Carbon Nanotube Chirality Determines Properties of EncapsulatedLinear Carbon ChainSebastian Heeg,† Lei Shi,‡ Lisa V. Poulikakos,§ Thomas Pichler,‡ and Lukas Novotny*,†

†ETH Zurich, Photonics Laboratory, 8093 Zurich, Switzerland‡University of Vienna, Faculty of Physics, 1090 Wien, Austria§ETH Zurich, Optical Materials Engineering Laboratory, 8093 Zurich, Switzerland

*S Supporting Information

ABSTRACT: Long linear carbon chains (LLCCs) encapsu-lated inside double-walled carbon nanotubes (DWCNTs) areregarded as a promising realization of carbyne, the truly one-dimensional allotrope of carbon. While the electronic andvibronic properties of the encapsulated LLCC are expected tobe influenced by its nanotube host, this dependence has notbeen investigated experimentally so far. Here we bridge thisgap by studying individual LLCCs encapsulated in DWCNTswith tip-enhanced Raman scattering (TERS). We reveal thatthe nanotube host, characterized by its chirality, determinesthe vibronic and electronic properties of the encapsulatedLLCC. By choice of chirality, the fundamental Raman mode(C-mode) of the chain is tunable by ∼95 cm−1 and its bandgap by ∼0.6 eV, suggesting this one-dimensional hybrid system to be a promising building block for nanoscale optoelectronics.No length dependence of the chain’s C-mode frequency is evident, making LLCCs a close to perfect representation of carbyne.

KEYWORDS: Linear carbon chains, carbyne, carbon nanotubes, Raman spectroscopy, TERS

Carbyne by definition is an infinitely long linear carbonchain (LLCC) with sp1 hybridization that forms the truly

one-dimensional allotrope of carbon at the one-atom cross-section limit.1−3 Its anticipated stiffness, strength, and elasticmodulus exceed that of any other known material.4 In its mostcommon form, carbyne is a polyyne with alternating single andtriple bonds originating from a Peierls distortion.5 This bond-length alternation (BLA) dominates the electronic andvibronic structure of carbyne.6−8 It opens up a direct bandgap that is sensitive to external perturbations, thus offeringtunability. Finite linear carbon chains are expected to exhibitthe properties of carbyne if they consist of 100 or more atomsas the BLA saturates.1 Exploring the fundamental properties ofcarbyne experimentally, however, has long been hindered by itsextreme chemical instability and short chain lengths of up to44 atoms.9

The synthesis of linear carbon chains inside carbonnanotubes, sketched in Figure 1(a), overcomes theseobstacles.10−16 The tubes act as nanoreactors, prevent chemicalinteraction of the chains with the environment, and allow forlong chain lengths. A major leap forward in forming carbyneare long linear carbon chains with lengths up to severalhundreds of nanometers that have recently been synthesizedinside double-walled carbon nanotubes (DWCNTs).17−21 Thelocal environment inside a nanotube, characterized by itschirality, is expected to affect encapsulated chains throughinteractions such as van-der-Waals (vdW) forces, charge

transfer, or dielectric screening and may even limit the chainlength.10−20 These interactions vary with chirality, modify theBLA, and effectively mask the intrinsic properties ofLLCCs.22,23 Recently, it was even suggested that there is aresidual length dependence of the chain’s properties far beyondthe currently accepted limit of 100 atoms.17,18,22 This wouldmean that LLCCs are not the finite realization of carbyne andthat the currently accepted models on the chain’s lengthdependence fail. However, while the properties of confinedlong linear carbon chains are governed by their nanotube hostand potentially by their length, the correspondence betweenthe host tube’s chirality, the properties of the encapsulatedchain, and the length of the chain have not been investigatedexperimentally.Raman spectroscopy is an excellent tool to study the

properties of the encapsulated chain and the characteristics ofthe encasing CNT. The dominant Raman mode of carbyne (C-mode) reports the bond-length alternation of the chain.1 Thechirality-specific Raman features of CNTs, in particular theradial breathing mode (RBM), are very well understood.24,25

Accordingly, Raman measurements of nanotubes hostingLLCCs allow us to correlate the electronic and vibronic

