Reports

Recent technological advances of materials fabrication have led to discoveries of a variety of superconductors at hetero-geneous interfaces and in ultrathin films; examples include superconductivity at oxide interfaces (1, 2), electric-double-layer interfaces (3), and mechanically cleaved (4), molecular-beam-epitaxy grown (5, 6), or chemical vapor deposited (7) atomically thin layers. These systems are providing oppor-tunities for searching for superconductivity at higher tem-peratures as well as investigating the intrinsic nature of two-dimensional (2D) superconductors, which are distinct from bulk superconductors because of enhanced thermal and quantum fluctuations.

One of the issues to be addressed is how zero electrical resistance is achieved or destroyed. In 2D superconductors exposed to magnetic fields, vortex pinning, which is neces-sary to achieve zero electrical resistance under magnetic fields, may be too weak. To address this question, supercon-ductivity in vacuum-deposited metallic thin films has been studied (8). The conventional way to approach the 2D limit is to reduce the film thickness, but this concomitantly in-creases disorder. In such thin films, a direct superconduc-tor-to-insulator transition (SIT) is observed in most cases when the system is disordered (8).This SIT has been under-stood in the framework of the so-called “dirty boson model” (9); however, this simple picture needed to be modified be-cause an intervening metallic phase between the supercon-ducting (SC) and insulating phases under magnetic fields

was observed in less-disordered systems (8, 10). Therefore, inves-tigating 2D superconductivity in even cleaner systems is desira-ble.

In contrast to the conven-tional metallic films, the recently discovered 2D superconductors are highly crystalline, displaying lower normal state sheet re-sistance. The electric-double-layer transistor (EDLT), which is composed of the interface be-tween crystalline solids and elec-trolytes, can be a good candidate to realize such a clean system, since the conduction carriers are induced electrostatically at the atomically flat surfaces without introducing extrinsic disorder. In addition, the EDLT has the greatest advantage of their ap-plicability to a wide range of materials, as exemplified by gate-induced superconductivity in three-dimensional SrTiO3 (3, 11, 12), KTaO3 (13), quasi-2D lay-ered ZrNCl (14), transition metal

dichalcogenides (15–17) and cuprates (18–22). Here, we re-port comprehensive transport studies on a ZrNCl-EDLT, which provide evidence of 2D superconductivity in this sys-tem based on several types of analyses. In particular, we found that the zero resistance state is immediately de-stroyed by the application of finite out-of-plane magnetic fields, and consequently, a metallic state is stabilized in a wide range of magnetic fields. This is a manifestation of the quantum tunneling of vortices due to the extremely weak pinning in the ultimate 2D system.

ZrNCl is originally an archetypal band insulator with a layered crystal structure (23, 24), in which a unit cell com-prises three (ZrNCl)2 layers (Fig. 1A). Bulk ZrNCl becomes a superconductor with a critical temperature, Tc, as high as 15.2 K by alkali–metal intercalation (25–28). Figure 1B shows the relation between the sheet conductance, σsheet, and the gate voltage, VG, for a ZrNCl-EDLT with a 20-nm-thick flake without any monolayer steps (29), measured at a source–drain voltage of VDS = 0.1 V and at a temperature of T = 220 K. σsheet abruptly increased at VG > 2 V, demonstrat-ing a typical n-type field-effect transistor behavior. As shown in the temperature dependence of the sheet re-sistance, Rsheet, at different VG values (Fig. 1C), the insulating phase is dramatically suppressed with increasing VG, and finally a resistance drop due to a SC transition appears at VG = 4 V. Zero resistance (below ~0.05 Ω) was achieved at VG = 6 and 6.5 V. Despite such relatively large gate voltages, any

Metallic ground state in an ion-gated two-dimensional superconductor Yu Saito,1 Yuichi Kasahara,1,2* Jianting Ye,1,3,4 Yoshihiro Iwasa,1,4† Tsutomu Nojima5† 1Quantum-Phase Electronics Center (QPEC) and Department of Applied Physics, The University of Tokyo, Tokyo 113-8656, Japan. 2Department of Physics, Kyoto University, Kyoto 606-8502, Japan. 3Zernike Institute for Advanced Materials, University of Groningen, Nijenborgh 4, 9747 AG Groningen, Netherlands. 4RIKEN Center for Emergent Matter Science (CEMS), Wako 351-0198, Japan. 5Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan.

*Present address: Department of Physics, Kyoto University, Kyoto 606-8502, Japan. †Corresponding author. E-mail: iwasa@ap.t.u-tokyo.ac.jp (Y.I.); nojima@imr.tohoku.ac.jp (T.N.)

