Band structure dependent electronic localization in macroscopic films of single-chirality single-wall carbon nanotubes
Weilu Gao, Davoud Adinehloo, Ali Mojibpour, Yohei Yomogida, Atsushi Hirano, Takeshi Tanaka, Hiromichi Kataura, Ming Zheng, Vasili Perebeinos, Junichiro Kono
BBand structure dependent electroniclocalization in macroscopic films ofsingle-chirality single-wall carbon nanotubes
Weilu Gao, ∗ , † , (cid:52) Davoud Adinehloo, ‡ Ali Mojibpour, ¶ Yohei Yomogida, § AtsushiHirano, (cid:107)
Takeshi Tanaka, (cid:107)
Hiromichi Kataura, (cid:107)
Ming Zheng, ⊥ Vasili Perebeinos, ‡ and Junichiro Kono ¶ , , @ † Department of Electrical and Computer Engineering, Rice University, Houston TX, 77005 ‡ Department of Electrical Engineering, University of Buffalo, Buffalo NY, 14228, U.S.A. ¶ Department of Electrical and Computer Engineering, Rice University, Houston TX,77005, U.S.A. § Department of Physics, Tokyo Metropolitan University, Hachioji, Tokyo 192-0397, Japan (cid:107)
Nanomaterials Research Institute, National Institute of Advanced Industrial Science andTechnology (AIST), Tsukuba, Ibaraki 305-8565, Japan. ⊥ National Institute of Standards and Technology, Gaithersburg MD, 20899, U.S.A.
Department of Physics and Astronomy, Rice University, Houston TX, 77005, U.S.A. @ Department of Materials Science and NanoEngineering, Rice Univesity, Houston TX,77005, U.S.A. (cid:52)
Present Address: Department of Electrical and Computer Engineering, University ofUtah, Salt Lake City UT, 84112
E-mail: [email protected] a r X i v : . [ c ond - m a t . m e s - h a ll ] J a n bstract Much understanding exists regarding chirality-dependent properties of single-wallcarbon nanotubes (SWCNTs) on a single-tube level. However, macroscopic manifes-tations of chirality dependence have been limited, especially in electronic transport,despite the fact that such distinct behaviors are needed for any applications of SWCNT-based devices. In addition, developing reliable transport theory is challenging since adescription of localization phenomena in an assembly of nanoobjects requires preciseknowledge of disorder on multiple spatial scales, particularly if the ensemble is het-erogeneous. Here, we report observation of pronounced chirality-dependent electroniclocalization in temperature and magnetic field dependent conductivity measurementson single-chirality SWCNT films. The samples included semiconducting (6,5) and (10,3)films, chiral metallic (7,4) and (8,5) films, and armchair (6,6) films. Experimental dataand theoretical calculations revealed variable-range-hopping dominated transport in allsamples except the armchair SWCNT film. We obtained localization lengths that fallinto three distinct categories depending on their band gaps. The clear deviation ofthe armchair films from the other films suggests their robustness toward defects andpossible additional transport mechanisms. Our detailed analyses on electronic trans-port properties of single-chirality SWCNT films provide significant new insight intoelectronic transport in ensembles of nanoobjects, offering foundations for designing anddeploying macroscopic SWCNT solid-state devices.
