Diameter-Dependent Superconductivity in Individual WS2 Nanotubes

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Diameter Dependent Superconductivity in Individual WS Nanotubes Feng Qin, Toshiya Ideue, Wu Shi, Xiao-Xiao Zhang, Masaro Yoshida, Alla Zak, Reshef Tenne, Tomoka Kikitsu, Daishi Inoue, Daisuke Hashizume, and Yoshihiro Iwasa Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.8b02647 • Publication Date (Web): 04 Oct 2018 Downloaded from http://pubs.acs.org on October 5, 2018

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Diameter Dependent Superconductivity in Individual WS2 Nanotubes Feng Qin1, Toshiya Ideue1*, Wu Shi1,2, Xiao-Xiao Zhang1,3, Masaro Yoshida4, Alla Zak5, Reshef Tenne6, Tomoka Kikitsu4, Daishi Inoue4, Daisuke Hashizume4, and Yoshihiro Iwasa1,4* 1

Quantum-Phase Electronics Center (QPEC) and Department of Applied Physics, the University of Tokyo, Tokyo 113-8656, Japan.

2

Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA.

3

Quantum Matter Institute, University of British Columbia, Vancouver BC, V6T 1Z4, Canada.

4

RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan.

5

Faculty of Sciences, Holon Institute of Technology, 52 Golomb Street, P.O. Box 305, Holon 58102, Israel.

6

Department of Materials and Interfaces, Weizmann Institute of Science, Rehovot 76100, Israel.

*Corresponding author:

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Toshiya Ideue: [email protected], Yoshihiro Iwasa: [email protected], Abstract: Transition metal dichalcogenide nanotubes are the fascinating platforms for the research of superconductivity due to their unique dimensionalities and geometries. Here we report the diameter dependence of superconductivity in individual WS2 nanotubes. The superconductivity is realized by electrochemical doping via the ionic gating technique, in which the diameter of the nanotube is estimated from the periodic oscillating magnetoresistance, known as the Little-Parks effect. The critical temperature of superconductivity displays an unexpected linear behavior as a function of the inverse diameter, i.e., the curvature of the nanotube. The present results are an important step in understanding the microscopic mechanism of superconductivity in a nanotube, opening up a new way of superconductivity in crystalline nanostructures. Keywords: Transition Metal Dichalcogenides, nanotube, superconductivity, ionic liquid gating.


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Superconductivity in van der Waals crystals is attracting broad interest in recent condensed matter physics from both fundamental and technological viewpoints, because the competition between condensations and fluctuations in low dimensional systems leads to a variety of unique superconducting behavior1-4 such as Berezinskii–Kosterlitz–Thouless transition5-8 and quantum metallic state9-12. Two-dimensional (2D) transition metal dichalcogenides (TMD) are one of the ideal platforms for studying such an exotic 2D superconductivity2,4,13. Characteristic superconducting properties are studied in exfoliated atomic layers of NbSe2

14,15,

field-effect devices based on TaS2 atomic layers16, and

ionic-gated MoS2 2,3,17-20. Recent studies further clarified that many semiconducting TMDs, including WS2, can exhibit superconductivity by both the electrostatic gating (Tc below 2 K for multilayers21 and enhanced to 4 K for monolayers22, defined by half-resistance) and the electrochemical gating13,23 (Tc = 8.3 K).

Following the series of reports on superconductivity in TMD flakes, we have recently discovered the superconductivity in an individual WS2 nanotube realized via an ionic gating technique23,24. Due to the unique geometry of these nanotubes, which is distinct from 2D materials, novel properties, originated from the quantum interference along the tube


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circumference and the chirality effect on superconductivity, have been observed24. Hence, the realization of superconductivity in an individual WS2 nanotube paves the way for searching the peculiar superconducting properties in tubular structures. For instance, it is theoretically expected that superconducting transition temperature will be enhanced by rolling the planar lattice into curved shape due to an increase of electron phonon coupling25,26. However, it is challenging to clarify the effect of curvature, i.e., tube diameter, on superconductivity. Although there have been intensive studies of superconductivity in carbon nanotubes27-30 hypothesizing on the possible enhancement of Tc

31,

it has been experimentally investigated only in an assembled form. Therefore, the

relation between superconductivity and curvature, i.e., tube diameter, has been still missing and waiting for experimental clarification.

