm−1, average ID/IG = 0.04 ± 0.04 for 9 coils)25

are both indicative of a very low density of structural defects.Moreover, imaging of the G-band shows that the coil and its freeends are all simultaneously in resonance with the same laserenergy, indicating that all the nanotube maintains a constantdiameter and chirality along the entire coil.An ideal electromagnetic coil is made up of a coil along which

an electric current is passed, and a uniform magnetic field isgenerated, with an intensity that is proportional to the number ofturns the current passes. To assess the functionality of our defect-free carbon nanotube coils for the construction of inductivedevices, we determine the effective number of turns that a currentpasses before it shorts by tunneling between adjacent turns. Thiswas done first by measuring the current as a function of bias andgate voltage and then by measuring the magnetic field over thecoil while applying a voltage between the free ends of the coil.On each selected coil (Figure 5b) we performed two four-

point probe electrical measurements, first on one free end ofthe coil (Figure 5c) and second between the two ends of thecoil (Figure 5d). From the first measurement while gating, wefound these nanotubes to be p-type semiconducting and alsodetermined the nanotube length resistivity (50−100 kΩ/μm).From the second measurement and this length resistivity, wecalculated the effective length of coiled nanotube followed by thecurrent. Taking that length, and dividing it by the circumferenceof the coil, we roughly estimate the effective number of turns thatthe current passed through to be 0.4 ± 0.3 (i.e., half a turn) forthe four coils tested. This suggests that the electrical behavior ofthe coil is dominated by tunneling between its turns (“inter-turntunneling”).In order to determine more directly the effective number of

turns the current flows through, we measured the magnetic fieldover the biased coil by scanning superconducting quantuminterference device (SQUID) microscopy correlated withAFM (Figure 5f,k,p). We compare the measured magnetic fieldgenerated by the current flow at the center of the coil to the fieldgenerated at uncoiled parts of the nanotube and the electrodes.The field at the coil center should appear as enhanced or reveredto the overall field, depending on the coiling direction of thenanotube coil. We reconstructed the current path from magneticflux measurement of the SQUID (Figure 5i,n,s) and comparedthem to the simulations. Based on the SEM and AFM images ofthe coils (Figure 5f,k,p) we resolved the direction of coiling foreach coil and calculated the expected magnetic flux image bythe Biot-Savart law (Figure 5i,j,n,o,s,t). Three different coilsamples were prepared, all of which were p-type semiconduct-ing. The magnetic flux at the center of the coils was measuredunder various bias and gate voltages. By comparing the results(Figure 5g,h,l,m,q,r) with the simulations, we determined theeffective number of turns to be less than one, consistent with theresult obtained from the resistance measurements (Figure 5c−d).Our results demonstrated that self-coiling of single-wall carbon

nanotubes leads to formation of defect-free coils, which are

Figure 3. Occurrence of twists in ribbon-like carbon nanotube coils.(a) SEM image of a coil with twists. (b−d) Zoomed-in images of theareas of the twists, marked by white frames 1−3, respectively. (e) A coilwith some vertically aligned sections (marked by white arrows). Thehorizontally aligned sections are clearly broader than the verticallyaligned ones.

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highly conductive and have free ends available for contacting, asrequired for the assembly of functional devices. However, theelectrical behavior of the defect-free nanotube coil is dominatedby interturn tunneling rather than end-to-end conduction. Thisfinding may seem surprising considering that intertube tunneling

in single-wall carbon nanotube ropes is usually weaker thanend-to-end conductance.29 One way of explaining this behavior isthat in a regular bundle of single-wall carbon nanotubes, eachnanotube has a different chirality, and hence the intertubetunneling involves a large change in crystal momentum, which

Figure 4. Formation mechanism of defect-free carbon nanotube coils. (a) A nanotube has grown above the surface, and begins to deposit onto it,creating a suspended half loop. (b−e) Four possible geometries that may form, depending on the relative forward (in the direction of the gas flow) anddownward (in the direction of the substrate) velocities, vf and vd, respectively. (b) vf is negligible in comparison with vd: the nanotube coils like a fallingrope, forming multiple turns. (c) vf is sufficiently lower than vd: the nanotube forms a single loop. (d) vf is roughly the same as vd: the suspended half loopfalls in the gas flow direction, and a serpentine U-turn is formed. (e) vf is higher than vd: the nanotube aligns in the direction of the gas flow, forming astraight segment. (f) Energy needed to bend a 3 μm (13,0) nanotube to a fraction of a turn. As curvature increases, so does the elastic energy cost. Whena full turn is completed, there is a small 7 nm nanotube overlap length, shown zoomed in at the inset. Because of the van der Waals attraction at theoverlapped region, the total energy of the full turn is smaller than that of the straight tube−that was defined as zero. (g) Evolution of the total, van derWaals, molecular and kinetic energies of a 3 μm (6,0) nanotube as it assembles into a coil. Initial energies were defined as zero. (h) Far view of theinitial structure used in the simulation, with nanotube diameter greatly exaggerated to improve visualization. (i) The structure at t = 12.2 ns. See alsoMovies S1 and S2.