Keywords electronic transport, localization, carbon nanotubes, single-chirality
Introduction
Single-wall carbon nanotubes (SWCNTs) make an ideal playground of investigating elec-tronic, optical, magnetic, and thermal properties in one-dimension (1D). They are cylindri-2al tubular crystals formed by rolling a two-dimensional (2D) graphene sheet along a vectorin the graphene lattice plane, which decides most properties in SWCNTs. Many exceptionalphenomena, such as lightweight electric wires with ultrahigh current carrying capacity and mechanical strength, strong and anisotropic excitonic optical absorption, large andanisotropic thermal conductivity, and substantial thermoelectric power, are rootedin the wrapping orientation of graphene, i.e., chirality, described by a pair index ( n, m ). Forsome orientations, SWCNTs are direct band semiconductors, while for other orientations,SWCNTs are metallic or narrow-bandgap semiconductors. However, the performance ofelectronic and optoelectronic devices and systems based on SWCNT ensembles is generallyfrustrated by the quality of SWCNT films, where the macroscopic manifestation of promisedextraordinary properties in nanoscale single tubes is missing because of defects, uninten-tionally doping, intertube interactions, random orientation, and most significantly, mixedchiralities. When SWCNTs are synthesized in high-temperature furnaces, many chiralitiesof SWCNTs are produced together, including both semiconducting and metallic tubes, andas a consequence, exotic charge carrier transport effects, such as quantum interference, have never been observed in ensembles. Thus, early transport studies exclusively focused onsingle-tube experiments, where, however, the contact resistance prevents study frombeing extended down to small-diameter SWCNTs (< 1 nm).Solution-based chirality separation techniques provide new opportunities for addressingchallenges of structural polydispersity in SWCNT ensembles. Current status of sorting meth-ods mainly modifies the hydrophilicity of SWCNTs in aqueous dispersion depending on theirelectronic structures. Among these techniques, aqueous two phase extraction (ATPE) andgel-chromatography methods have been widely used for large-scale separation, and especiallywith the assist of DNA selectivity, ultrahigh purity and single-chirality SWCNT suspensionscan be prepared in substantial amounts. Furthermore, solution-based large-scale assembly,such as vacuum filtration, can preserve the chirality purity and produce wafer-scale uniformsamples. These two aspects of the advancement in materials preparation facilitate macro-3copic metrology, including both electronic and optical methods. Despite prior reports ofSWCNT film transport phenomena in metallicity-enriched samples, the mixed chiralitiesin films complicate the clear and comprehensive understanding. Thus, it is crucial to study single-chirality SWCNT film transport, which has not been reported before.In this work, we systematically investigate temperature-dependent conductivity and lowtemperature magneto-resistance (MR) of single-chirality SWCNT films, including semicon-ducting (6,5) and (10,3) tubes, chiral metallic (7,4) and (8,5) tubes, and armchair (6,6)tubes, which are prepared through solution-based chirality separation techniques and large-scale vacuum filtration assembly. We observe that variable-range-hopping (VRH) conductiondominates the transport behavior of semiconducting SWCNTs and chiral metallic SWCNTs.However, armchair SWCNTs display significant discrepancy from VRH conduction even atslightly elevated temperature. Moreover, extracted localization lengths strongly dependson SWCNT band structures, clearly showing three categories: the tubes with ( n − m ) mod ± have the smallest localization length and the largest bandgaps; the tubes with ( n − m )mod and n (cid:54) = m have both medium values; and the tubes with n = m have the largestlocalization lengths and the smallest bandgaps. MR measurement confirms the order of lo-calization length. Theoretical calculations recovers these three categories and quantitativelyagree with experimental results. Despite similar defect densities in different chirality tubes,armchair metallic SWCNTs are less affected to the presence of defects, which could be dueto other transport mechanism. These measurements and analysis provide insight for futureSWCNT electronic and optoelectronic devices. Results and discussion
Figure 1 summarizes the preparation and characterization of chirality-sorted suspensions,films, and fabricated electronic devices. The preparation of single-chirality SWCNT sus-pensions utilized two solution-based separation techniques, aqueous two phase extraction4ATPE) and gel-chromatography. Figure 1a display all sorted suspensions, including (6,5),(6,6), (7,4), (8.5), and (10,3) from the left to right. (6,5), (6,6), and (7,4) suspensions wereprepared using standard ATPE method; details are described in references.