Received: April 25, 2018Revised: August 2, 2018Published: August 8, 2018

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properties of the LLCC to the properties of the nanotube andhelp to identify the dominating interaction between host andguest. Importantly, such a correlation cannot be establishedthrough bulk measurements because it is impossible to verifythat the Raman signal of both chain and tube arises from thesame pair. While this can be achieved through confocal Ramanmeasurements, the length of the investigated chain remainsunknown. Tip-enhanced Raman scattering (TERS), on theother hand, offers the nanoscale spatial resolution necessary tofind and characterize individual pairs of carbon nanotube andchain, measure the length of the chain, and unveil thecorrelation between the nanotube’s chirality and the chain’sproperties.17−19

In this letter, we present TERS measurements thatquantitatively link the C-mode frequency of long linear carbonchains entirely to the chirality of the encapsulating carbonnanotubes. We observe that the frequency of the C-modedecreases as the inner nanotube diameter is reduced, pointingtoward van-der-Waals forces as the dominating interactionbetween nanotube and chain. The chain’s properties show nolength dependence and have hence converged to the limit ofinfinite length. This provides strong evidence that long linearcarbon chains encapsulated in carbon nanotubes are the finiterealization of carbyne in different local environments.Details of our experimental setup have been described in

previous reports.26−28 In short, a focused radially polarizedlaser beam (λ = 633 nm) irradiates a gold pyramid fabricatedby template stripping.28 The enhanced field at the tip apexdefines a localized excitation source for Raman scattering.Raman-scattered light is collected in backscattering config-uration either by a combination of bandpass filters that

transmit the spectral region of the linear carbon chain’s C-mode (1770 cm−1 to 1870 cm−1)10−21 followed by a single-photon counting avalanche detector or by a combination ofspectrograph and charge-coupled device (resolution ∼3 cm−1).To avoid sample degradation due to heating, we used laserpowers of 115 μW for TERS and 1.15 mW for confocal (CF)imaging. Integration times are 25 ms/pixel for imaging and upto 60 s for acquiring full Raman spectra. LLCCs were growninside DWCNTs in a high-temperature and high-vacuumprocess as described in ref 17. The tubes were then purified,individualized, and dispersed on thin glass cover slides usingchlorosulfonic acid in an oxygen-free atmosphere.To locate individual carbon chains inside DWCNTs we first

perform confocal Raman raster scans (not shown). Once thesignature of a linear carbon chain is detected, we verify itspresence by observing the C-mode of the chain in a confocalRaman spectrum (black) as shown in Figure 1(b). We thenposition the tip near the surface (<1 nm) and record high-resolution topographical (see Supporting Information) andTERS images as shown in Figure 1(c). The TERS imagereveals that the DWCNT contains a linear carbon chain oflength 200 nm. The inset in Figure 1(c) shows a line profile(white) extracted from the TERS image indicating a resolutionof 23 nm.The TERS spectrum (red), shown in Figure 1(b), exhibits a

peak at 1798 cm−1 originating from the chain’s C-mode, alongitudinal-optical phonon that arises from the in-phasestretching of the triple bonds along the chain. It is the onlyRaman-active phonon in polyynic carbyne. The group of peakswith the dominant component at 1588 cm−1 is the G-modes,typical signatures of CNTs.24 The strong RBM at 348 cm−1

belongs to the inner carbon nanotube that is in resonance withthe excitation wavelength.29,30 The RBM corresponds to aradial displacement of the carbon atoms forming the nanotubeand enables us to determine its chirality.24,25,31 We do notobserve any signature of the defect-induced D-mode (∼1350cm−1), indicating that the nanotubes are pristine and largelyfree of defects.24 Upon increasing the tip−sample distance theRaman intensity drops exponentially as shown for the C-modein Figure 1(d), which confirms the local and enhanced natureof our TERS signal as compared to the confocal Raman spectra(black) in Figure 1(b). Notably, the enhancement of the C-mode is smaller than that of the CNT Raman modes, which iscurrently being studied. The difference may be attributed, i.e.,to the effect of spatial coherence or screening effects thatreduce the near-field intensity in the CNT’s interior where thechain is located.24,32

We identified and characterized 14 different chain−nano-tube systems that exhibit both a single C-mode frequency anda single RBM frequency. We present the corresponding TERSspectra with a focus on RBMs in Figure 2(a) and C-modes inFigures 2(b). As we are interested in peak positions only, theRBMs and C-modes are independently normalized to the sameamplitude and offset for clarity with decreasing RBM frequencyfrom top to bottom. For all spectra in Figure 2, a single RBMcan clearly be assigned to a corresponding single C-mode.Around 40 additional TERS measurements showed a single C-mode but lacked RBM signatures, which shows that theresonance condition of the CNTs is the bottleneck in ourexperiments. Further ∼20 measurements showed multipleRBM and/or C-modesprohibiting the correlation betweenthe nanotube’s chirality and the chain’s propertiesand werediscarded as they arose from bundles or CNT agglomerates.