Recently emerging two-dimensional (2D) superconductors in atomically thin layers and at heterogeneous interfaces are attracting growing interest in condensed matter physics. Here, we report that ion-gated ZrNCl surface, exhibiting a dome-shaped phase diagram with a maximum critical temperature of 14.8 K, behaves as a superconductor persisting to the 2D limit. The superconducting thickness estimated from the upper critical fields is ≅ 1.8 nanometers, which is thinner than one-unit-cell. The majority of the vortex phase diagram down to 2 K is occupied by a metallic state with a finite resistance, owing to the quantum creep of vortices caused by extremely weak pinning and diminishing disorder. Our findings highlight the potential of electric-field-induced superconductivity, establishing a new platform for accessing quantum phases in clean 2D superconductors.

/ sciencemag.org/content/early/recent / 1 October 2014 / Page 1 / 10.1126/science.1259440

on April 26, 2020

http://science.sciencem

ag.org/D

ownloaded from

signature of electrochemical process was not observed (figs. S1 and S2) (29). The tail of the resistance drop at 6.5 V can be explained in terms of the Berezinskii-Kosterlitz-Thouless (BKT) transition (Fig. 1D), which realizes a zero-ohmic-resistance phase driven by the binding of vortex-antivortex pairs. To determine the BKT transition temperature, we use the Halperin-Nelson equation (30, 31), which shows a square-root-cusp behavior that originates from the energy dissipation due to the Bardeen-Stephen vortex flow above the BKT transition temperature. On the other hand, a grad-ual decrease of Rsheet at temperatures far above Tc, leading to a broadened SC onset (Fig. 1D, inset), was observed. This feature can be well reproduced by an analysis that takes both the Aslamazov-Larkin and Maki-Thompson terms (32–34) for the 2D fluctuation conductivities into account (fig. S4) (29). These results suggest that 2D superconductivity is achieved at zero magnetic field.

Figure 2, A and B, display temperature-dependent Rsheet(T) values at VG = 6.5 V for magnetic fields applied per-pendicular and parallel to the surface of ZrNCl, respectively. For the out-of-plane magnetic fields, Tc is dramatically sup-pressed with a considerable broadening of the SC transition even at a small magnetic field of μ0H = 0.05 T, which is in marked contrast to those observed in the in-plane magnetic field geometry (see also fig. S5). Such a large anisotropy suggests that the superconductivity is strongly 2D in nature and indicates a significant contribution of the vortex motion in the out-of-plane field geometry. Figure 2C shows the an-gular dependence of the upper critical field, μ0Hc2 (θ) (θ represents the angle between the c-axis of ZrNCl and ap-plied magnetic field directions), at 13.8 K, which is just be-low Tc (= 14.5 K at zero magnetic field). Tc (Hc2) was defined as the temperature (magnetic field) where Rsheet becomes 50% of the normal state resistance, RN, at 30 K (29). A cusp-like peak is clearly resolved at θ = 90° (Fig. 2C, inset), and is qualitatively distinct from the three-dimensional anisotropic mass model but is well described by the 2D Tinkham model (35). Similar observations have been reported in a SrTiO3-EDLT (36), implying that the EDLT is a versatile tool for creating 2D superconductors. Figure 2D shows the tempera-

ture dependence of μ0Hc2 at θ = 90° ( ||0 c2Hµ ) and at θ = 0°

( 0 c2H ⊥µ ), which exhibits a good agreement with the phe-

nomenological Ginzburg-Landau (GL) expressions for 2D SC films.

00 c2 2

GL c

12 (0)

TH

T⊥ Φ

µ = −πξ

(1)

|| 00 c2

GL SC c

121

2 (0)

TH

d T

Φµ = −

πξ (2)

where Φ0 is the flux quantum, ξGL(0) is the extrapolation of the GL coherence length, ξGL, at T = 0 K, and dsc is the tem-perature-independent SC thickness. As a result of the fit, we

