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1 Atomic structure and dynamic behaviour of truly one-dimensional ionic chains inside carbon nanotubes Ryosuke Senga 1, Hannu-Pekka Komsa 2, Zheng Liu 1, Kaori Hirose-Takai 1, Arkady V. Krasheninnikov 2 and Kazu Suenaga 1* 1 Nanotube Research Center, National Institute of Advanced Industrial Science and Technology (AIST), AIST Central 5, Tsukuba , Japan. 2 Department of Applied Physics, Aalto University, P.O. Box 11100, Aalto, Finland *Correspondence to: suenaga-kazu@aist.go.jp NATURE MATERIALS 1

2 Materials and Methods CsI crystals encapsulated in CNTs were prepared by the sublimation method, which is a typical method for forming C 60 encapsulated CNTs (so called peapods). The oxidized CNTs and CsI solid (a powder) were encapsulated in a glass tube in vacuum and heated at around 550 o C. The resulting CNT-encapsulated CsI crystals were dispersed in methanol and dropped on W grids. STEM-EELS experiments. A JEOL JEM-2100F instrument equipped with Delta correctors for the probe and imaging was used for STEM EELS analyses 1. EELS data were recorded using a Gatan Quantum spectrometer installed on the microscope. A typical probe current was 40 pa in 0.1nm probe at an acceleration voltage of 60 kv. A fast Fourier transform of a typical ADF image indicates that the microscope can resolve 0.21 nm in the STEM mode (Fig. S2). Image simulation and modeling were performed by using QSTEM software 2. Calculation details All density-functional theory calculations were carried out using projector augmented wave approach in the plane-wave basis as implemented in VASP 3,4. For the plane-wave basis, energy cut-off 350 ev was found to yield converged total energies for CsI, whereas 500 ev was required whenever CNT was included in the calculation. The band dispersions are minor in large-gap CsI, and therefore 8 k-points per unit cell (per dimension) were sufficient. Inclusion of spin-orbit coupling yields a splitting of the VBM (I-5p) states, but does not affect the geometries. The lattice constants were evaluated with various exchange and correlation 2 NATURE MATERIALS

3 functionals and the results are shown in Table S1. On the basis of these results, we have adopted PBEsol and AM05VV10sol functionals 5,6. Both PBEsol and the bare AM05 functionals are designed to yield good lattice parameters for solids. The van der Waals interactions are accounted for in the AM05VV10sol form and this functional was used whenever the chain was embedded within CNT. Indeed, the optimal bond lengths obtained with these functionals are in good agreement with experimentally determined values. Four CNTs with different diameters were chosen. Each model contains three CsI units. Their chiral indexes were (9,0), (10,0), (11,0) and (12,0) with the diameters of 7.05, 7.83, 8.62 and 9.40 Å The formation energy for the chain and bulk (bcc structure) geometries as a function of the Cs-I bond length are shown in Fig. S3(a). Formation energy is given with respect to the same number of isolated CsI molecules. For small bond lengths, the chain prefers to distort into a zigzag form. The lowest energy configuration is shown in the figure, but the energy difference for such distortion is extremely small. The band gap dependence calculated with the PBEsol functional is also shown in Fig. S3(b). At the optimized lattice constants the band gaps are rather similar. Due to different dimensionality, however, the actual optical spectra are expected to behave very distinctively. We show in Fig. S8(a-c), the band structures and the imaginary part of dielectric function calculated in the independent particle picture. Due to the strongly ionic nature of CsI, the general features of the band structures are very similar and each band can be assigned to originate from a particular atomic orbital. On the other hand, different dimensionality of the system leads to completely different DOS, joint DOS, and absorption spectra. In particular, in 3D, the joint DOS has E 1/2 behavior around band NATURE MATERIALS 3

4 extremum, while in 1D the E -1/2 behavior leads to divergence close to band edge. In order to accommodate CsI wire inside CNT, subject to the boundary conditions imposed by the supercell geometry, we search CNTs with lengths matching with the CsI bond length. Pure zigzag or armchair nanotubes are preferred as the diameter can then be varied without changing the length. Fortunately, 5 units of zigzag CNT was found to yield very small strain with respect to 3 units of CsI chain. Finally, in order to scan the experimentally relevant tube diameters ( nm), we adopt indices ranging from (9,0) to (12,0), as shown in Table S2. The intercalation energy is obtained simply from the difference of chain inside CNT and chain and CNT separately. Energy minimum is found at about 8 Å in agreement with the experiment. The van der Waals interaction adds up to 0.5 ev per CsI unit to the intercalation energy, but does not affect significantly the position of the energy minimum. The vacancies were considered both in isolated straight wires and inside CNTs. In both cases, the supercell contained 6 units of CsI. The vacancy formation energies, defined as E ( V f X tot X ) E ( V ) E ( host) tot X with X either Cs or I and E tot denoting the total energy, are listed in Table S3. Iodine rich conditions [μ(i)=e(i 2 )/2 and μ(cs)=e(csi chain)-μ(i)] were adopted as suggested by the experimental data. The bulk vacancy formation energies are calculated in 4x4x4 supercell (128 atoms) using 2x2x2 k-point sampling. The formation energy of vacancies in chain is found to be lower than in bulk. We assign this to the higher energy of the pristine reference system. Vacancy formation within nanotube is found to yield further decrease in the formation energy, which is 4 NATURE MATERIALS

5 ascribed to charge transfer between the vacancy levels and the tube. NATURE MATERIALS 5