Briefly, well-dispersed SWCNT suspensions consisting of multiple chiralities were mixed with a polymersolution including two polymers of different hydrophilicity. By carefully manipulating sur-factant concentration and combinations, SWCNTs of different band structures have differenthydrophilicity and thus partition across two polymers in different fraction. By extracting onephase containing more shares of targeted species and adding a fresh new polymer phase, thepartition and sorting process continue to purify suspension till nearly single-chirality suspen-sions. (8,5) suspensions were sorted and separated from as-grown SWCNT powder followingsimilar procedures used in ATPE technique. The difference, however, is that instead of dis-persing SWCNTs with surfactant combinations, the dispersant used is DNA molecule. DNAmolecules have better selectivity and resulting SWCNT purity and the details of theseparation process can be found in references. Finally, (10,3) suspensions were prepared using column chromatography and details aredescribed in reference. Briefly, well-dispersed SWCNT suspensions were fed into a con-ventional chromatography system, whose column was filled with gel beads. SWCNTs withdifferent band structures have different bound strength with gel beads, where metallic andnarrow-bandgap tubes are unbounded on beads. After elution of unbound SWCNTs withan aqueous surfactant solution, the adsorbed SWCNTs were eluted and collected throughstepwise elution chromatography with gradually increased surfactant concentration. At cer-tain concentration, single-chirality (10,3) SWCNTs were eluted. All sorted suspensions wereinspected using UV-Vis-NIR spectroscopy for evaluating the obtained purity. Signature ex-citonic absorption peaks in semiconducting (e.g. (6,5) and (10,3)), chiral metallic (e.g. (7,4)and (8,5)), and armchair metallic (e.g. (6,6)) SWCNTs have been clearly observed; seeFig. 1b. Except a few residue (6,5) tubes in (7,4) suspension, all other suspensions demon-strate ultrahigh purity beyond 90%. See
Supporting Information Section 1 for suspension5 a) (c)
500 750 1000 1250
Wavelength (nm) N o r m a li z e d A b s o r p t i o n (d)(b) (6,5)(6,6)(7,4)(8,5)(10,3) (6,5)(7,4)(6,6) IV(6,5) (6,6) (7,4) (8,5) (10,3) Figure 1:
Single-chirality SWCNT suspensions, films, and electronic devices. (a) Sorted single-chirality SWCNT suspensions of (6,5), (6,6), (7,4), (8,5), and (10,3).(b) UV-Vis-NIR spectroscopy of those sorted SWCNT suspensions. (c) Large-scale uniformfilms of single-chirality SWCNTs obtained from vacuum filtration. (d) Fabricated devicesfor electronic transport measurements using standard micro/nanofabrication processes.preparation details.Large-area uniform films of single-chirality SWCNTs were produced using vacuum filtra-tion. Figure 1b shows the filtrated system and a few examples of produced (6,5), (6,6), and(7,4) films. The obtained suspensions sorted using aforementioned techniques were pouredinto the funnel in the filtration system, where a 80-nm pore size filter membrane was placedbelow the funnel to retain SWCNTs on top of it with smaller molecules, such as water andsurfactants, penetrating through the membrane. As a result, large-scale SWCNT films havebeen deposited on the filter membrane. Due to the self-limiting nature of vacuum filtra-tion process, the film thickness is uniform and can be carefully controlled. Specifically,we tried to have the same film thickness used in this study, which is ∼ nm; see atomicforce microscope image and height profile of a representative film in Supporting InformationSection 2 .The obtained films can be transferred onto nearly arbitrary substrates and are compatible6ith micro/nanofabrication processes. As shown in Fig. 1d, the films were first transferredonto silicon oxide/silicon substrates and patterned into geometries using standard lithog-raphy and oxygen dry etching processes. Fabricated devices were then annealed under Aratmosphere at 350 ◦ C for 30 min. The outer large electrodes of the area ∼ mm in fabricateddevices were bonded to a gold wire through indium cold welding, and the gold wire connectsto electric connection in a cryostat. The indium cold welding helps protect devices fromsoldering