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cannot be acquired by coupling to phonons under low biasconditions.30 However, in our defect-free coils, all the paralleltubes, each being a different turn of the same nanotube, haveexactly the same diameter and chirality. Therefore, the electronscan easily tunnel from one turn to another without changing theircrystal momentum.31 Consequently, the nanotube shortswith itself as an unsheathed wire. On one hand, this may be adisappointing conclusion from the perspective of the envisagedinductive applications. On the other hand, it is a mandatorylesson to be learned, which can lead to progress whenknowledgeably addressed. How can one effectively sheathesingle-wall carbon nanotubes to inhibit intertube shorting? Onepossible solution that we propose is using double-wall carbonnanotubes,32 so that the inner tube is sheathed by the outer wall

having a different chirality. This will require and inspire manynew and intriguing theoretical and experimental studies. In anycase, we believe that the formation and characterization of defect-free carbon nanotube coils demonstrated here represents a majordevelopment toward the production of a large variety ofnanotube coil devices.

■ ASSOCIATED CONTENT

*S Supporting InformationThe Supporting Information is available free of charge on the ACSPublications website at DOI: 10.1021/acs.nanolett.5b03417.

Movie of molecular dynamics simulations of the formationof defect-free carbon nanotube coils (AVI)

Figure 5.Optical, electrical, and magnetic characterization. (a) Overlaid Raman measurements of the free end (black spectrum, position 1 in left inset)and coil (red spectrum, position 2 in left inset) segments of the same nanotube (identified as semiconducting26). Left inset shows a G-band Ramanimage of the coil, where the coil section, which is composed of the signal of several nanotube turns, gives a significantly stronger signal than the free end.There are no apparent bundling induced changes in high (>1000 cm−1) modes. Right inset is the low frequency region of the spectrum, showing theradial breathing mode (RBM) peak from the single-wall carbon nanotube at ∼90 cm−1, obtained from the free end segment, as well as another peak at∼180 cm−1, which is probably an RBM overtone (see Supporting Information for further discussion).27 Interestingly, the RBM peak is highly broadenedin the coil segment, a result that has been predicted theoretically as due to van der Waals interactions,28 but never measured in carbon nanotube bundlesformed by different (n,m) tubes. (b) SEM image of a measured nanotube with Pd electrodes. (c and d) Four-point probe measurements on the free endand coil segments of the nanotube, respectively. These measurements were performed using a gating voltage of−10 V, as the nanotube was found to bep-type. (e) Cross-sectional TEM of the lamella taken at the position marked by a white dashed line in b. The image shows that the coil comprised threecomplete turns and an additional ∼1/4 turn. (f, k, and p) AFM images of coils contacted by Pd electrodes. The nanotubes and the source and drainelectrodes are falsely colored for emphasis. The boundary lines visible in k and p surrounding the area of the nanotubes are due to the oxygen plasmatreatment used to remove other nanotubes on the sample (see methods section for more details). The white arrows indicate the coiling direction of thenanotubes. (g, l, and q) The magnetic flux captured by scanning SQUIDmicroscopy, at 4 K, AC current of 100, 100, and 20 nA, and gate voltage of−10,−10, and −7 V, respectively. Color bar spans 0.6, 0.6, and 0.3 mΦ0, respectively. Red (blue) represents positive (negative) flux response. (h, m, and r)The respective current paths reconstructed from the flux data (a.u.). (i, n, and s) The respective magnetic flux images calculated for current flow fromelectrode to electrode passing through one effective turn of the nanotube coil. (j, o, and t) The respective magnetic flux images calculated for the shortestcurrent path. The outline of the measured nanotube in black or white was added to g−j, l−o, and q−t for reference.