In this letter, we report the systematic study of the diameter dependent superconductivity in individual WS2 nanotubes. The superconductivity is realized by potassium intercalation induced through the ionic gating technique. The anisotropic superconducting properties of individual WS2 nanotubes are further studied by applying an external magnetic field. Especially, in the presence of magnetic field parallel to the axis of


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the nanotube, Little-Parks oscillation32, the characteristic interference effect along the superconducting nanotube circumference, has been observed, providing the information of the effective diameter. We found that the critical temperature of superconductivity decreases linearly as a function of the inverse diameter of the nanotube, which implies that superconductivity is affected by the curvature effect of the nanotube, i.e., tube diameter. The observed systematic relation between the critical temperature and the diameter of nanotube will give us the insight to understand the microscopic mechanism of superconductivity in an individual nanotube.

Samples used in this study are multi-walled WS2 nanotubes as shown in the TEM picture (Fig.1a). Typical size of the nanotube diameter ranges from several tens of nanometer to one hundred and several tens of nanometer24,33. By dispersing IPA (isopropyl alcohol) suspended nanotube on the substrate and using the electron beam lithography technique (See SI, section 1), we have fabricated individual WS2 nanotube devices, like the one shown in Fig. 1b, and controlled the carrier density by using the ionic gating (Fig.1c)23,24. A typical gate response of source-drain current IDS is displayed in Fig.1d, in which both the electrostatic and electrochemical doping have been observed. When we


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apply the gate voltage VG at constant sweeping rate of 50 mV·s-1, IDS rapidly increases at VG ~ 1 V by two orders of magnitude and saturates around VG ~ 3 V. This behavior is similar to the case of 2D WS2 13,23. Considering that both saturation behavior around VG ~ 3 V and ambipolar operation within -2 V < VG < 3 V are reversible and repeatable13,23,24, we conclude that electrostatic doping is realized in this region, where the potassium ions K+ are accumulated on the surface of WS2 nanotube as shown in the inset of Fig. 1d (left). When the gate voltage was kept at 8 V for several minutes, a second dramatic increase of IDS by more than two orders of magnitude has occurred, indicating that an electrochemical reaction happened as shown in the inset of Fig. 1d (right), where potassium ions K+ thermally diffuse (as well as driven by electric field) into the WS2 nanotube sample and are intercalated between the layers13,23,24. Such intercalation induced by ionic gating provides a powerful technique to realize heavy electron doping and resultant electronic phase transition in layered compounds.


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Figure 1. Device configuration and intercalation. (a) Transmission Electron Microscope (TEM) picture of an individual multi-walled WS2 nanotube. Inner/outer diameter can be estimated as 67/100 nm, respectively. (b) Photograph of an individual WS2 nanotube device. (c) Schematic figure of electric-double-layer transistor device of an individual WS2 nanotube. The gate medium used for liquid gating is electrolyte made of KClO4/polyethylene glycol, according to refs. [13][23][24]. (d) A typical gate response of the source-drain current (IDS) during the potassium intercalation


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process. IDS is plotted as a function of gate voltage VG and waiting time, in which the first and second increases of IDS correspond to the electrostatic and electrochemical doping, respectively. Insets are schematic figures representing electrostatic doping (left) and electrochemical doping (right), respectively. With applying gate voltage, the negative and positive ions in the electrolyte separate and move oppositely by the external electric field, accumulating on the gate pad and WS2 nanotube sample, respectively.

After the electrochemical K+ intercalation, the WS2 nanotube becomes metallic and finally shows superconductivity at low temperature. The temperature and magnetic field dependence of the resistance during the superconducting phase transition are shown in Fig. 2. Sample 1 displays superconducting transition at Tc = 5.3 K which is defined by half value of normal resistance. The anisotropic nature of superconductivity in the nanotube is confirmed by the temperature dependent resistance of the superconducting transition when the magnetic field is applied parallel (Fig. 2a) and perpendicular (Fig. 2b) to the axis of the nanotube. Under parallel magnetic field (Fig. 2a), clear superconductivity has been observed even at T = 2 K and under μ0H = 9 T, whereas it is rapidly diminished under magnetic field perpendicular to the nanotube axis (Fig. 2b). The upper critical magnetic


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field at zero temperature is expected to exceed the Pauli limit (μ0HP ~ 9.7 T for Tc = 5.3 K), which is indicative of the nontrivial Cooper pairing due to strong spin-orbit interaction in the WS2 nanotube.