damage. The cryostat can span temperature ranges from ∼ K to ∼ K. Afour-point measurement was employed, as shown in Fig. 1d. The current was supplied fromthe two outmost electrodes and the voltage was measured on a geometry of µ m width and µ m length. At each temperature point, a current-voltage sweep was performed and theconductivity value was extracted in the linear region. (1/K ) − − C o ndu c t i v i t y ( n S ) (6,5)(10,3)(8,5)(7,4)(6,6) Figure 2: Film conductivity for all 5 single-chirality samples. Solid dots are experimentaldata and dashed lines are fitting curves based on 1D VRH model.Figure 2 shows the conductivity of all five samples and an universal trend of decreasingconductivity with decreasing temperature is displayed. All temperature-dependent conduc-7ivity were fit with 1D VRH model stating σ ( T ) = σ exp ( − ( T T ) / ) , where T is temperature, σ is conductivity, σ is a fitting conductivity prefactor, and T is fitting characteristic tem-perature. The obtained T of five samples clearly falls into three categories; see Exp. T inTable 1. Large-gap semiconducting SWNCTs (6 , and (10 , have T on the order of 1000s,narrow-gap metallic SWCNTs (8 , and (7 , have T on the order of 100s, and armchairSWCNT (6,6) has T on the order of 10s. The localization length ξ is inversely proportionalto T through T = β/ DOS ( ε ) ξ , where DOS ( ε ) is the density of states at energy ε . Consid-ering similar sample preparation procedures and similar density of defects, the appearanceof three category T and thus ξ suggests that the localization mechanism originates fromdistinct band structures of five SWCNTs. Furthermore, (6 , SWCNTs show observablediscrepancy from 1D VRH model, which suggests other mechanism and the detailed calcula-tion will be included in future works. Also, from the comparison for these three categories,armchair SWCNTs display the longest localization length and are more robust and immuneto the existence of defects.Table 1: Characteristic temperature and localization length of five samples from bothexperiments and calculationsCNTs (6,5) (10,3) (8,5) (7,4) (6,6)Exp. T (K) 2025 1765 366 876 51 E g (eV) 1.27 0.99 0.446 0.379 0.193Cal. T (K) 2250 1420 580 800 355Cal. ξ (nm) 0.21 0.44 2.7 1.7 8.0To better understand the relation between band structure and localization mechanism,Figure 3 summarizes our calculated localization lengths as a function of doping densities forfive single-chirality samples. The localization length ξ in the presence of disorder can beestimated as following ξ ( ε ) = | v ( ε ) | τ ( ε ) , (1)where ε is energy and τ is the scattering time due to the disorder, which can be evaluated8sing the Fermi-Golden rule τ ( ε ) = 2 π ¯ h (cid:104)|(cid:104) Ψ ε | H | Ψ ε (cid:105)| (cid:105) dis DOS( ε ) , (2)where DOS( ε ) = 4 L/π ¯ hv ( ε ) is the density of states of a SWCNT of length L .In the Anderson model with a random on-site potential disorder in the range [ − W/ , W/ the averaged square of the matrix element is given by (cid:104)|(cid:104) Ψ ε | H | Ψ ε (cid:105)| (cid:105) dis = W N , (3)where N = Lπd/A c is the number of carbon atoms in a SWCNT of diameter d = a √ n + nm + m /π and A c = a √ / is the area per carbon atom in graphene with a unit cell length a = 2 . Å.Putting the results of Eqs. 1–3 together we obtain ξ ( ε ) = d
32 ¯ h v ( ε ) W A c . (4)A hyperbolic dispersion velocity is given by v ( ε ) = v F (cid:113) ε − E g / /ε , where E g is a SWCNTbandgap and v F = 10 cm/s is a Fermi velocity in graphene.We assume that all SWCNTs have the same level of disorder W since the fabricationand processing conditions are very similar and also assume that the doping level n is thesame for all SWCNTs, which relates to the Fermi energy ε F at zero temperature according to ε F = (cid:113) E g / π ¯ hv F n/ . Therefore, in order to compare values of ξ in different SWCNTs,we use the following relation ξ ( n ) = d