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Movie of zoomed out view of molecular dynamics simu-lations of the formation of defect-free carbon nanotubecoils (AVI)(1) Additional SEM, AFM, and TEM images of carbonnanotube coils and their cross sections. (2) Raman spectraof defect-free nanotube coils and their analysis. (3)Discussion of the effect of gas flow on the formation ofdefect-free coils. (4) Discussion on the orientation ofribbon-like nanotube coils and the occurrence of twists.(5) Discussion on the energetics of the formation ofdefect-free carbon nanotube coils. (6) Electrical character-ization of the effects of bundling in nanotube coils. (7)Details of the experimental methods (PDF)

■ AUTHOR INFORMATIONCorresponding Author*E-mail: ernesto.joselevich@weizmann.ac.il. Phone: +972-8-9342350. Fax: +972-8-9344138.NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSWe thank John R. Kirtley and Kathryn A. Moler for their helpwith the scanning SQUID measurements at Stanford University,Amos Sharoni and Tony Yamin for their help with Nb sputtering,Palle von Huth and David Tsivion for assistance with the FIB,Avishai Benyamini, Jonah Waissman, and Assaf Hamo forassistance with low-temperature electrical measurements, andDavid Rakhmilevich and Shahal Ilani for helpful discussions. Thisresearch was supported by the Israel Science Foundation, theHelen and Martin Kimmel Center for Nanoscale Science, theMoscowitz Center for Nano and Bio-Nano Imaging, and thePerlman Family Foundation. E.J. holds the Drake FamilyProfessorial Chair of Nanotechnology. B.K. acknowledgessupport of the European Research Council ERC-2014-STG-639792, ISF (ISF #1102/13), and CIG FP7-PEOPLE-2012-CIG-333799. L.N. acknowledges financial support by the SwissNational Science Foundation (grant 200021_149433). L.D.M.and D.S.G. thank CNPq and CCES for financial support throughFAPESP/CEPID Grant # 2013/08293-7. The Scanning SQUIDMicroscope was constructed with support from the NationalScience Foundation DMR-0957616 and is part of the StanfordNano Shared Facilities.

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1

Defect-Free Carbon Nanotube Coils

Nitzan Shadmi†, Anna Kremen‡, Yiftach Frenkel‡, Zachary J. Lapin§, Leonardo D.

Machado┴, Sergio B. Legoas

║, Ora Bitton#, Katya Rechav#, Ronit Popovitz-Biro#,

Douglas S. Galvão┴, Ado Jorio∇, Lukas Novotny§, Beena Kalisky‡, and Ernesto

Joselevich†*

†Department of Materials and Interfaces and #Chemical Research Support, Weizmann Institute of Science, Rehovot, 76100, Israel. ‡Department of Physics, Nano-magnetism Research Center, Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan, 52900, Israel. §ETH Zürich, Photonics Laboratory, Zürich, 8093, Switzerland. ┴Instituto de Física “Gleb Wataghin”, Universidade Estadual de Campinas, C. P. 6165, 13083-970 Campinas, Sao Paulo, Brazil.

║Departamento de

Fisica, CCT, Universidade Federal de Roraima,69304-000 Boa Vista, Roraima, Brazil. ∇Departamento de Física, Universidade Federal de Minas Gerais, Belo Horizonte, MG, 31270-901, Brazil.

*e-mail: ernesto.joselevich@weizmann.ac.il

Supporting Information Contents:

- Figure S1. Identification of carbon nanotube coils - Figure S2. Additional images of carbon nanotube coils and their cross-sections - Figure S3. Raman spectra of defect-free nanotube coils - Effect of gas flow on the formation of defect-free coils - Orientation of ribbon-like nanotube coils and the occurrence of twists - Energetics of the formation of defect-free carbon nanotube coils - Raman characterization of nanotube coils - Electrical characterization of nanotube coils - Figure S4. Bundling induced change in gate response - Figure S5. Characterization of the change in gate response in coiled nanotubes - Methods - References

2

Figure S1. Identification of carbon nanotube coils. a, Low-magnification SEM image

showing several coils (marked by yellow arrows). b, AFM height image of a coil (marked

by dashed yellow frame in a). The blue dashed line shows the position of the topographic

cross-section shown in c. c, The heights of the two sides of the coil are 14.0±0.3 nm (left)

and 13.3±0.3 nm (right), and the height of the nanotube tails is 2.0±0.3 nm.

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Figure S2. Additional images of carbon nanotube coils and their cross-sections. a, b, f and

g, AFM (a, b) and SEM (f, g) images of coils from which lamellae were cut at the

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positions marked by a white dashed line. c-e, h and i, The corresponding cross-sectional

TEM images of the coils. c and d (cross-section of a) show 41 turns. e (cross-section of

b) shows at least 21 turns. h (cross-section of f) shows 74 turns (the cross-section at the

opposite position on this coil is shown in Fig. 2h). i (cross-section of g) shows 29 turns.

