Chirality of materials are known to affect optical, magnetic and electric properties, causing a variety of nontrivial phenomena such as circular dichiroism for chiral molecules, magnetic Skyrmions in chiral magnets and nonreciprocal carrier transport in chiral conductors. On the other hand, effect of chirality on superconducting transport has not been known. Here we report the nonreciprocity of superconductivity—unambiguous evidence of superconductivity reflecting chiral structure in which the forward and backward supercurrent flows are not equivalent because of inversion symmetry breaking. Such superconductivity is realized via ionic gating in individual chiral nanotubes of tungsten disulfide. The nonreciprocal signal is significantly enhanced in the superconducting state, being associated with unprecedented quantum Little-Parks oscillations originating from the interference of supercurrent along the circumference of the nanotube. The present results indicate that the nonreciprocity is a viable approach toward the superconductors with chiral or noncentrosymmetric structures.
Chirality of crystal or magnetic structures in solids was recently recognized as a powerful source of unique optical and electronic properties and novel functionalities. For instance, it is well known that polarization of light or spin of electron are sensitive to the chirality of lattice or magnetic structure1,2,3,4 and electric transport reflecting the chiral structure are also reported5,6,7. Among them, effects of chiral structures on superconductivity have not been investigated so far because of the lack of suitable materials. One of the interesting superconducting materials with chirality is carbon nanotube (NT)8,9. Chiral structures and their relations to the electronic properties in carbon NTs have been well studied by Raman scattering10,11, scanning tunnel microscope12 and even magneto-chiral transport6. However, since superconductivity in carbon NTs13,14,15,16 has been investigated only in the assembled form of single, double or multi-walled NTs, relations between superconducting transport and the chirality in individual tubes have remained elusive.
Tungsten disulfide (WS2) is a member of transition metal dichalcogenides (TMDs), which are now attracting significant attention as two dimensional (2D) materials beyond graphene with the potential application for electronics, photonics, spintronics, mechanics, as well as valleytronics17,18. Recent systematic studies clarified many TMDs including WS2, which are semiconductors without carrier doping, exhibit superconductivity under the ionic gating19,20. Importantly, TMD can form tubular structures with noncentrosymmetric chiral structures21,22,23,24,25,26. The semiconducting property of the WS2 NT was indeed demonstrated using the field effect transistor devices24. Superconductivity in such a noncentrosymmetric chiral cylinder, once it is realized, is a potential candidate for searching the exotic quantum phenomena and nontrivial Cooper pairing27,28. One of the manifestations of the chiral structure in the electronic transport is the unidirectional resistance. As shown in Fig. 1a,b, the two directions of current injection are not identical due to the chiral nature of the conducting substance when the magnetic field is applied parallel to the tube. Such nonreciprocity is highly anticipated to yield nontrivial quantum transport particularly in the superconducting states.
In this study, the transport properties of individual WS2 NT have been investigated by using the ionic liquid gating technique and resistance measurement on both first and second harmonic signals in alternative current (AC) mode. We have observed ambipolar transfer curve in electrostatic doping region and the emergence of superconductivity by electrochemical doping. The superconducting properties of individual WS2 NT have been further investigated, in which the observed anisotropy of the superconductivity and Little-Parks (LP) oscillation29 are consistent with tubular structure of WS2 NT. More importantly, we have experimentally discovered nonreciprocal superconducting transport via the second harmonic signal, being suggestive of chirality effect on superconductivity. Such nonreciprocal signal is largely enhanced in the superconducting state and affected by the magnetic flux quantum, showing periodic oscillations. The present study paves a route for studying the interplay between superconductivity and chirality or noncentrosymmetry.