Figure 1. TERS characterization of long linear carbon chains. (a)Sketch of a linear carbon chain (red) encapsulated in a double-walledcarbon nanotube (blue/yellow). (b) Confocal (CF, black) and TERS(red) Raman spectra of the same double-walled carbon nanotube andencapsulated long linear carbon chain. The RBM arises from a (6,4)inner carbon nanotube. (c) TERS image of a linear carbon chain. Theimage contrast corresponds to the intensity of the C-mode centered at1798 cm−1. An intensity profile (inset) extracted along the white lineshows a resolution of ∼23 nm. (d) Normalized TERS C-modeintensity as a function of the separation z between the tip and sample.

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Some of the RBMs and C-modes in Figure 2(a) have slightshape asymmetries. We primarily assign these to the limitedspectral resolution in our TERS experiments, as we sacrificespectral resolution for the high signal throughput necessary todetect faint RBM signals even with TERS enhancement. Adetailed analysis of the C-mode’s peak shape and width withhigh spectral resolution is beyond the scope of this work andwill be the subject of future studies.We now analyze in detail the correlation between the chain

and encasing nanotube by extracting the peak positions (singleLorentzian fits) from Figure 2 and plotting the C-modefrequency as a function of RBM frequency in Figure 3(a),including the singular data point from ref 19. The plot revealsthree distinct characteristics. First, each RBMrepresentingthe chirality of the encasing nanotubeuniquely correspondsto one specific C-mode frequencyrepresenting the linearchainto within ±3 cm−1. We refer to such a combination ofRBM and C-mode from now on as “pairing”. Second, specificpairings of RBM and C-mode occur multiple times. Thepairing for the RBM at 348 cm−1 and the C-mode at 1798cm−1 (dashed circle in Figure 3(a)) is particularly pronouncedand applies to half of our measurements. These RBMs arisefrom the same inner nanotube chirality, and the encapsulatedchains show similar Raman frequencies. The length of thechains, depicted in Figure 3(b) for all measured pairings, doesnot affect the chain’s C-mode frequencies. This is the coreobservation of our experiments because it is in stark contrast tothe pronounced length dependence of the C-mode frequenciesfor short linear carbon chains.2,3 Our measurements reveal aunique correspondence between nanotube RBM and carbon

chain C-mode frequencies, independent of the length of thecarbon chain as observed by TERS. We conclude that the innercarbon nanotube chirality represented by this RBM uniquelydetermines the chain’s bond-length alternation and hence itsvibronic and electronic structure.Before we assign RBMs to nanotube chiralities, we verify

that the presence of a linear carbon chain does not modify theRBMs of inner and outer nanotubes, which could otherwisefalsify our chirality assignment. We show this for one of thepairings (326 cm−1/1835 cm−1), where we also observe theRBM of the outer nanotube at 187 cm−1. This pairing iscompared to an empty DWCNT formed by the same innerand outer nanotube chiralities (see Supporting Information).For both the empty and the filled DWCNT, the RBMfrequencies of the inner and outer nanotube each agree towithin 1 cm−1. This uncertainty is negligible compared to theeffect of the outer CNT discussed in the next paragraph andwill not be taken into account when assigning RBMs tonanotube chiralities.Assigning RBMs to chiralities is not straightforward for

double-walled carbon nanotubes because one particular innertube can reside in different outer tubes. This variation in thediameter difference between inner and outer tube influencesthe wall-to-wall interactions. It renders the simple inverserelation between nanotube diameter and RBM frequency forsingle-walled carbon nanotubes invalid.24,31 Instead, the innertube’s RBM frequency increases by up to 35 cm−1 dependingon the outer nanotube’s diameter, while the diameters of bothinner and outer tubes effectively remain unchanged.29,30,33,34

As a consequence, DWCNT spectra show more RBMs thanthere are chiralities, and RBMs of different frequencies maybelong to the same inner tube chirality. This means that wecannot directly extract a linear trend from Figure 3(a) and thateach RBM frequency has to be analyzed and assigned to ananotube chirality individually. We perform this assignmentbased on experimental Raman studies on DWCNTs anddescribe it in detail in the Supporting Information. Inambigious cases, we additionally make use of the chiral angledependence of the nanotube’s G−-mode for small tube

Figure 2. TERS spectra of 14 pairs of long linear carbon chains andencapsulating carbon nanotubes. (a) RBM spectra of the innernanotube from highest (top) to lowest frequency. The RBMscorrespond to the (6,4), (6,5), (7,2), and (8,0) chiralties, respectively(see main text and Supporting Information). (b) C-mode Ramanmodes of the chains corresponding to the RBMs shown in (a). RBMand C-mode spectra are normalized independently to the same peakheight.