Figure S3. Raman spectra of defect-free nanotube coils. The overlaid spectra of eight

different nanotube coils show a prominent G-band at (~1600 cm-1) and a negligible D-

band (~1350 cm-1), thus indicating a very low defect density.

Effect of gas flow on the formation of defect-free coils

Following our suggested formation mechanism (Fig. 4a-b), we examined the effect

of lowering the gas flow rate on the yield of the carbon nanotube coils. We grew

nanotubes at different gas flow rates, from 70 to 2000 sccm, and have not seen a

significant effect on coil yield. At a higher gas flow rate of 2500 sccm we did see much

fewer coils; however, this can be attributed to a general low yield of long (>100 µm)

carbon nanotubes, possibly due to a change in the flow regime.1-2 We also grew

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nanotubes under “zero flow” conditions, by closing off the gas flow to the inlet of the

CVD reactor; nevertheless, we did not observe an increase in the resulting yield of coils.

These results suggest that effects that are relatively insensitive to the range of flow

rates we tested, such as turbulence or thermal fluctuations, dominate the effect of the gas

flow rate, at least at the microscopic level. This corresponds to our findings for other

curved nanotube structures, the disordered serpentines, as the geometric properties of

these serpentines were shown to be fairly insensitive to changes of gas flow rates in the

range of 500 to 2500 sccm.3

Orientation of ribbon-like nanotube coils and the occurrence of twists

In some coils we have noticed sections with different heights (Fig. 2f-h). It seems

that this is caused at some point during the coil formation, probably when it finished

forming, or close to it, when its orientation with relation to the substrate changed at

certain locations. We hypothesize that the coil was formed preferentially in the vertical

direction, thus forming a ribbon and then, in some sections, “fell” to its side, which, due

to the strong van der Waals attraction between the nanotubes and the substrate, is the

energetically favored orientation. Such a change of orientation could have been facilitated

by thermal or flow fluctuations which could cause the wide side of the cross-section to

get near enough to the substrate to be pulled in by the van der Waals forces. This

explanation also accounts for twists we have observed in some of the coils, which would

be formed when part of the vertically aligned coil falls to one side, and part of it to the

other, as shown in Fig. 3. Interestingly, such twists may affect changes in the electronic

properties of the bundled nanotubes.4

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Energetics of the formation of defect-free carbon nanotube coils

We carried out molecular dynamics (MD) simulations to examine the energetics of

carbon nanotube coil formation. Interestingly, we found that the formation of the first and

of the other subsequent turns is fundamentally different (in terms of energy), with only

the first step requiring the presence of an external source of energy.

In order to form a carbon nanotube coil, an elastic cost must be overcome, since the

carbon nanotube has to be bent. This energy could be provided either by an external

source (thermal energy and surface interactions for instance) or by interactions between

parts of the system (inter-coil interactions, for instance). For the first turn, the analysis is

straightforward: external energy is required, since its formation does not provide any

structural energy gains. For the subsequent turns, we must consider that contact between

turns lowers the van der Waals energy of the system, and this might (or not) be enough to

overcome the bending cost.

In order to estimate the energy needed for the formation of the first turn of the coil,

we bent a 3 µm (13,0) carbon nanotube (1 nm diameter) into a single loop with a coil

diameter of 0.95 µm. Note that this carbon nanotube and loop diameters are within the

range of the structures reported in the experiments. We used the well-known and tested

CHARMM5 force field to describe the interaction between the atoms, and the LAMMPS6

package to compute the energies – the results are shown in Fig. 4f.

Our results show that the bending cost was rather low. Since the structure had

around 370,000 atoms, the highest bending cost per atom for the structures used was of

0.23 cal/mol. In fact, the cost was so low that the van der Waals gains provided by the

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nanotube overlapping lengths of just 7 nm were enough to overcome the energy cost of

bending the entire nanotube. These results suggest that once the first turn is formed, no

external energy source was needed for the subsequent turns.

To further investigate this issue, we carried out fully atomistic MD simulations of

the formation of defect-free carbon nanotube coils. A 3 µm (6,0) carbon nanotube was

partially bent to form an initial loop with a diameter of 65 nm. The rest of the nanotube

remained suspended above the substrate (Fig. 4h), and the system was set to freely

evolve. A Nosé-Hoover thermostat was employed to keep the temperature at 10 K, and a

time-step of 1 femtosecond was used to integrate the equations of motion. Low

temperature was used to reduce thermal fluctuations, ensuring that they did not play an

important role during the dynamics. The falling process is also smoother under these

conditions, thus allowing a better visualization of the carbon nanotube dynamics.