Figure 2. Transport properties and Little-Parks oscillation. (a) (b) Temperature dependence of the resistance during superconducting transition under magnetic field parallel (a) and perpendicular (b) to the axis of nanotube (sample 1), respectively. (c) Magnetoresistance at T = 2 K under magnetic field parallel to the axis of nanotube (sample 4). A periodically oscillating component is clearly observed. (d) The plot of the peak position of each maximum and minimum versus index N in the oscillations.


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When the magnetic field is parallel to the axis of the nanotube (sample 4), the magnetoresistance shows periodical oscillating behavior (Fig. 2c) known as Little-Parks oscillations31.

Such

periodic

oscillations

in

the

magnetoresistance

during

the

superconducting transition originate from quantum interference of the superconducting current flow along the circumference of the nanotube and resultant oscillation of Tc

34,35.

Thus, the observation of Little-Parks oscillations indicates that superconductivity is realized truly in a tubular structure, topologically distinct from the bulk samples. In Fig. 2c, each minimum of the oscillations corresponds to the superconducting state with integer fluxoid 𝜙0 = ℎ (2𝑒) piercing into the nanotube. The positions of the maximum and minimum as a function of index number are plotted in Fig. 2d. Here, the linear relationship reflects the periodic nature of the Little-Parks oscillation. From the oscillations period, the effective diameter of the WS2 nanotube was estimated as 70.3 ± 0.3 nm by the equation shown below: 𝜋 𝜇0∆𝐻 ∙ 𝐷2 = 𝜙0 4

(1)

where 𝐷 is the diameter of the WS2 nanotube and 𝜇0∆𝐻 is the period of Little-Parks oscillations observed in the WS2 nanotube.


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We have further investigated the properties of superconductivity in the WS2 nanotube with different diameter and also compared them with that in a WS2 flake sample with K intercalation by the same technique of ionic gating. Fig. 3a shows the normalized Little-Parks oscillations of WS2 nanotube samples under magnetic field parallel to the axis of the nanotube. The oscillating component is extracted by subtracting the quadric background from the measured magnetoresistance (See SI, section 2). According to the periods of Little-Parks oscillations, the diameter of each WS2 nanotube were estimated as 107.8 ± 0.4 nm (sample 1, red), 100.8 ± 0.3 nm (sample 2, orange), 85.2 ± 0.5 nm (sample 3, green), and 70.3 ± 0.3 nm (sample 4, blue), respectively, and they are consistent with the values measured by AFM (See SI, section 3). Fig. 3b shows the temperature dependence of the normalized resistance for different WS2 samples. Sample 1 to 4 represent WS2 nanotubes with different diameter, and sample 0 (black) corresponds to the WS2 flake as comparison (data reproduced from ref. [13]), respectively. The superconducting transition is sharp in the WS2 flake while it is broadened in the WS2 nanotube, which is probably related to the phase slip phenomenon in quasi-1D system due to the both thermal and quantum fluctuations36,37. Judging from the half resistance the critical temperature, Tc of the different WS2 samples are estimated as Tc = 8.3 K (sample 0), 5.3 K (sample 1), 4.8 K


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(sample 2), 4.3 K (sample 3), and 3.3 K (sample 4). Assuming that the diameter of WS2 flake sample is infinite (i.e., curvature is zero for the case of flake), the relation between the critical temperature Tc and inverse diameter 𝐷 ―1 (curvature of the sample) is plotted in Fig. 3c.

Figure 3. Diameter dependence of superconductivity. In this figure, identical color represents identical sample. (a) Little-Parks oscillations of different WS2 nanotube samples. The oscillating component is calculated by subtracting the polynomial background from the magnetoresistance of different WS2 nanotube sample and normalized by amplitude of the oscillations. (b) The temperature dependence of the resistance for different WS2 nanotube samples with different diameters. The data are


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normalized by the resistance at 10 K. (c) The critical temperature as a function of inverse effective diameter of the nanotubes. The critical temperature of each nanotube is defined by half-resistance from (b) and the diameter of each nanotube is estimated by the oscillating 𝜋

period from (a) by the relation of 𝜇0∆𝐻 ∙ 4𝐷2 = 𝜙0, where 𝜇0∆𝐻 is the period of Little-Parks oscillation, 𝐷 is the diameter of nanotube, and 𝜙0 is the magnetic flux ℎ

quantum that is 𝜙0 = 2𝑒 = 2.07 × 10 ―15Wb.