32 ¯ h v F W A c n n + 4 E g / ( π ¯ hv F ) . (5)The simulations of ξ according to Eq. 5 for W = 0 . eV are shown in Fig. 1, for the choice ofthe bandgaps given in Table 1. For the semiconducting SWCNTs we use conventional values9rom reference. For the metallic armchair (6,6) SWCNT we use a correlation bandgapvalue suggested in reference. For the chiral metallic SWCNTs we use a combination ofthe curvature induced gap and the electron correlation induced gap. For a typical carrierdensity of n = 0 . e/nm, shown by a vertical line in Fig. 3, we can find a good match betweenthe simulated values of T and the experimentally obtained values except for (6,6) SWCNT.In the latter case, we find a factor of 7 larger value of calculated T than the experimentalvalue. This indicates that the origin of temperature dependence is different in (6,6) sampleand armchair SWCNTs are less affected by defects and thus weakly localized. Indeed underour assumption for the same values of disorder strength and carrier density in differentSWCNTs that follows from the similar fabrication conditions, we find that localization lengthin (6,6) SWCNT would have been 8 nm. Therefore, the condition for the applicability forthe VRH mechanism L CNT (cid:29) ξ is weakened in (6,6) film as compared to other SWCNTsamples, where L CNT ∼ nm in our samples. n (e/nm) ξ ( n m ) (6,6)(8,5)(7,4)(10,3)(6,5) Figure 3: Localization lengths for all five single-chirality samples. The solid vertical linerepresents the assumed doping level for all samples.10 .0 2.5 5.0 7.5 10.0
Magnetic Field (T) M a g n e t o - R e s i s t a n ce (10,3)(7,4)(8,5)(6,6) Figure 4: MR of single-chirality films. Solid dots are experimental data for four samples. (6 , samples have the resistance out of measurement range. Green dashed line is the fittingcurve for (10 , sample, while others are used for connecting experimental data.11inally, we further performed MR measurements of five films at T = 20 K and threekinds of behaviors have been again clearly observed; see Fig. 4. Specifically, (10 , filmsdisplay strong positive MR while (6 , films show negative MR, up to the magnetic field( B ) 10 T. (7 , and (8 , instead demonstrate a combination of two trends. In (10 , films, strong localization paradigms including two positive MR contribution created by wave-function shrinkage and spin-dependent hopping feature a scaling dependence of B . We fitexperimental data (green dots in Fig. 4) with the expression ln [ ρ ( B ) /ρ (0)] = B B , where B = √ φ πξ (cid:113) T T , φ = he is the flux quantum, and ρ ( B ) is the resistance under magnetic field B . The extracted B is ∼ T and ξ for (10 , films is ∼ . nm. This value qualitativelyagrees with values obtained from theoretical calculations based on temperature-dependentconductivity measurements. Moreover, (6 , films display the signature of weak localizationand negative MR, suggesting the largest localization length. Also, the behaviors of (7 , and (8 , films stay in the middle with medium localization strength. The indication oflocalization strength from MR measurements is consistent with results from temperature-dependent conductivity.In summary, we reported temperature-dependent conductivity and MR of single-chiralitySWCNT films of three representative categories, which are ( n, m ) SWCNTs with ν = ( n − m ) mod 3 equal ± and , respectively. Despite similar defect densities in films, the localizationlength strongly depends on SWCNT bandgaps and falls into three categories, where chiralsemiconducting SWCNTs have the largest bandgap and the smallest localization length, chi-ral metallic SWCNTs have medium bandgap and localization length, and armchair SWCNTshave the smallest bandgap and the largest localization length. Theoretical calculations con-firm the observation both qualitatively and quantitatively, except for armchair SWCNTs.It suggests the breakdown of self-consistence of VRH formula in armchair SWCNTs and anadditional mechanism might be responsible for the observed temperature dependence, whichdeserves further investigation. This immunity and robustness of armchair SWCNTs towarddefects and impurity in macroscopic samples makes it promising for future electronic and12ptoelectronic applications. 13 upporting Information Available The Supporting Information is available free of charge.Information on the sample preparation and characterization (PDF).
References (1) Bockrath, M.; Cobden, D. H.; Lu, J.; Rinzler, A. G.; Smalley, R. E.; Balents, L.;McEuen, P. L. Luttinger-liquid behaviour in carbon nanotubes.