For these simulations we used smaller structures than the ones in the bending tests,

due to the high computational costs to simulate carbon nanotube coils. The cost to bend

an elastic rod with circular cross-sectional radius r is ∈#= %&'() - in this expression, E is

the Young’s modulus, κ is the curvature and * = +,-. is the area moment of inertia. By

decreasing the coil diameter we increased the curvature, and by decreasing the carbon

nanotube radius we decreased the area moment of inertia.

The evolution of the total energy and its components during a MD simulation of a

coil formation is shown in Fig. 4g (See also Movies S1 and S2). The so-called molecular

energy is composed of bond, angle and dihedral terms, and basically it is a measure of the

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structural elastic energy. Note that at the beginning of the simulation the energy actually

decreased, which is an unexpected result for a structure that is gradually becoming more

curved. The reason for this is that the initial structure was generated bent, and was not

fully relaxed at the start of the simulation. Relaxation was completed at t ≈ 3 ns, and after

that the energy remained nearly constant until t ≈ 13 ns. That the bending of the nanotube

into turns occurred with little elastic energy cost is consistent with our energy

calculations discussed above. At t ≈ 14 ns there was a sudden increase in the molecular

energy of the system. Examining the MD trajectory (see Movie S1), we observed that this

corresponded to the falling of the suspended end in a shape that had high curvature.

Regarding the kinetic energy, it remained constant throughout the simulation, as is

expected for a simulation that was carried out using a constant temperature ensemble.

If we examine the evolution of the total energy, however, we see that the two terms

above play only a secondary role during coil formation. For the most part, the total

energy trends follow closely the van der Waals component behavior, continuously

decreasing throughout the whole process. In fact, for an isolated nanotube, our results

indicate that the coil structure is more stable than the straight configuration. This result is

analogous to the finding that the energy of a graphene sheet decreases when it is turned

into a scroll.7 The final energy gain per atom, ~ 0.6 kcal/mol (26 meV), is about half the

adhesion energy for planar hydrocarbons atop graphite.8 Fig. 4i shows a snapshot of the

simulation 12.2 ns after its start.

The overall picture that emerges from our MD simulations for the formation of

carbon nanotube coils is: (1) external forces (due to thermal effects / gas flow, substrate

interactions, etc.) drive the formation of the first turn; (2) this first turn works as a

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template for the assembly of other turns, which spontaneous drives the system towards

equilibrium configurations.

Raman characterization of nanotube coils

The defect-free carbon nanotube coils may be considered as chirally homogeneous

carbon nanotube bundles, each bundle consisting of identical nanotubes. By comparing

the physical properties of the coils to those of their free ends, bundling effects can be

isolated and studied. While the effects of bundling on the properties of the nanotubes

have been previously studied theoretically9-14 and experimentally,12, 15-22 the theoretical

works focused on ideal bundles with perfect packing, whereas the experimental studies

were performed on heterogeneous bundles, containing nanotubes of different diameters

and chiralities. The heterogeneity of the bundles severely affected the density and order

of the packing of the nanotubes within them, thus obscuring different bundling effects.19

We used Raman spectroscopy to compare the nanotube coils and their free ends.

We did not find significant bundling-induced differences in the G-band and G’-band

(overtone of the D-band) of the nanotubes. We also did not observe a significant

difference in the intensity of the D-band relative to the G-band, which was negligibly

small in both the coil and its free ends. This finding is consistent with the self-coiling

mechanism, where the coil is formed after the nanotube has grown unperturbed in the gas

phase. Contrary to these findings, we did observe a noticeable difference in the RBM,

which we were able to measure in one of the nanotube coils we characterized, both in the

coil and in its free end (Fig. 5a). While theoretical works have reported that bundling of

carbon nanotubes should result in an upshift of the RBM,9-11, 14 this effect has not been

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reliably reproduced experimentally.19 Interestingly, the RBM of the nanotubes in our

coiled bundle exhibits a pronounced broadening, rather than a shift, when compared to

the free end of the coil (Fig. 5a). The broadening that we observe could be attributed to

an emergence of transversal phonons from the combination of RBMs in the bundle. It

could also be due to small differences in the RBMs of each nanotube turn comprising the

bundle, which stem from their relative position in the bundle, and the finiteness of the

bundle. The outlying nanotube turns, in the circumference of the bundle, do not

experience the same isotropic intertube interaction as the nanotubes that are within the

core of the bundle.