obtained ξGL(0) ≅ 12.8 nm and dsc ≅ 1.8 nm. The latter pa-rameter approximately corresponds to the bilayer thickness of the (ZrNCl)2 layer, which is less than one-unit-cell thick. The estimated thickness is indeed in the atomic scale, and demonstrates that the superconductivity persists to the ex-treme 2D limit. The dsc for this system is much smaller than the reported value of approximately of 11 nm for the inter-face superconductivity on SrTiO3 (1, 36), which is presuma-bly owing to the huge dielectric constant in the incipient ferroelectric SrTiO3. Recently, it was suggested based on theoretical calculations that the depth of the induced charge carriers in ion-gated superconducting ZrNCl is only one lay-er (37). The difference from the present observation might be ascribed to the proximity effect of the superconductivity, which is a phenomenon whereby the Cooper pairs in a SC layer (the topmost layer, in the present case) diffuse into the neighboring non-SC layers (the second layer), resulting in broadening of the effective thickness. This could occur even if there are only a small number of electrons in the second layer. Another possibility for this discrepancy might come from the situation that the measured Hc2 is suppressed be-cause of the paramagnetic effect as compared with the or-bital limit, leading to the estimated dsc thicker than the real value.

In the present system, we found that the Pippard coher-

ence length, Pippardξ , is equal to 43.4 nm, as calculated from

Pippard F (0)vξ = π∆ by using F F *,v k m= ( )1/2

2D4 'Fk n ss= πand the Bardeen–Cooper–Schrieffer (BCS) energy gap of

Δ(0) = 1.76kBTc = 2.2 meV, where vF, kF, m*, , s and s′ are the Fermi velocity, the Fermi wave number, the effective mass, Planck’s constant divided by 2π, the spin degree of freedom and the valley degree of freedom, respectively, for VG = 6.5 V (the sheet carrier density of n2D = 4.0 × 1014 cm−2) with Tc = 14.5 K and the effective mass of m* = 0.9m0 (38). Here s and s′ are both 2. The Pippard coherence length is

larger than kF−1 = 0.28 nm, and much larger than dsc ≅ 1.8

nm. We also note that the ||

c2H may exceed the Pauli limit for

weak coupling BCS superconductors, BCS

0 PHµ = 1.86Tc = 27.0 T.

However, to confirm this phenomenon, it is necessary to investigate Hc2 at lower temperatures by using high magnet-ic fields.

Having estimated dsc, we can now compare the phase di-agrams of electric-field-induced 2D and bulk superconduc-tors (28) (Fig. 3). A direct comparison is made by using n2D estimated from Hall-effect measurements in ZrNCl-EDLTs (fig. S6) (29) and n2D in the (ZrNCl)2 bilayer for the bulk. In contrast to the bulk, where Tc abruptly appears at n2D = 1.5 × 1014 cm−2 followed by a decrease with increasing n2D, ZrNCl-EDLTs exhibit a gradual increase of Tc, forming a dome-like SC phase with a maximum Tc of 14.8 K at n2D = 5.0 × 1014 cm−2. The different phase diagrams between electric-field-induced and intercalated superconductivity in Fig. 3 suggest

/ sciencemag.org/content/early/recent / 1 October 2015 / Page 2 / 10.1126/science.1259440

on April 26, 2020

http://science.sciencem

ag.org/D

ownloaded from

the importance of two dimensionality and broken inversion symmetry in the presence of an electric field, which may lead to exotic superconducting phenomena such as the spin-parity mixture state and the helical state. On the other hand, the coincidence of the critical n2D in the 2D and bulk system implies that the mysterious phase diagram in the bulk LixZrNCl; that is, an abrupt drop of Tc near n2D ~ 1 × 1014 cm−2, might be related to the quantum SIT phenomena realized in the 2D limit (8). Similar dome-like SC phases have already been reported in EDLTs based on the band insulators KTaO3 (13) and MoS2 (15), suggesting a common-ality among electric-field-induced superconductors.

In an Arrhenius plot of Rsheet(T) for out-of-plane magnet-ic fields at VG = 6.5 V (Fig. 4A), Rsheet(T) exhibits an activated

behavior just below Tc described by ( )B c'exp ( )R R U H k T= − ,

where kB is Boltzmann’s constant, as shown by the dashed lines. The magnetic field dependence of the extracted activa-tion energy U(H) (Fig. 4B), and the relation between

U(H)/kBTc and 'ln R (Fig. 4B, inset) are consistent with the thermally-assisted collective vortex-creep model in two di-

mensions (39), ( )0( ) lnU H H H∝ and

B cln ' ( ) const.R U H k T= + The activation energy becomes

almost zero at μ0H ≅ 1.3 T, allowing the vortex flow motion above this field as explained below.