6 Extended Data Figures Figure S1: ADF low magnification images of CsI atomic chains encapsulated in DWNTs. The filling rate observed in our experiments was more than 90%. 6 NATURE MATERIALS

7 Figure S2: Typical ADF image and its FFT pattern of CsI atomic chain in a CNT. a, ADF image of CsI atomic chain encapsulated in a DWNT. b,c FFT pattern of a. (b, unprocessed, c, with guide lines or diagrams on the spots corresponding to the atomic structure of CNT (yellow) and CsI atomic chain (blue)). From the FFT pattern, (1/L CNT )/(1/L CsI )=1.6. By applying the value of hexagonal gap distance in CNT (L CNT =0.21nm), the bond-length in CsI is obtained to be 0.34 nm. NATURE MATERIALS 7

8 Figure S3: Calculated formation energy and minimum band gap for CsI bulk and CsI chain. The dashed line denotes the results for zig-zag chain, in which case x-axis of the plot corresponds to the Cs-I bond length projected on the chain axis (d z ), which is an experimentally accessed quantity. The optimal bond lengths are denoted with vertical dotted lines. 8 NATURE MATERIALS

9 Figure S4: Non-equivalent ADF contrast corresponding to the CNT diameter. a, plots of bond length as a function of the diameter of inner CNTs b-d, ADF images of CsI atomic chain chosen from a. The chosen points are indicated by red and indicated in a. e, f, line profiles of Cs (e) and I (f) atoms taken from lines across each atom, as indicated by the orange (Cs) and blue (I) lines in b,c,d. NATURE MATERIALS 9

10 Fig. S5 The intensity profile with averaged lines (integrated in a blue rectangle) compared with one single-line on the top-intensity positions (red-dotted line). We see the inverse intensity (less pronounced Cs contrast) much in the red line plot, while the blue line shows more similar contrast for Cs and I. 10 NATURE MATERIALS

11 Figure S6: ADF intensity profile of each atom near a single vacancy in a CsI atomic chain. a-b, ADF image of a CsI atomic chain and a corresponding chemical map obtained from EELS spectra. c, ADF line profile along the atomic chain in a. Note that the ADF intensity of I atoms at the vicinity of V Cs is substantially lower than the other I atoms. Although we cannot rule out any existence of a lighter atom such as hydrogen atom at the vacancy site, the distance between two I atoms found here is not consistent with the I-H-I bond 7. NATURE MATERIALS 11

12 Figure S7: Probability of V Cs and V I under the experimental condition. a-b, ADF images of both kinds of vacancies and chemical maps obtained by EELS analysis. c, The histogram for the number of vacancy depending on their sites. V Cs and V I stand for the vacancies at Cs and I sites, respectively. dv CsI stands for the di-vacancy at Cs and next I atoms. However, we have never observed the di-vacancy stably existing. 12 NATURE MATERIALS

13 Figure S8: Band structures and absorption spectra for CsI bulk and CsI chain. The atomic orbital characters for each band and the location of the minimum band gap are also shown. In the case of chain, the absorption spectrum is different depending whether the polarization of light is parallel ( ) or perpendicular( ) to the chain. NATURE MATERIALS 13

14 Figure S9: STEM ADF images of the other chains inside CNTs. a, CsCl, b, CsF, c, NaI, d, AuBr 3. They prove a wide applicability of the present method to produce the 1D atomic chains of the other materials. 14 NATURE MATERIALS

15 Extended Data Tables Table S1: Optimized bond length for CsI bulk and CsI chain calculated with various exchange-correlation functionals. The bulk lattice constant may be obtained by multiplying the bond length by 2/ 3. The experimental value for bulk is taken from Ref. [8]. Functional Bond length, bulk (Å) Bond length, chain (Å) PBE PBEsol AM AM05VV10sol HSE PBE experimental ~3.4 (in CNT, this work) Table S2: Experimental diameter and band gap of zigzag CNTs considered in this work. The intercalation energy (per CsI unit) between CsI chain and CNT as calculated with PBEsol/AM05VV10sol functionals are also given. (9,0) (10,0) (11,0) (12,0) Diameter (Å) Band gap (ev) E intercal (ev) -0.15/ / / /-0.71 NATURE MATERIALS 15

16 Table S3: Cs and I vacancy formation energies in CsI systems (in ev). E f (V Cs ) (ev) E f (V I ) (ev) bulk CsI isolated CsI chain CsI chain in CNT Supplemental References 1. Suenaga, K. Koshino, M. Atom-by-atom spectroscopy at graphene edge. Nature 468, (2010). 2. Koch, C. T. Ph. PhD thesis, Arizona State University Kresse, G. & Hafner, J. Ab initio molecular dynamics for liquid metals. Phys. Rev. B 47, 558 (1993). 4. Kresse, G. & Furthmüller, J. Efficiency of ab-initio Total Energy Calculations for Metals and Semiconductors Using a Plane-Wave Basis Set. Comput. Mat. Sci. 6, 15 (1996). 5. Perdew, J. P. et al. Restoring the Density-Gradient Expansion for Exchange in Solids and Surfaces. Phys. Rev. Lett. 100, (2007). 6. Björkman, T. van der Waals density functionals for solids. Phys. Rev. B 86, (2012). 7. Visscher, L., Styszyn ski, J. & Nieuwpoort, W. C. Relativistic and correlation effects on molecular properties. II. The hydrogen halides HF, HCl, HBr, HI, and HAt. J. Chem. Phys. 105, 1987 (1996). 8. Rymer, T. B. & Hambling, B. G. The lattice constant of caesium iodide. Acta Cryst. 4, 565 (1951). 16 NATURE MATERIALS