Nature , ,598–601.(2) Yao, Z.; Kane, C. L.; Dekker, C. High-field electrical transport in single-wall carbonnanotubes. Phys. Rev. Lett. , , 2941.(3) Wang, X.; Behabtu, N.; Young, C. C.; Tsentalovich, D. E.; Pasquali, M.; Kono, J.High-Ampacity Power Cables of Tightly-Packed and Aligned Carbon Nanotubes. Adv.Funct. Mater. , , 3241–3249.(4) Behabtu, N.; Young, C. C.; Tsentalovich, D. E.; Kleinerman, O.; Wang, X.; Ma, A.W. K.; Bengio, E. A.; ter Waarbeek, R. F.; de Jong, J. J.; Hoogerwerf, R. E.; Others,Strong, light, multifunctional fibers of carbon nanotubes with ultrahigh conductivity. Science , , 182–186.(5) Bai, Y.; Zhang, R.; Ye, X.; Zhu, Z.; Xie, H.; Shen, B.; Cai, D.; Liu, B.; Zhang, C.; Jia, Z.,et al. Carbon nanotube bundles with tensile strength over 80 GPa. Nat. Nanotechnol. , , 589–595.(6) Ando, T. Excitons in carbon nanotubes. J. Phys. Soc. Jpn. , , 1066–1073.(7) Wang, F.; Dukovic, G.; Brus, L. E.; Heinz, T. F. The optical resonances in carbonnanotubes arise from excitons. Science , , 838–841.148) Gao, W.; Li, X.; Bamba, M.; Kono, J. Continuous transition between weak and ultra-strong coupling through exceptional points in carbon nanotube microcavity exciton-polaritons. Nat. Photonics , , 362–367.(9) Katsutani, F.; Gao, W.; Li, X.; Ichinose, Y.; Yomogida, Y.; Yanagi, K.; Kono, J. Di-rect observation of cross-polarized excitons in aligned single-chirality single-wall carbonnanotubes. Phys. Rev. B , , 35426.(10) Fujii, M.; Zhang, X.; Xie, H.; Ago, H.; Takahashi, K.; Ikuta, T.; Abe, H.; Shimizu, T.Measuring the thermal conductivity of a single carbon nanotube. Phys. Rev. Lett. , , 065502.(11) Pop, E.; Mann, D.; Wang, Q.; Goodson, K.; Dai, H. Thermal conductance of an in-dividual single-wall carbon nanotube above room temperature. Nano Lett. , ,96–100.(12) Yamaguchi, S.; Tsunekawa, I.; Komatsu, N.; Gao, W.; Shiga, T.; Kodama, T.; Kono, J.;Shiomi, J. One-directional thermal transport in densely aligned single-wall carbon nan-otube films. Appl. Phys. Lett. , , 223104.(13) Hicks, L. D.; Dresselhaus, M. S. Thermoelectric figure of merit of a one-dimensionalconductor. Phys. Rev. B , , 16631.(14) Blackburn, J. L.; Ferguson, A. J.; Cho, C.; Grunlan, J. C. Carbon-Nanotube-BasedThermoelectric Materials and Devices. Adv. Mater. , , 1704386.(15) Ichinose, Y.; Yoshida, A.; Horiuchi, K.; Fukuhara, K.; Komatsu, N.; Gao, W.;Yomogida, Y.; Matsubara, M.; Yamamoto, T.; Kono, J., et al. Solving the Thermo-electric Trade-Off Problem with Metallic Carbon Nanotubes. Nano Lett. , ,7370–7376. 1516) Kong, J.; Yenilmez, E.; Tombler, T. W.; Kim, W.; Dai, H.; Laughlin, R. B.; Liu, L.;Jayanthi, C.; Wu, S. Quantum interference and ballistic transmission in nanotube elec-tron waveguides. Phys. Rev. Lett. , , 106801.(17) Deshpande, V. V.; Chandra, B.; Caldwell, R.; Novikov, D. S.; Hone, J.; Bockrath, M.Mott insulating state in ultraclean carbon nanotubes. Science , , 106–110.(18) Senger, M. J.; McCulley, D. R.; Lotfizadeh, N.; Deshpande, V. V.; Minot, E. D. Uni-versal interaction-driven gap in metallic carbon nanotubes. Phys. Rev. B , ,035445.