At low temperatures, on the other hand, each Rsheet–T curve clearly deviates from the activated behavior and then is flattened at a finite value down to the lowest temperature (= 2 K) even at μ0H (= 0.05 T) ~ μ0Hc2/40. This implies that a metallic ground state exists for at least μ0H > 0.05 T and may be a consequence of the vortex motion driven by quan-tum mechanical processes. Our results are markedly distinct from conventional theories that predict a vortex-glass state and a direct SIT at T = 0 with RN close to the quantum re-sistance RQ = h/4e2 = 6.45 kΩ, where h and e is Planck’s con-stant and the elementary charge, respectively. The metallic ground state has been reported in MoGe (10) and Ta (40)

thin film materials, where RN values (≥ 1 kΩ) are smaller than RQ. In the ZrNCl-EDLT, RN at VG = 6 and 6.5 V is ~120 and ~200 Ω, respectively, which are even lower, reaching

values as small as ~1/50 of RQ. This leads to kFl = 2

N

1 2 1

'

h

ss e R~

77 – 130 (RN ~ 120 – 200 Ω) with the mean free path l, which is much larger than the Ioffe-Regel limit (kFl ~ 1), indicating that the normal states are relatively clean. We also note that the estimated values of l ~ 35 nm (6 V) and 18 nm (6.5 V)

result in the relation≅Pippardξ

1.1 – 2.4 l, which is far from the

dirty limit Pippard( )lξ >> . Indeed, the expression for ξGL(0) in

the dirty limit, 1/ 2

Pippard0.855 ( )lξ , is not applicable to our result.

Furthermore, our Rsheet-T data under magnetic fields do not follow the scaling relations for a magnetic-field-induced SIT,

which has been demonstrated in disordered systems (8). All of these features indicate that the ZrNCl-EDLT at VG = 6.5 V is out of the disordered regime and may be entering a mod-erately clean regime with weak pinning.

The most plausible description of the metallic state is temperature-independent quantum tunneling of vortices (quantum creep). In this model, the resistance obeys a gen-eral form in the limit of the strong dissipation (41).

c2sheet 2 2

N

1~ , ~ exp

4 1

H HR C

e e R H

−κκ

− κ

(3)

where C is a dimensionless constant. As seen in Fig. 4C, the Rsheet –H relation at 2 K is well fitted by Eq. 3 up to 1.3 T, indicating that the quantum creep model holds for a wide range. It should be noted that (a) finite-size effects (42) or, (b) the model of random Josephson junction arrays that originate from surface roughness (for example, amorphous Bi thin films) (31) or inhomogeneous carrier accumulation, both of which can cause the flattening of the resistance with a finite value, can be excluded because of following reasons: (a) a BKT transition, and a zero resistance state (below ~0.05 Ω) are observed (see Fig. 1D). (b) The channel surface preserved atomically-flat morphology with the average mean square roughness of ~0.068 nm, which is less than 4% of dsc, even after all the measurements (fig. S3) (29). Also, all the different voltage probes used to measure the longitudi-nal resistances and the tranverse Hall resistances in four-terminal geometry (29) showed almost the same values with the differences of less than 5% at the high carrier concentra-tions (VG = 6 and 6.5 V), which suggests the surface carrier accumulation in the present system is homogeneous. Above 1.3 T, Rsheet is well described by an H-linear dependence (Fig. 4C, inset), indicating pinning-free vortex flow. The crossover from the creep to the flow motion occurs at ≅ 1.3 T, where U(H) for the thermal creep approaches zero (Fig. 4B), imply-ing that the pinning or the elastic potential effectively dis-appears at high magnetic fields. Based on the above observations, we obtained the field-temperature phase dia-gram of ion-gated ZrNCl shown in Fig. 4D. A true zero re-sistance state occurs only at very small magnetic fields below 0.05 T. The key parameters here are the dimensional-ity and RN of the system. The former enhances the quantum fluctuations, whereas the latter controls the coupling of vor-tices to a dissipative bath, which stabilizes the metallic re-gion when RN is low (43). Our results indicate that the EDLT provides a model platform of clean 2D superconductors with weak pinning and diminishing disorder, which may potentially lead to realizing intrinsic quantum states of mat-ter.

REFERENCES AND NOTES 1. N. Reyren, S. Thiel, A. D. Caviglia, L. F. Kourkoutis, G. Hammerl, C. Richter, C. W.