Figure 3. Correlation between C-mode and RBM. (a) C-mode ofencapsulated linear carbon chains vs radial breathing mode of theencasing inner carbon nanotubes extracted from the TERS spectrashown in Figure 2. Labels indicate the assignment of the RBMs to(n,m) chiralities (see main text and Supporting Information). (b)Length of LLCCs shown in (a) as observed by TERS in nm and asnumber of carbon atoms # forming the LLCC with 0.2558 nm latticeconstant.17

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diameters and arrive at a robust chirality assignment for allRBMs shown in Figure 3(a). Table 1 lists our tentativeassignment of the pairings of RBM and C-mode in Figure 3(a)to the chiralities of the inner carbon nanotubes and thecorresponding tube diameters d.We find that the two RBMs around 327 cm−1 and 335 cm−1

belong to the (6,5) inner nanotube, while the RBMs around348 cm−1 and 364 cm−1 belong to the (6,4) inner nanotube.These assignments intuitively make sense because chains withsimilar C-modes are allocated to inner tubes of the samechirality. The variation in the C-mode frequency for differentpairings belonging to the same inner nanotube is then ameasure for the effect of the outer nanotube on theencapsulated chain. We find this variation once for the (6,5)nanotube, for which the difference in C-mode frequencyamounts to 4 cm−1 (c.f. Table 1). This difference may arisefrom the fact that one outer nanotube is metallic while theother outer tube is very likely semiconducting (see SupportingInformation for a detailed discussion).Our third observation from the plot in Figure 3(a) is the

decrease of the C-mode frequency with increasing RBMfrequency. Making use of our assignment of RBMs to innernanotube chiralities (c.f. Table 1), we plot in Figure 4(a) theC-mode frequencies of the encapsulated chains as a function ofthe encasing inner carbon nanotube’s diameter. The data showa clear decrease in the chain’s C-mode frequency ωC withdecreasing diameter d and yields the linear relation

ω = + ·d a b d( )C (1)

with a = 1487 ± 36 cm−1 and b = 462 ± 41 cm−1 nm−1. Thisrelation excellently describes our observations and is plotted asthe black line in Figure 4(a). Note that we use the average C-mode frequency given in Table 1 instead of all 14 measured C-mode values for fitting eq 1 such that each pairing carries equalweight.The linear decrease of the encapsulated chain’s C-mode

frequency with decreasing nanotube diameter is strongevidence that the properties of the encapsulated chains aredominated by vdW interactions with the encasing inner carbonnanotube. This general trend has recently been postulatedqualitatively by Wanko et al.22 We assign the small deviationsfrom this linear trend, which amount to maximally 9 cm−1 forthe (7,2) inner nanotube, to charge transfer between the hostnanotube and the encapsulated chain. By measuring chainsencapsulated in different DWCNTs, our TERS measurementsrandomly probe different levels of charge transfer that varywith the four different inner CNT chiralities, labeled in Figure4(a), that are in resonance with the excitation. The overalleffect of charge transfer, however, remains small compared tothe effect of vdW interactions.In the following we use eq 1 to assign CNT diameters to the

tubes for which the RBM is not observed. This is possible

because inverting eq 1 provides a robust estimate of the innernanotube’s diameters based on the C-mode frequency alone.This estimate is relevant for the ∼40 TERS measurementswithout RBM signatures, as only a few of the inner nanotubechiralities present in the sample are in resonance with ourexcitation wavelength (c.f. Figure 3(a) and Table 1), and theresonance window of the RBM only spans around 50meV.24,25,31 Very rarely this is compensated by TERSenhancement. Figure 4(b) lists a representative set ofmeasured C-mode frequencies for which no RBM appearedin the corresponding TERS spectrum. The blue arrowsillustrate the assignment to diameters following eq 1. Weexpect the C-mode at 1808 cm−1, for instance, to reside insidea tube with d = 0.694 nm, very close to the (7,3) chirality withd = 0.696 nm, the resonance of which is at ∼2.5 eV and hencefar from our excitation (1.96 eV).29,35 Additional details onassigning C-modes to CNT diameters/chiralities are presentedin the Supporting Information.