We also measured a peak at twice the frequency of the RBM, which we suspect is the

overtone (Fig 5a). Unlike the RBM, when comparing this peak in the spectrum of the coil

and the spectrum of its free end, we do not find a pronounced broadening, as we did for

the RBM peak. While this unexpected result could potentially be explained by the peak

not being an RBM overtone of the nanotube we measured, but rather being an RBM of an

additional nanotube present in the coil, and not an overtone of the RBM, we find this

possibility very improbable for several reasons: (1) Resonance Raman spectroscopy relies

on the carbon nanotube to be in resonance with excitation wavelength, a matter

dependent on the chirality of the nanotube, and for a random distribution of chiralities, as

in our nanotubes, it is not likely that one coil happens to include two nanotubes which are

both in resonance. (2) Furthermore, it is known that the RBM is difficult to measure in

carbon nanotubes.23 Though we successfully measured the Raman signal of nine coils, we

only succeeded in measuring one RBM. Therefore, it would be surprising had we

managed to measure two RBMs of two different nanotubes in the same coil. (3) Finally

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the fact that the higher frequency happens to be at double the frequency of the lower

RBM adds another aspect of improbability. Our result concerning the effect of bundling

of identical nanotubes on their low frequency Raman modes seems highly interesting and

should be further studied in the future.

Electrical characterization of nanotube coils

We used electrical characterization to compare the properties of the coils and their

free ends. We performed electrical measurement under different gating voltages of 23

coiled nanotubes. Nine of the nanotubes were metallic, which is just over the

theoretically expected fraction of one third, and 14 were p-type semiconductors, reaching

an “off-state” for large enough positive gate voltages. Out of those 14, seven were found

to show a diminished response to changes in gate voltage in the coil, ranging from no

response at all (Fig. S4d) to a modulation in current, without reaching the off-state (Fig.

S5c,f). None of the nanotubes exhibited a rectifying behavior when measured between an

electrode on the coil and an electrode on a free end (except for one case). This behavior is

different from that of typical semiconductor-metallic carbon nanotube junctions, where

rectification is usually observed due to the formation of a Schottky barrier.24-25

In one of the semiconducting carbon nanotubes we measured three sections: the

coil, the free end preceding the coil and the free end succeeding it. We found that while

both free ends displayed a strong p-type semiconducting gate response (Fig. S5b,d), the

coil displayed a significantly reduced gate response (Fig. S5c). This suggests that the

change in the band gap is fully reversible, and occurs only in the coil. We measured

another carbon nanotube which featured a modulation of the band gap in the coil both in

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room temperature and at 4 K. We found that the coil only reached an off-state at low

temperature, showing that its band gap was significantly smaller than that of its free end

(Fig. S5g).

While it is possible that mutual screening in carbon nanotube bundles could reduce

the gate response,26-27 the semiconducting free ends shown in Figs. S4 and S5 are in the

off-state under zero gate voltage. This means that: (i) these nanotubes could not provide

effective screening, and (ii) even if all the gate voltage had been screened, the bundle

should have been in the off-state. This is not to say that screening does not occur in the

coil, since once there is a change in its electrical properties, it could facilitate screening.

However, screening would then not be the cause of the change, but rather a result and

possibly an enhancement of it.

A change in the gate response of a nanotube could potentially be caused by a defect

induced change in its chiral index during synthesis.28 While we cannot completely

exclude such a change, we find this possibility highly unlikely for several reasons: (i) A

change in nanotube chirality would entail a change in its resonance energy. As shown in

Fig. 5a, the resonance energy is maintained throughout the length of the nanotube. (ii)

The defect density in our nanotube coils is negligibly low (Fig. S3). (iii) A change in the

chiral index of the nanotube would cause both instances of semiconducting nanotubes

displaying a metallic character and vice versa. Consistently, where we observed a change

in the gate response of the CNT, the change was from semiconducting in the free ends to

metallic in the coiled section. Also, we found this change to be reversible (Fig. S5b-d).

This reversibility is not consistent with a change in chirality.

13

Reich et al. have performed density functional theory calculations with local

density approximations to show that bundling could induce a decrease in the band gap of

semiconducting nanotubes, and also completely close it.13 They also showed the effect to

differ in magnitude for nanotubes of different band gaps,13 which would explain why we

have observed it only in some of our semiconducting nanotubes. Based on these

calculations, one could in principle suggest that our nanotube coils made of a

semiconducting single-wall carbon nanotube may become metallic due to bundling

effects. However, our Raman measurements show that the resonance energy, and hence

the electronic structure of the nanotube, remain unchanged upon coiling. Therefore, the

fact that a coil made of a semiconducting nanotube exhibits metallic behavior is not yet

understood.