Schneider, T. Kopp, A. S. Rüetschi, D. Jaccard, M. Gabay, D. A. Muller, J. M. Triscone, J. Mannhart, Superconducting interfaces between insulating oxides. Science 317, 1196–1199 (2007). Medline

/ sciencemag.org/content/early/recent / 1 October 2015 / Page 3 / 10.1126/science.1259440

on April 26, 2020

http://science.sciencem

ag.org/D

ownloaded from

2. A. Gozar, G. Logvenov, L. F. Kourkoutis, A. T. Bollinger, L. A. Giannuzzi, D. A. Muller, I. Bozovic, High-temperature interface superconductivity between metallic and insulating copper oxides. Nature 455, 782–785 (2008). Medline doi:10.1038/nature07293

3. K. Ueno, S. Nakamura, H. Shimotani, A. Ohtomo, N. Kimura, T. Nojima, H. Aoki, Y. Iwasa, M. Kawasaki, Electric-field-induced superconductivity in an insulator. Nat. Mater. 7, 855–858 (2008). Medline doi:10.1038/nmat2298

4. D. Jiang, T. Hu, L. You, Q. Li, A. Li, H. Wang, G. Mu, Z. Chen, H. Zhang, G. Yu, J. Zhu, Q. Sun, C. Lin, H. Xiao, X. Xie, M. Jiang, High-Tc superconductivity in ultrathin Bi2Sr2CaCu2O8+x down to half-unit-cell thickness by protection with graphene. Nat. Commun. 5, 5708 (2014). Medline doi:10.1038/ncomms6708

5. S. Qin, J. Kim, Q. Niu, C. K. Shih, Superconductivity at the two-dimensional limit. Science 324, 1314–1317 (2009). Medline

6. Q. Y. Wang, Z. Li, W.-H. Zhang, Z.-C. Zhang, J.-S. Zhang, W. Li, H. Ding, Y.-B. Ou, P. Deng, K. Chang, J. Wen, C.-L. Song, K. He, J.-F. Jia, S.-H. Ji, Y.-Y. Wang, L.-L. Wang, X. Chen, X.-C. Ma, Q.-K. Xue, Interface-induced high-temperature superconductivity in single unit-cell FeSe films on SrTiO3. Chin. Phys. Lett. 29, 037402 (2012). doi:10.1088/0256-307X/29/3/037402

7. C. Xu, L. Wang, Z. Liu, L. Chen, J. Guo, N. Kang, X.-L. Ma, H.-M. Cheng, W. Ren, Large-area high-quality 2D ultrathin Mo2C superconducting crystals. Nat. Mater. 2015, 10.1038/nmat4374 (2015). doi:10.1038/nmat4374

8. A. M. Goldman, Superconductor-insulator transitions. Int. J. Mod. Phys. B 24, 4081–4101 (2010). doi:10.1142/S0217979210056451

9. M. P. A. Fisher, Quantum phase transitions in disordered two-dimensional superconductors. Phys. Rev. Lett. 65, 923–926 (1990). Medline doi:10.1103/PhysRevLett.65.923

10. D. Ephron, A. Yazdani, A. Kapitulnik, M. R. Beasley, Observation of quantum dissipation in the vortex state of a highly disordered superconducting thin film. Phys. Rev. Lett. 76, 1529–1532 (1996). Medline doi:10.1103/PhysRevLett.76.1529

11. Y. Lee, C. Clement, J. Hellerstedt, J. Kinney, L. Kinnischtzke, X. Leng, S. D. Snyder, A. M. Goldman, Phase diagram of electrostatically doped SrTiO3. Phys. Rev. Lett. 106, 136809 (2011). Medline doi:10.1103/PhysRevLett.106.136809

12. P. Gallagher, M. Lee, J. R. Williams, D. Goldhaber-Gordon, Gate-tunable superconducting weak link and quantum point contact spectroscopy on a strontium titanate surface. Nat. Phys. 10, 748–752 (2014). doi:10.1038/nphys3049

13. K. Ueno, S. Nakamura, H. Shimotani, H. T. Yuan, N. Kimura, T. Nojima, H. Aoki, Y. Iwasa, M. Kawasaki, Discovery of superconductivity in KTaO₃ by electrostatic carrier doping. Nat. Nanotechnol. 6, 408–412 (2011). Medline doi:10.1038/nnano.2011.78

14. J. T. Ye, S. Inoue, K. Kobayashi, Y. Kasahara, H. T. Yuan, H. Shimotani, Y. Iwasa, Liquid-gated interface superconductivity on an atomically flat film. Nat. Mater. 9, 125–128 (2010). Medline doi:10.1038/nmat2587

15. J. T. Ye, Y. J. Zhang, R. Akashi, M. S. Bahramy, R. Arita, Y. Iwasa, Superconducting dome in a gate-tuned band insulator. Science 338, 1193–1196 (2012). Medline doi:10.1126/science.1228006