WS2 NTs were synthesized following the literature21,22,23. Figure 1c shows a transmission electron microscope (TEM) image of a single WS2 NT (see Supplementary Fig. 1). The tube has a multi-walled structure, with the outer/inner diameters estimated as 132/107 nm, respectively, indicating that the layer number is ∼20. According to the literature21,22,23, the tube part has a 2H-polymorph-layered structure of WS2, where each tungsten atom is surrounded by six sulfur atoms in a trigonal biprism coordination (space group P63/mmc). The outer diameter distribution of tubes in the batch used for this measurement takes a broad maximum around 100 nm (See Supplementary Fig. 4). An electron diffraction pattern of a single WS2 NT is displayed in Fig. 1d. The red arrow and yellow hexagon represent the direction of tube axis and diffraction pattern from the zigzag type NT, respectively. The different walls of the tube can have different chirality. In addition to the contribution of the zigzag type NT, we can see the pair of tilted hexagonal pattern which confirms the co-existence of chiral structures in this NT. The TEM analysis indicates that the tubes used for the transport measurement are multi-walled WS2 NTs with chirality, having the outer diameter of nearly 100 nm (See Supplementary Fig. 4).
Ionic liquid gating on WS2 NT and superconductivity
We fabricated an individual tube device as shown in Fig. 1e,f, and measured gate responses of the transport characteristics. Based on our previous research on the systematic study of superconductivity in TMDs19, we used KClO4/polyethylene glycol electrolyte as the gate medium to facilitate electrochemical intercalation of potassium ions into the layered structure of WS2.
Figure 2a displays the source-drain current (IDS) of the individual WS2 NT device against the gate voltage (VG) between −2 and 3 V. The device nicely operates in an ambipolar mode, in a similar manner to the 2D devices, showing marked contrast with the unipolar response of WS2 NTs in the solid gated field effect transistor24. This indicates the strong gate coupling of the presently used ionic medium. The transistor operation is most likely in the electrostatic mode in this regime, considering the ambipolar behaviour is reversible and repeatable. When VG was increased to 8 V at a constant rate of 50 mV s−1, we found a saturation of IDS, similarly to the case of 2D WS2 (ref. 19). When VG was kept at 8 V for a couple of minutes, we encountered another dramatic increase of IDS by more than two orders of magnitude as shown in Fig. 2b. This IDS increase is presumably attributed to intercalation of K+ ions into WS2 NTs.
When we cooled down the device to 2 K keeping VG at 8 V, superconductivity appeared at Tc=5.8 K, defined as the temperature corresponding to the half of normal state resistance (Fig. 2c). In contrast to the K-intercalated 2D WS2 multilayer with Tc of 8.6 K (ref. 19), the superconducting transition here is shifted to lower temperature and considerably broadened, potentially due to the reduced dimensions or lack of commensurability between the different walls.
We then investigated the anisotropy of the observed superconductivity for sample 3 (VG=6 V). Figure 2d,e displays the temperature variation of the resistance under magnetic field H for H⊥z and H||z, respectively. Here z represents the tube axis direction. In the case of the H||z, the superconductivity is robust against the magnetic field and remains undefeated even under μ0H=9 T at T=2 K, while the superconducting phase rapidly disappears for the H⊥z configuration with increase of magnetic field. The anisotropic superconductivity was also confirmed by the angular dependence (Fig. 2f) and temperature dependence (Fig. 2g) of the upper critical magnetic field. In Fig. 2f, the estimated upper critical field at T=3.5 K are well fitted by the anisotropic Ginzburg–Landau model with fitting parameters a=0.13 T−1 and b=0.75 T−1. The temperature dependence of the critical magnetic field (Fig. 2g) cannot be explained either by the simple 2D or 3D models, implying that the system is of intermediate dimension. Here we should note that the upper critical field at T=0 K for the H||z configuration seemingly exceeds the Pauli paramagnetic limit (Δ is the superconducting gap at T=0 K), being suggestive of a strong spin-orbit interaction and nontrivial Cooper pairing in the present system (See Supplementary Note 2).