14

Figure S4. Bundling induced change in gate response. a, SEM image of a nanotube

with three consecutive sections contacted by electrodes: 1 – free end, 2 – free end and

coil, 3 – coil. b-d, Gate voltage dependence of the current under source-drain bias voltage

(b,c - 100 mV, d – 10 mV) for sections 1-3, respectively. Insets in b-d indicate the

measured sections of the nanotube.

15

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Figure S5. Characterization of the change in gate response in coiled nanotubes. a,

SEM image of a nanotube with three consecutive sections contacted by electrodes: 1 –

free end, 2 – coil, 3 – free end. The boundary lines surrounding the area of the nanotube

are due to the oxygen plasma treatment used to remove other nanotubes on the sample

(see methods section for more details). b-d, Gate voltage dependence of the current

under source-drain bias voltage (b and d - 100 mV, c – 10 mV) for sections 1-3,

respectively. e, SEM image of a nanotube with two sections contacted by electrodes: 1’ –

free end and 2’ – coil. f, g Gate voltage dependence of the current in section 1’ under

source-drain bias voltage of 10 mV DC and 1 mV AC, at room temperature and at 4 K,

respectively. h, i Gate voltage dependence of the current in section 2’ under source-drain

bias voltage of 100 mV DC and 1 mV AC, at room temperature and at 4 K, respectively.

Insets in b-d and f-i indicate the measured sections of the nanotube.

Methods

Carbon nanotube synthesis: Si/SiO2 (Si (100) with a thermal oxide layer of 300 nm,

purchased from Silicon Valley Microelectronics, or 1 µm, purchased from International

Wafer Service Inc.) wafers were cut to samples, roughly 8 × 8 mm2 in size. Samples were

cleaned by sonication in acetone for 10 min, followed by rinsing in acetone and

isopropanol, and drying by N2.

Parallel stripes (25 µm wide, 25 nm thick) of amorphous SiO2 (Kurt J. Lesker,

99.99%), followed by a thin layer (nominally 0.3 nm) of Fe (Kurt J. Lesker, 99.95%)

growth catalyst were deposited on the substrate by standard photolithography and

electron-beam evaporation. Lift-off was done in acetone. The samples were introduced

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into a tube furnace (Lindberg blue) and aligned so the catalyst stripes were roughly

perpendicular to the gas flow direction. The samples were heated at 550 °C for 20 min in

air to remove organic contaminations. Single-wall carbon nanotubes were grown by

CVD: samples were heated to 900 °C, in an atmosphere of 60% Ar (Oxygen & Argon

Industries, 99.996%) and 40% H2 (Gordon Gas, 99.999%), followed by introduction of

~0.2% C2H4 (Gordon Gas, 99.9%). Flow rates typically ranged between 70 and 500 sccm

for a growth time of 45 min. At the end of the growth time, samples were left to cool in

Ar.

Imaging: Nanotubes were imaged by SEM (LEO Supra 55VP FEG and Ultra 55 Zeiss)

at low working voltages of 0.5–1.5 kV as well as by AFM (Veeco, Multimode

Nanoscope 7.30) in air tapping mode using 70 kHz silicon tips (Olympus). Thin lamellae

for TEM characterization of the nanotube coils were made using a Helios 600 FIB/SEM

DualBeam microscope (FEI). Prior to cutting the lamellae by ion beam milling, a

protective layer of ~40 nm of Pt was evaporated on the coil, by in-situ electron beam

induced deposition followed by ion beam induced deposition of Pt of ~2 µm. In most

cases, no deposition of conductive coating was done prior to the preparation of the

lamellae, due to the resulting deteriorated imaging contrast of the carbon nanotubes29.

However, we found that prior marking of the coils by electron beam lithography (as

described below for the fabrication of electrodes) and evaporation of 40 nm of Au

(Holland Moran Ltd., 99.999%) followed by deposition of conducting carbon (Edwards

carbon coater), significantly lowered the probability of charging induced misalignment of

the lamellae. The lamellae were inspected with a CM 120 TEM (Philips), operating at an

acceleration voltage of 120 kV.

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Electrical measurements: Alignment marks and contact pads were patterned on carbon

nanotube samples by standard photolithography and electron beam deposition of 5 nm of

Cr (Kurt J. Lesker, 99.95%) and 80-100 nm of Au. The samples were scanned for

nanotube coils by SEM, and mapped. The samples were then scanned by AFM, which

allowed to qualitatively estimate the number of turns in the coil.