16. S. Jo, D. Costanzo, H. Berger, A. F. Morpurgo, Electrostatically induced superconductivity at the surface of WS₂. Nano Lett. 15, 1197–1202 (2015). Medline doi:10.1021/nl504314c

17. W. Shi, J. Ye, Y. Zhang, R. Suzuki, M. Yoshida, J. Miyazaki, N. Inoue, Y. Saito, Y. Iwasa, Superconductivity series in transition metal dichalcogenides by ionic gating. Sci. Rep. 5, 12534 (2015). Medline doi:10.1038/srep12534

18. S. G. Haupt, D. R. Riley, J. T. McDevitt, Conductive polymer/high-temperature superconductor composite structures. Adv. Mater. 5, 755–758 (1993). doi:10.1002/adma.19930051017

19. S. G. Haupt, D. R. Riley, J. Zhao, J.-P. Zhou, J. H. Grassi, J. T. McDevitt, Reversible modulation of superconductivity in YBa2Cu3O7-δ/polypyrrole sandwich structures. Proc. SPIE 2158, 238–249 (1994). doi:10.1117/12.182687

20. A. T. Bollinger, G. Dubuis, J. Yoon, D. Pavuna, J. Misewich, I. Božović, Superconductor-insulator transition in La2-xSrxCuO4 at the pair quantum resistance. Nature 472, 458–460 (2011). Medline doi:10.1038/nature09998

21. X. Leng, J. Garcia-Barriocanal, S. Bose, Y. Lee, A. M. Goldman, Electrostatic control of the evolution from a superconducting phase to an insulating phase in ultrathin YBa₂Cu₃O7-x films. Phys. Rev. Lett. 107, 027001 (2011). Medline doi:10.1103/PhysRevLett.107.027001

22. S. W. Zeng, Z. Huang, W. M. Lv, N. N. Bao, K. Gopinadhan, L. K. Jian, T. S. Herng, Z. Q. Liu, Y. L. Zhao, C. J. Li, H. J. Harsan Ma, P. Yang, J. Ding, T. Venkatesan,

Ariando, Two-dimensional superconductor-insulator quantum phase transitions in an electron-doped cuprate. Phys. Rev. B 92, 020503 (2015). doi:10.1103/PhysRevB.92.020503

23. S. Shamoto, T. Kato, Y. Ono, Y. Miyazaki, K. Ohoyama, M. Ohashi, Y. Yamaguchi, T. Kajitani, Structures of β-ZrNCl and superconducting Li0.16ZrNCl: Double honeycomb lattice superconductor. Physica C 306, 7–14 (1998). doi:10.1016/S0921-4534(98)00357-8

24. X. Chen, L. Zhu, S. Yamanaka, The first single-crystal X-ray structural refinement of the superconducting phase Li0.2(1) ZrNCl derived by intercalation. J. Solid State Chem. 169, 149–154 (2002). doi:10.1016/S0022-4596(02)00034-8

25. S. Yamanaka, H. Kawaji, K. Hotehama, M. Ohashi, A new layer-structured nitride superconductor. Lithium-intercalated β-zirconium nitride chloride, LixZrNCl. Adv. Mater. 8, 771–774 (1996). doi:10.1002/adma.19960080917

26. T. Ito, Y. Fudamoto, A. Fukaya, I. M. Gat-Malureanu, M. I. Larkin, P. L. Russo, A. Savici, Y. J. Uemura, K. Groves, R. Breslow, K. Hotehama, S. Yamanaka, P. Kyriakou, M. Rovers, G. M. Luke, K. M. Kojima, Two-dimensional nature of superconductivity in the intercalated layered systems Lix HfNCl and Lix ZrNCl: Muon spin relaxation and magnetization measurements. Phys. Rev. B 69, 134522 (2004). doi:10.1103/PhysRevB.69.134522

27. T. Takano, A. Kitora, Y. Taguchi, Y. Iwasa, Modulation-doped-semiconductorlike behavior manifested in magnetotransport measurements of Lix Zr N Cl layered superconductors. Phys. Rev. B 77, 104518 (2008). doi:10.1103/PhysRevB.77.104518

28. Y. Taguchi, A. Kitora, Y. Iwasa, Increase in Tc upon reduction of doping in LixZrNCl superconductors. Phys. Rev. Lett. 97, 107001 (2006). Medline doi:10.1103/PhysRevLett.97.107001

29. See the supplementary materials on Science Online. 30. B. I. Halperin, D. R. Nelson, Resistive transition in superconducting films. J. Low