Figure 3a shows the AC magnetoresistance of sample 4 (VG=12 V) at various temperatures around Tc in H||z configuration. In addition to the robustness of the superconductivity discussed above, the magnetoresistance observed via the first harmonic signals in AC resistance (Rω) shows periodically oscillating behaviour in the low-magnetic field region. These oscillations during the superconducting transition known as LP effect29 originate from the interference of the superconducting current along the NT circumference and the resultant oscillations of Tc (refs 29, 30). During the application of a parallel magnetic field, the total flux piercing the NT should have a quantized value of Nφ0=Nh/2e and induce the oscillation of the free energy, manifested by the resistance oscillation with the period of φ0=h/2e as observed in Fig. 3a (h and e represent the Plank constant and charge of the electron, respectively, while N is an integer representing the number of flux quantum). Similar LP oscillations have been also observed in sample 3 (See Supplementary Fig. 11). We plotted the oscillating components at different temperatures in Fig. 3b after subtracting the polynomial background from Fig. 3a. The magnitude of the oscillating components reaches a maximum around Tc (see also Fig. 4f). From the periods of LP oscillations Δ(μ0H), we can estimate the effective diameter d of the superconducting NT to be 100 and 80 nm for sample 3 and 4, respectively, according to the relation (Fig. 3c). This is consistent with the diameter distribution histogram of the same batch shown in Supplementary Fig. 4. These results provide firm evidence that superconductivity occurs in the tubular region in the present WS2 sample.
Nonreciprocal superconducting transport in chiral WS2 NT
To clarify the characteristic properties due to the chiral structure, we have measured the second harmonic signals in the AC resistance (R2ω). In noncentrosymmetric systems, the cross term of magnetic field H and electric current I in the resistance is allowed on the basis of the symmetry argument, which indicates the difference between the forward and backward transports under magnetic field5,6,7. This term generates the nonlinear voltage response, which can be measured as the second harmonic components in the AC resistance (See Supplementary Note 3).
Especially in chiral systems, this nonreciprocal electric transport called magneto-chiral anisotropy has been reported in several materials with different chiral degrees of freedom5,6,7. Phenomenologically, magneto-chiral anisotropy can be expressed as
where both the magnetic field H and electric current I are parallel to the chiral axis and γ is the ratio of R2ω to the normal resistance R0. So far, there has been no report of such a phenomenon in superconducting phase and it is of great interest whether excitation or quasiparticle in superconducting state without inversion symmetry generates such an unidirectional magnetoresistance.
Figure 4a shows the magnetic field dependence of second harmonic components R2ω in the AC resistance measured in sample 4. Finite antisymmetric R2ω signals were observed in the superconducting region, which unambiguously indicate the unidirectional electrical transport due to the chiral symmetry (Fig. 1a,b). In sharp contrast, R2ω signals are negligibly small in the normal state (see Fig. 4c), indicating that magneto-chiral anisotropy signals are significantly enhanced in the superconducting phase due to the coherent nature of superconductivity.
The observed R2ω signal has the two characteristic structures: that is, the broader antisymmetric components and the periodically oscillating terms in the low-magnetic field region. In the broader antisymmetric components, there are characteristic minima indicated by small triangles in Fig. 4a, which are dependent on temperature and enhanced at low temperature. The temperature dependence of the characteristic minima show similar behaviour as the critical magnetic field (Fig. 4b), strongly suggesting that the observed signals are related to the superconducting transition. (We show the details of temperature dependence of the antisymmetrized signals in the Supplementary Fig. 12 and discuss the possible co-existence of different chiral types in WS2 NTs in the Supplementary Note 3) The oscillating terms, on the other hand, show the periodicity of φ0 (Fig. 4c–e) and enhancement around Tc (Fig. 4f) similar to the LP oscillations (Fig. 3b), indicating that both have the same origin. Interestingly, this term shows the stepwise behaviour at low temperature (Fig. 4e, from μ0H=−1 T to 1 T) distinct from the conventional linear relation of the external magnetic field according to equation (1). This analysis indicates that the nonreciprocal supercurrent also has the interference nature and is affected by the flux quanta passing through the NT.