It is clearly shown that Tc systematically decreases with inverse diameter 𝐷 ―1. To a first order approximation, Tc is well fitted by a linear function of the inverse of the diameter. Since the Tc of superconductivity in K intercalated WS2 flake is constant against the amount of intercalated K 13, it is most likely that the superconducting KxWS2 is a line phase compound with a fixed value of x, rather than a solid solution, where x and thus Tc are tunable (See SI, section 4). Such staging behavior is well known in many layered materials including graphite intercalation compounds38. Thus, the systematic variation of the critical temperature discussed above is considered to originate purely from the difference in the sample geometry, such as diameter or wall thickness of the nanotube.


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We note that observed systematic Tc variation cannot be explained by the simple size effect of quantum confinement by decreasing the nanotube diameter39,40, because the nanotube diameter (nearly 100 nm) is one order of magnitude larger than the typical length scale of quantum confinement effect39,40 (below 10 nm). However, the quantum confinement effect can originate from wall thickness of the nanotube41, and it is known that the thickness of sample can affect the superconductivity through various mechanisms42-44. Therefore, we need to separate the wall thickness dependent effect from the diameter-dependent effect (Fig. 3c). Because the diameter of nanotube is effectively large24,33, we can treat our sample as curved 2D film, and the dimensionality or the effective thickness of superconducting nanotube can be estimated by measuring the temperature dependence of the upper critical field in the same manner as in flakes45 (See SI, section 5 , we clarified through a Ginzburg-Landau calculation that dimensional crossover in the cylindrical superconductor is not affected by radius but essentially driven by the change in thickness of the wall.)

Fig. 4a and b show the upper critical field of sample 1 and 2 in the both parallel and perpendicular magnetic field as a function of the temperature. When the magnetic field is


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applied perpendicularly to the nanotube axis, there appears an intermediate state owing to the tubular structure. In this intermediate state, superconductivity is broken in the part locally perpendicular to the magnetic field, while superconductivity survives in the part locally parallel to the field. (See SI, section 6). On the other hand, for the case of magnetic field applied parallel to nanotube axis, the upper critical field can be well-fitted by the power law relation

(

𝑇 𝐻c2(𝑇) = 𝐻c2(0) 1 ― 𝑇c

𝛼

)

(2) 1

where α is the power index reflecting the dimensionality of the superconductivity (2 < α < 1). According to the Ginzburg-Landau theory, α = 1 indicates that the Landau level is not affected by the sample thickness and superconductivity can be treated as 3D-like, while α = 1/2 corresponds to the 2D-like superconductivity in which Landau level is strongly modified by the sample thickness. As seen in Fig. 4a and b, although the diameter and Tc of the two samples are similar, the temperature dependence of the upper critical field displays a striking difference. Fig. 4c summarizes the power index α for all samples (See SI, section 7), estimated from the fitting curve by Eq(2). This figure clearly displays that there is no systematic relation between α and the diameter of the nanotube.


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Since α is an indicator of the wall thickness, these results imply that the wall thickness of the nanotube (dimensionality of the superconductivity) does not affect Tc in our samples and thus the Tc variation mentioned in Fig. 3c is predominantly determined by the diameter (or curvature, which might lead to some strain effects) due to the tubular structure.

Figure 4. Upper critical field and dimensionality of superconductivity. (a) (b) The temperature dependence of the upper critical field for two nanotubes with similar diameter of nearly 100 nm. Two samples display the similar superconducting transition temperatures and Little-Parks oscillation periods but distinct power index behavior. (c) The plot of the power index depending on the inverse diameter. The two plots in the yellow-hatched arear corresponds to the samples shown in (a) and (b). The power index is very much different between the two samples, despite the similar diameters. It


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seems that there is no systematic relation between the power index and the diameter of nanotube, and thus, there is no systematic relation between the thickness of the wall and the diameter of nanotube. This leads us to conclude that Tc is determined solely by the diameter.

The effect of curvature on the critical temperature of carbon nanotubes was discussed before25,26. It was proposed that the curvature of the lattice will lead to enhancement of the critical temperature due to enhancement of the electron phonon coupling because new electron phonon scattering channels open due to the deformation of the carbon nanotube lattice. On the other hand, the present result of superconductivity in individual WS2 nanotubes infers an opposite conclusion. Microscopically, the complex lattice distortions and the resultant unconventional electron phonon interaction may play an essential role, affecting the paring mechanism i.e. the superconducting properties of TMD nanotubes.