Temp. 36, 599–616 (1979). doi:10.1007/BF00116988 31. Y.-H. Lin, J. Nelson, A. M. Goldman, Suppression of the Berezinskii-Kosterlitz-

Thouless transition in 2D superconductors by macroscopic quantum tunneling. Phys. Rev. Lett. 109, 017002 (2012). Medline doi:10.1103/PhysRevLett.109.017002

32. L. G. Aslamazov, A. I. Larkin, The influence of fluctuation pairing of electrons on the conductivity of normal metal. Phys. Lett. 26A, 238–239 (1968). doi:10.1016/0375-9601(68)90623-3

33. K. Maki, The critical fluctuation of the order parameter in type-II superconductors. Prog. Theor. Phys. 39, 897–906 (1968). doi:10.1143/PTP.39.897

34. R. S. Thompson, Microwave, flux flow, and fluctuation resistance of dirty type-II superconductors. Phys. Rev. B 1, 327–333 (1970). doi:10.1103/PhysRevB.1.327

35. M. Tinkham, Introduction to Superconductivity (Dover, New York, ed. 2, 2004). 36. K. Ueno, T. Nojima, S. Yonezawa, M. Kawasaki, Y. Iwasa, Y. Maeno, Effective

thickness of two-dimensional superconductivity in a tunable triangular quantum well of SrTiO3. Phys. Rev. B 89, 020508 (2014). doi:10.1103/PhysRevB.89.020508

37. T. Brumme, M. Calandra, F. Mauri, Electrochemical doping of few-layer ZrNCl from first principles: Electronic and structural properties in field-effect configuration. Phys. Rev. B 89, 245406 (2014). doi:10.1103/PhysRevB.89.245406

38. T. Takano, Y. Kasahara, T. Oguchi, I. Hase, Y. Taguchi, Y. Iwasa, Doping variation of optical properties in ZrNCl superconductors. J. Phys. Soc. Jpn. 80, 023702 (2011). doi:10.1143/JPSJ.80.023702

39. M. V. Feigel’man, V. B. Geshkenbein, A. I. Larkin, Pinning and creep in layered superconductors. Physica C 167, 177–187 (1990). doi:10.1016/0921-4534(90)90502-6

40. Y. Qin, C. L. Vicente, J. Yoon, Magnetically induced metallic phase in superconducting tantalum films. Phys. Rev. B 73, 100505 (2006). doi:10.1103/PhysRevB.73.100505

41. E. Shimshoni, A. Auerbach, A. Kapitulnik, Transport through quantum melts. Phys. Rev. Lett. 80, 3352–3355 (1998). doi:10.1103/PhysRevLett.80.3352

42. T. Schneider, S. Weyeneth, Suppression of the Berezinskii-Kosterlitz-Thouless and quantum phase transitions in two-dimensional superconductors by finite-size effects. Phys. Rev. B 90, 064501 (2014). doi:10.1103/PhysRevB.90.064501

43. N. Mason, A. Kapitulnik, Dissipation effects on the superconductor-insulator transition in 2D superconductors. Phys. Rev. Lett. 82, 5341–5344 (1999). doi:10.1103/PhysRevLett.82.5341

44. H. T. Yuan, H. Shimotani, A. Tsukazaki, A. Ohtomo, M. Kawasaki, Y. Iwasa, High-

/ sciencemag.org/content/early/recent / 1 October 2015 / Page 4 / 10.1126/science.1259440

on April 26, 2020

http://science.sciencem

ag.org/D

ownloaded from

density carrier accumulation in ZnO field-effect transistors gated by electric double layers of ionic liquids. Adv. Funct. Mater. 19, 1046–1053 (2009). doi:10.1002/adfm.200801633

45. H. Yuan, H. Shimotani, J. Ye, S. Yoon, H. Aliah, A. Tsukazaki, M. Kawasaki, Y. Iwasa, Electrostatic and electrochemical nature of liquid-gated electric-double-layer transistors based on oxide semiconductors. J. Am. Chem. Soc. 132, 18402–18407 (2010). Medline doi:10.1021/ja108912x

46. A. Glatz, A. A. Varlamov, V. M. Vinokur, Fluctuation spectroscopy of disordered two-dimensional superconductors. Phys. Rev. B 84, 104510 (2011). doi:10.1103/PhysRevB.84.104510

47. T. I. Baturina, S. V. Postolova, A. Y. Mironov, A. Glatz, M. R. Baklanov, V. M. Vinokur, Superconducting phase transitions in ultrathin TiN films. Eur. Phys. Lett 97, 17012 (2012). doi:10.1209/0295-5075/97/17012