Electrodes were patterned by an electron beam lithography system, either by SEM

(JEOL 6400 equipped with JC Nabity Nanopattern Generator System) or e_line plus

Raith system, using a bilayer of positive electron beam resist (either methyl methacrylate

(MMA 8.5, EL8) and poly(methyl methacrylate) (PMMA) 950 A4, or PMMA 495 A3

and PMMA 950 A4, all purchased from Microresist Technology GmbH). 20 nm of Pd

(Kurt J. Lesker, 99.95%), for ohmic contacting,30 and 10 nm of Au, to protect the

electrodes from oxidation, were evaporated onto the sample by electron beam

evaporation. In order to prevent other carbon nanotubes on the sample from short-

circuiting the electrodes, an additional pattern was created by electron beam lithography,

using negative electron beam resist (ma-N 2403, Microresist Technology GmbH), which

served as a protective mask for the coils. The sample was next ashed by oxygen plasma

(March Plasmod GCM 200, 60-100 seconds, 1 sccm of O2, 250 W) to remove the

unprotected carbon nanotubes, followed by lift-off in acetone. The results of the ashing

were verified by AFM, SEM, and electrical measurements.

A back gate was prepared by scratching the oxide layer at the back of the sample using

a diamond tip scriber to contact the heavily doped Si, and attaching the sample to a

copper electrode by applying silver paste. The electrical measurements were performed

19

using a homemade probe station, connected to a Keithley 2400 source meter and a PC

DAQ card (National Instruments PCI-6030E).

Magnetic measurements: Measurements were performed by scanning SQUID in liquid

He. The SQUID has a 3 µm pick-up loop, centered in a single-turn field coil. The

magnetic field generated by the current flowing in the sample was captured by the

SQUID pick-up loop as function of position.

In order to guide the scanning SQUID to the nanotube coils, an additional lithography

step was required. We used electron beam lithography followed by sputtering 100 nm of

Nb (critical temperature ~8.7 K) to create superconducting triangular markers, pointing at

the carbon nanotube coils. Using Nb markers allowed us, in case it was needed, to “turn

off” the magnetic signal from the markers by heating the sample over the critical

temperature of the Nb. Then, the sample was fit onto a chip carrier, which was a piece of

sapphire wafer with patterned pads, prepared by electron beam evaporation through a

shadow mask of Cr (5 nm) and Au (150 nm), and wire-bonded.

We navigated the SQUID using the Nb markers by mapping the diamagnetic response

of the superconductor due to the Meissner effect. This is done by applying a small local

field with a second coil around the pick-up loop. The markers are also observed in DC

magnetometry as they distort the ambient magnetic field lines. Measuring the DC

magnetic landscape, the AC diamagnetic response, and the AC response to current in the

sample can be done simultaneously.

Raman scattering measurements: Samples for optical measurements were prepared by

two different methods:

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(1) Growing nanotubes, following the procedure described above, on thin (200 µm) AT

cut quartz (The Roditi International Corporation Ltd).

(2) Growing nanotubes on Si/SiO2 substrates, as described above, and transferring them

to thin (~150 µm) fused quartz slides (Laser Optex Inc.).

The transfer method we used is similar to a previously reported method:31 poly(methyl

methacrylate) (PMMA) 950 A4 (Microresist Technology GmbH), was spin coated (3000

RPM, 1 minute) on the Si/SiO2 sample with carbon nanotubes. The sample was baked for

2 hours at 170 °C, and then placed in 1 M KOH aqueous solution at 80 °C for a minute to

initiate the separation of the PMMA film. The sample was briefly submerged in

deionized water and dried with a gentle flow of N2. Thermal tape (Revalpha, Nitto

Denko) was firmly pressed onto the sample, and then was gently peeled, removing the

PMMA film. The PMMA film, still attached to the thermal tape, was strongly (200 psi

pressure) pressed against a clean fused quartz substrate, using a homemade pneumatically

operated nanoimprint setup. The fused quartz substrate was then baked at 80-100 °C for 5

minutes, releasing the thermal tape. PMMA was removed by gentle shaking in acetone

for one minute, followed by rinsing in acetone and isopropanol, and drying by N2.

Raman scattering measurements were performed on a modified Nikon TE-300 inverted

confocal microscope. A frequency doubled ND:YAG laser (λ = 532 nm) was incident on

a 50/50 non-polarizing beam-splitter (Chroma) and was focused onto the sample with a

high NA oil-immersion objective (Nikon Plan APO 100x NA 1.4). Both linear and

circular polarized excitations were used. Scattered optical signal was collected by the

same objective, transmitted though the non-polarizing beam-splitter, and directed to a

single photon counting APD, with the appropriate filter set, or a spectrometer (Princeton

21

Instruments) fitted with a charge-coupled device (CCD). The sample was placed on a

piezo X-Y scan stage (Mad City Labs) and was raster scanned to form images.

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