In conclusion, we have studied the diameter dependence of the superconductivity in individual WS2 nanotubes. The critical temperature of superconductivity decreases linearly as a function of the inverse diameter of nanotube. In addition, judging from the


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dimensionality analysis, the effect of thickness variation on Tc can be also ruled out. As a result, we attribute the decrease of critical temperature to purely geometric effect, whereby the curvature might play the central role for the change in Tc. We believe that the present results provide crucial information for understanding the microscopic mechanism of superconductivity in an individual nanotube.

Associated Content: Supporting Information contents: 1. Method, including nanotube synthesis, device fabrication and transport measurement. 2. Little-Parks oscillation in WS2 nanotubes. 3. AFM data of all four samples measured after experiments. 4. Staging effect in ionic liquid gating superconductors. 5. Numerical calculation of anisotropic Ginzburg-Landau (GL) theory. 6. The intermediate state under perpendicular magnetic field. 7. Upper critical field and dimensionality of each nanotube sample.

*Corresponding author:


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Toshiya Ideue: [email protected], Yoshihiro Iwasa: [email protected],

Author Contributions: F. Q. and T. I. wrote the manuscript. F. Q., W. S. and M. Y. fabricated devices and performed the transport measurement. F. Q. and X.-X. Z. performed the numerical calculation, A. Z. and R. T. synthesized and provided the WS2 nanotube sample, T. K., D. I. and D. H. obtained the TEM image of sample. F.Q., T.I. and Y.I. led the physical discussions. All authors have given approval to the final version of the manuscript.

Acknowledgements: F. Q. acknowledges Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for Scientific Research (No. 18J14154). X.-X. Z acknowledges JSPS Grant-in-Aid for Scientific Research (No. 16J07545). Y. I. acknowledges JSPS Grant-in-Aid for Specially Promoted Research (No. 25000003). T. I. acknowledges the support of Grant-in-Aid for Challenging Research (Exploratory) (JSPS KAKENHI Grant Number JP17K18748) and Grant-in-Aid for Scientific Research on Innovative Areas "Topological Materials Science"


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(JSPS KAKENHI Grant Number 18H04216) from JSPS. R. T. acknowledges the support of the Kimmel Center for Nanoscale Science; the Perlman Family Foundation; the Irving and Azelle Waltcher Foundation in honour of Prof M. Levy. A. Z. acknowledges the support of Israel Science Foundation (ISF).

Conflict of Interest: The authors declare no competing financial interests.

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(29) Takesue, I.; Haruyama, J.; Kobayashi, N.; Chiashi, S.; Maruyama, S.; Sugai, T.; Shinohara, H. Superconductivity in Entirely End-Bonded Multiwalled Carbon Nanotubes. Phys. Rev. Lett. 2006, 96, 057001. (30) Shi, W.; Wang, Z.; Zhang, Q.; Zheng, Y.; Ieong, C.; He, M.; Lortz, R.; Cai, Y.; Wang, N.; Zhang, T.; Zhang, H.; Tang, Z.; Sheng, P.; Muramatsu, H.; Kim, Y. A.; Endo, M.; Araujo, P. T.; Dresselhaus, M. S. Superconductivity in Bundles of Double-Wall Carbon Nanotubes. Sci. Rep. 2012, 2, 625. (31) Zhang, B.; Liu, Y.; Chen, Q.; Lai, Z.; Sheng, P. Observation of high Tc one dimensional superconductivity in 4 angstrom carbon nanotube arrays. AIP Advances 2017, 7, 025305. (32) Little, W. A.; Parks, R. D. Observation of Quantum Periodicity in the Transition Temperature of a Superconducting Cylinder. Phys. Rev. Lett. 1962, 9, 9-12. (33) Zak, A.; Sallacan-Ecker, L.; Margolin, A.; Genut, M.; Tenne, R. Insight into the Growth Mechanism of WS2 Nanotubes in the Scaled-Up Fluidized-Bed Reactor. NANO 2009, 4, 91-98. (34) Tinkham, M. Consequences of Fluxoid Quantization in the Transitions of Superconducting Films. Rev. Mod. Phys. 1964, 36, 268-276.


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Diameter-Dependent Superconductivity in Individual WS2 Nanotubes

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