(19) Yanagi, K.; Udoguchi, H.; Sagitani, S.; Oshima, Y.; Takenobu, T.; Kataura, H.;Ishida, T.; Matsuda, K.; Maniwa, Y. Transport mechanisms in metallic and semicon-ducting single-wall carbon nanotube networks. Acs Nano , , 4027–4032.(20) Wang, X.; Gao, W.; Li, X.; Zhang, Q.; Nanot, S.; Hároz, E.; Kono, J.; Rice, W.Magnetotransport in type-enriched single-wall carbon nanotube networks. Phys. Rev.Mater. , , 116001.(21) Khripin, C. Y.; Fagan, J. A.; Zheng, M. Spontaneous partition of carbon nanotubes inpolymer-modified aqueous phases. J. Am. Chem. Soc. , , 6822–6825.(22) Subbaiyan, N. K.; Cambré, S.; Parra-Vasquez, A. N. G.; Hároz, E. H.; Doorn, S. K.;Duque, J. G. Role of Surfactants and Salt in Aqueous Two-Phase Separation of CarbonNanotubes toward Simple Chirality Isolation. ACS Nano , , 1619–1628.(23) Fagan, J. A.; Khripin, C. Y.; Silvera Batista, C. A.; Simpson, J. R.; Hároz, E. H.;Hight Walker, A. R.; Zheng, M. Isolation of specific small-diameter single-wall carbonnanotube species via aqueous two-phase extraction. Adv. Mater. , , 2800–2804.(24) Zheng, M.; Jagota, A.; Strano, M. S.; Santos, A. P.; Barone, P.; Chou, S. G.;Diner, B. A.; Dresselhaus, M. S.; Mclean, R. S.; Onoa, G. B.; Others, Structure-based16arbon nanotube sorting by sequence-dependent DNA assembly. Science , ,1545–1548.(25) Tu, X.; Manohar, S.; Jagota, A.; Zheng, M. DNA sequence motifs for structure-specificrecognition and separation of carbon nanotubes. Nature , , 250.(26) Ao, G.; Streit, J. K.; Fagan, J. A.; Zheng, M. Differentiating left-and right-handedcarbon nanotubes by DNA. J. Am. Chem. Soc. , , 16677–16685.(27) Zheng, M. Sorting carbon nanotubes. Topics in Current Chemistry , .(28) Yomogida, Y.; Tanaka, T.; Zhang, M.; Yudasaka, M.; Wei, X.; Kataura, H. Industrial-scale separation of high-purity single-chirality single-wall carbon nanotubes for biolog-ical imaging. Nat. Commun. , , 12056.(29) Wu, Z.; Chen, Z.; Du, X.; Logan, J. M.; Sippel, J.; Nikolou, M.; Kamaras, K.;Reynolds, J. R.; Tanner, D. B.; Hebard, A. F.; Others, Transparent, conductive carbonnanotube films. Science , , 1273–1276.(30) He, X.; Gao, W.; Xie, L.; Li, B.; Zhang, Q.; Lei, S.; Robinson, J. M.; Hároz, E. H.;Doorn, S. K.; Wang, W.; Vajtai, R.; Ajayan, P. M.; Adams, W. W.; Hauge, R. H.;Kono, J. Wafer-scale monodomain films of spontaneously aligned single-walled carbonnanotubes. Nat. Nanotechnol. , , 633–638.(31) Takashima, K.; Konabe, S.; Yamamoto, T. Carrier localization length in edge-disordered graphene nanoribbons with sub-100 nm length. J. Appl. Phys. , ,024301.(32) Nunez, C.; Orellana, P.; Rosales, L. Electron localization due to side-attached moleculeson graphene nanoribbons. J. Appl. Phys. , , 164310.(33) Weisman, R. B.; Bachilo, S. M. Dependence of optical transition energies on structure17or single-walled carbon nanotubes in aqueous suspension: an empirical Kataura plot. Nano Lett. , , 1235–1238. 18 raphical TOC Entry SemiChiralMetalArmchair (1/K ) − − C o ndu c t i v i t y ( n S ) (6,5)(10,3)(8,5)(7,4)(6,6)(6,5)(10,3)(8,5)(7,4)(6,6)