Table 1. Average RBM Frequencies, Chiralities, and Diameters of the Inner Nanotubes Together with the Associated AverageC-Mode Frequencies and Band Gaps of the Encapsulated Chainsa

RBM (cm−1) 326 ± 1 335 ± 3 348 ± 2 364 ± 3 371 ± 1 391 ± 3

(n,m) CNTin (6,5) (6,4) (7,2) (8,0)d (nm) 0.747 0.683 0.641 0.626C−m (cm−1) 1835 ± 1 1831 ± 3 1798 ± 2 1798 ± 3 1792 ± 1 1772 ± 3EG (eV)18 2.11 2.08 1.87 1.83 1.70

aFor the pairings measured multiple times, the errors are given by the standard deviation of the average values. For individual pairings, the

experimental error is given. The diameter d of a (n,m) nanotube is given by π= + +d a n nm m/ 2 2 with a = 0.246 nm.24

Figure 4. Correlation between diameter of encasing inner carbonnanotube vs C-mode frequency and band gap of encapsulated longlinear carbon chain. (a) C-mode frequency of LLCC as a function ofthe encasing inner tube’s diameter. (b) C-mode frequencies of LLCCsfor which no RBM from the inner tube could be detected. (c) Bandgap EG as a function of C-mode from ref 18 (triangles) together with alinear fit that provides EG for the C-modes in this work (stars). (d)LLCC band gap EG as a function of inner CNT diameter d.

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We now compare our observations to recent wavelength-dependent Raman measurements on dense samples of LLCCsin DWCNTS.18 In these bulk measurements, the Ramanspectra were dominated by seven C-mode frequency bands at1793 cm−1 to 1865 cm−1. Three of these bands are within ourmeasurement range (1793 cm−1, 1802 cm−1, and 1832 cm−1)and agree well with our data (c.f. Figure 3(a) and (b)), wherewe also find a strong clustering of the C-modes around 1800cm−1 and 1830 cm−1. It suggests that eq 1 connecting thediameter of the inner carbon nanotube to the C-modefrequency also holds for higher C-mode frequencies notobserved in our TERS experiments. The highest observed C-mode at 1865 cm−1 corresponds to an inner tube diameter of d= 0.818 nm. This value is in very good agreement with recenttransmission electron microscopy studies, which found d =0.81 nm as the largest CNT diameter hosting long linearcarbon chains.15 Overall, our experimental data suggest thatLLCCs with C-mode frequencies from 1772 cm−1 to 1865cm−1 grow inside nanotubes with diameters from 0.626 to0.818 nm. Accordingly, eqs 1 and 2 hold true for this diameterrange.Combining the linear relationship between C-mode

frequencies and band gaps EG of encapsulated linear carbonchains, which was established in ref 18 for bulk and confirmedfor single chains in ref 36, with eq 1 allow us to express EG as afunction of the encasing inner nanotube’s diameter. We extractEG corresponding to a particular C-mode frequency from ref18 and plot the data (triangles) in Figure 4(c) together with alinear fit (see Supporting Information). This allows us toobtain EG corresponding to the C-modes observed here (starsin Figure 4(c) and Table 1) and to plot EG as a function of theinner nanotube’s diameter in Figure 4(d). We find the bandgap of encapsulated chains to increase linearly with thediameter of the inner nanotube as

= + ·E d c f d( )G (2)

with c = −0.14 ± 0.25 eV and f = 2.98 ± 0.37 eV nm−1.Our observation of fixed pairings of RBM and C-mode

frequencies indicates that we only observe chains for which thelength does not affect the C-mode. Commonly acceptedtheoretical models predict that the length dependence of thechain’s properties wears off for chains that consist of more than100 atoms (length ≥13 nm).8 As this is below our spatialresolution, we are unable to probe this limit. From the shortestchain measured by TERS in this work (length ∼30 nm, c.f.Figure 3(b)), however, we obtain a lower experimental limit of∼230 atoms for which no length dependence of the chain’sproperties is evident. Long linear carbon chains inside double-walled carbon nanotubes as measured in this work cantherefore be regarded as the finite realization of carbyne. Itfollows that the carbyne C-mode frequency and band gappredominantly depend on the local environment given by thechirality of the inner CNT.We would like to stress that eqs 1 and 2 will no longer hold