The observed second harmonic signals in AC resistance, together with LP oscillations in the first harmonic signals, are the direct manifestations of superconductivity in chiral NTs, however, the detailed mechanisms of the asymmetric electric transport and pairing symmetry (parity mixing) in the superconducting state needs to be further pursued. In light of this work, we expect various superconducting materials with broken inversion symmetry offer a similar transport, which provides a powerful approach for probing the exotic superconducting state in a variety of noncentrosymmetric systems.
The WS2 NTs were synthesized following the literature22,23. The starting materials for the WS2 NT synthesis route were spherical tungsten oxide nanoparticles, which were sulfurized by solid-gas reaction with hydrogen and hydrogen sulfide at elevated temperatures (>800 °C). During this one-pot reaction, tungsten suboxide whiskers grow and are subsequently sulfurized into WS2 NTs of ∼100 nm in diameter and up to 20 micron in length. These two main steps of the reaction—oxide whiskers growth and sulfurization—occur under the same H2S/H2 gas flow regime and are not separated in space following each other in a self-controlled mechanism.
WS2 NTs were dispersed in isopropyl alcohol solvent by ultrasonication for 20 min. A droplet of the suspension was spin-coated on a Si/SiO2(3,000 Å) substrate, and immediately covered by polymethyl methacrylate. The isolated WS2 NTs were subsequently chosen by an optical microscope. The device pattern was designed via standard electron beam lithography techniques and developed by mixed solution of methyl isobutyl ketone and isopropyl alcohol with the ratio of methyl isobutyl ketone:isopropyl alcohol=1:3. After the deposition of Cr/Au (5 nm/90 nm), pads and gate electrode were covered by photoresist and Cr/SiO2 (5 nm/20 nm) was subsequently deposited to protect electrodes from the chemical reaction by ionic gating. Finally, we removed the redundant polymethyl methacrylate and gold by dipping the substrate into acetone for more than 1 h. KClO4/polyethylene glycol was selected as a gate medium19.
All the transport properties have been measured in a Quantum Design Physical Property Measurement System with a horizontal rotator probe under He-purged and high-vacuum environments. High-vacuum mode was used when the temperature was higher than 200 K, while the system was kept under He-purged condition below 200 K. Gate voltage was applied by a Keithley 2400 sourcemeter at 300 K with a sweeping rate of 50 mV s−1 under high-vacuum condition. Both the first and the second harmonic signals of the AC resistance have been measured by a lock-in amplifier (Stanford Research Systems Model SR830 DSP) with a frequency of 13 Hz. During the AC resistance measurements, the phase of the first (or second) harmonic signal was kept around 0 , which is consistent with the theoretical expectation. All of the Rω (or R2ω) signals discussed in the main text were obtained as x (or y)-component of the lock-in measurement.
All of the experimental data supporting this study are available from the corresponding author.
How to cite this article: Qin, F. et al. Superconductivity in a chiral nanotube. Nat. Commun. 8, 14465 doi: 10.1038/ncomms14465 (2017).
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We thank R. Popovitz-Biro for experimental help (HRTEM analysis) and R. Wakatsuki, M. Ezawa and N. Nagaosa for discussions. Y.I. acknowledges Grant-in-Aid for Specially Promoted Research (No. 25000003) from JSPS. T.I. acknowledges Grant-in-Aid for Research Activity Start-up (No.15H06133) from MEXT of Japan. R.T. acknowledges the support of Israel Science Foundation grant No. 265/12; the Kimmel Center for Nanoscale Science; the Perlman Family Foundation; the Irving and Azelle Waltcher Foundation in honour of Prof M. Levy. R.T. and A.Z. acknowledge the support of the FTA action No. 711543 of the Israel National Nano Initiative. A.Z. acknowledges the support of Pazi foundation.
Supplementary Figures 1-13, Supplementary Table 1, Supplementary Notes 1-3 and Supplementary References