for very short carbon chains since the C-mode frequencybecomes dependent on the number of atoms for shorterchains. This does not exclude the existence of shorter chains inCNTswe merely expect them to occur at higher excitationenergies and C-mode frequencies, i.e., as reported in ref 37.With few inner tube chiralities hosting LLCCs, the number

of different local environments that affect the properties of theencapsulated chains is limited and distinct in nature. This factis reflected in all experimental studies on linear carbon chains

encapsulated in carbon nanotubes known to the authors.10−18

The observed C-modes are well separated into differentfrequency bands that vary around comparable meanfrequencies. In very good agreement with our measurementsno C-modes between 1810 cm−1 and 1825 cm−1 are reported.According to eq 1, only the C-mode of chains encapsulated inthe metallic (9,0) and (8,2) nanotubes fall in this range. Onemay speculate that this apparent lack of LLCCs in metallicnanotubes is due to a less efficient growth process as comparedto semiconducting tubes, which would prohibit us and othersfrom observing the corresponding C-modes. Alternatively, theinteraction between a chain and a metallic tube may differ fromthe interaction with a semiconducting nanotube, leading to adeviation from the linear trend in eq 1.Our results suggest that tunability of carbyne of up to ∼95

cm−1 in C-mode frequency (c.f. Figure 4(a)) and 0.6 eV inband gap (c.f. Figure 4(c) and (d)) can be achieved bychoosing the right nanotube host, a property that can haveinteresting applications in low-dimensional optoelectronics.Long linear carbon chains encapsulated in nanotubes with anarrow diameter distribution, for instance, may serve asabsorptive elements with a uniform band gap in nanoscalephotodetection despite the strong variations of the hostnanotube’s optical resonances with chirality. This work shows(i) which inner nanotube diameters and chiralities shouldgenerally be aimed for and (ii) which C-mode frequencyshould be used to monitor the growth of carbyne with thedesired properties.In conclusion, using tip-enhanced Raman spectroscopy we

have investigated isolated pairs of double-walled carbonnanotubes and encapsulated long linear carbon chains. Thechain’s Raman frequency is governed by the chirality of theinner tube and reduces with decreasing inner tube diameter.This points toward van-der-Waals forces as the dominatinginteraction mechanism between the host nanotube and theencapsulated chain. No length dependence of the chain’sRaman mode frequency is evident for the long linear carbonchains investigated, suggesting that they can be viewed as aclose to perfect representation of carbyne. Our experimentaldata establish a firm link between the local environment of thehost nanotube and properties of the encapsulated linear carbonchainthereby explaining the variation in the chain’s Ramanmode frequencyand identify parameters for tuning thephononic and electronic properties of carbyne for deviceapplications.

■ ASSOCIATED CONTENT*S Supporting InformationThe Supporting Information is available free of charge on theACS Publications website at DOI: 10.1021/acs.nano-lett.8b01681.

Topography recorded during TERS imaging; effect ofencapsulated chains on the RBM of DWCNT; assigningchiralities to the RBMs of inner carbon nanotubes; onthe effect of the outer NCT on the encapsulated LLCC;assigning chain band gaps to pairings of RBM and C-mode; assigning CNT chiralities to C-mode frequencieswithout RBMs (PDF)

■ AUTHOR INFORMATIONCorresponding Author*E-mail: lnovotny@ethz.ch, sheeg@ethz.ch.

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ORCIDSebastian Heeg: 0000-0002-6485-3083Lei Shi: 0000-0003-4175-7803Lisa V. Poulikakos: 0000-0002-1118-789XThomas Pichler: 0000-0001-5377-9896Lukas Novotny: 0000-0002-9970-8345NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSThe authors thank M. Frimmer, M. Parzefall, and S. Reich forfruitful discussions. This research was supported by the SwissNational Science Foundation (grant no. 200021_165841). S.Heeg acknowledges financial support by ETH Zurich CareerSeed Grant SEED-16 17-1. T.P acknowledges support of theAustrian Science Fund Project P27769-N20.

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Nano Letters Letter

DOI: 10.1021/acs.nanolett.8b01681Nano Lett. 2018, 18, 5426−5431

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