48. L. B. Ioffe, A. I. Larkin, A. A. Varlamov, L. Yu, Effect of superconducting fluctuations on the transverse resistance of high-Tc superconductors. Phys. Rev. B 47, 8936–8941 (1993). Medline doi:10.1103/PhysRevB.47.8936

49. V. V. Dorin, R. A. Klemm, A. A. Varlamov, A. I. Buzdin, D. V. Livanov, Fluctuation conductivity of layered superconductors in a perpendicular magnetic field. Phys. Rev. B 48, 12951–12965 (1993). Medline doi:10.1103/PhysRevB.48.12951

ACKNOWLEDGMENTS

We thank M. Nakano and Y. Nakagawa for technical support, M. Yoshida for fruitful discussions, and N. Shiba for useful comments on the manuscript. Y.S. is supported by the Japan Society for the Promotion of Science (JSPS) through a research fellowship for young scientists. This work was supported by the Strategic International Collaborative Research Program (SICORP-LEMSUPER) of the Japan Science and Technology Agency, Grant-in-Aid for Specially Promoted Research (No. 25000003) from JSPS and Grant-in Aid for Scientific Research on Innovative Areas (No. 22103004) from MEXT of Japan.

SUPPLEMENTARY MATERIALS www.sciencemag.org/cgi/content/full/science.1259440/DC1 Materials and Methods Supplementary Text Figs. S1 to S6 References (44–49) 31 July 2014; accepted 15 September 2015 Published online 1 October 2015 10.1126/science.1259440

/ sciencemag.org/content/early/recent / 1 October 2015 / Page 5 / 10.1126/science.1259440

on April 26, 2020

http://science.sciencem

ag.org/D

ownloaded from

Fig. 1. Crystal structure of ZrNCl and transport properties of a ZrNCl-EDLT. (A) Ball-and-stick model of a ZrNCl single crystal. The monolayer is 0.92 nm thick. (B) Sheet conductance, σsheet, of a ZrNCl-EDLT as a function of gate voltage, VG, at 220 K. (C) Temperature, T, dependence of the sheet resistance, Rsheet, at different gate voltages, VG, from 0 V to 6.5 V. The device was cooled down to low temperature after applying VG gate voltages at 220 K. (D) Resistive transition at zero magnetic field and VG = 6.5 V, plotted on a semi-log scale (linear scale in the inset). The black solid line represents the BKT transition using

the Halperin–Nelson equation (30), 1/2

c00

BKT

exp 2T T

R R bT T

−= −

−

, where R0 and b

are material parameters. This gives a BKT transition temperature of TBKT = 12.2 K with b = 1.9. The red dashed line in the inset represents the superconducting amplitude fluctuation taking into account the 2D Aslamazov–Larkin (32) and Maki–Thompson terms (33, 34), which give the temperature, Tc0, at which the finite amplitude of the order parameter develops (fig. S4) (29).

/ sciencemag.org/content/early/recent / 1 October 2015 / Page 6 / 10.1126/science.1259440

on April 26, 2020

http://science.sciencem

ag.org/D

ownloaded from

Fig. 2. Two-dimensional superconductivity in ion-gated ZrNCl. (A and B) Sheet resistance of a ZrNCl-EDLT as a function of temperature at VG = 6.5 V, for (A) perpendicular magnetic fields,

0 c2H ⊥µ , varying in 0.05 T steps from 0 T to 0.1 T, in 0.1 T steps from 0.1 T to 0.9 T, and in 0.15 T

steps from 0.9 T to 2.7 T, and of 3 T and 9 T, and (B) parallel magnetic fields, ||

0 c2Hµ , varying in 1 T

steps from 0 T to 9 T, respectively. The inset of Fig. 2B is a magnified view of the region between 12 K and 16 K. (C) Angular dependence of the upper critical fields μ0Hc2(θ) (θ represents the angle between a magnetic field and the perpendicular direction to the surface of ZrNCl). The inset shows a close-up of the region around θ = 90°. The blue solid line and the green dashed line are the theoretical representations of Hc2(θ), using the 2D Tinkham formula

( )2||

c2 c2 c2 c2( ) sin ( ) cos 1H H H H ⊥θ θ + θ θ = and the three-dimensional anisotropic mass model

( )1 2|| 2 2 2

c2 c2( ) sin cosH Hθ = θ + γ θ with ||

c2 c2H H ⊥γ = , respectively. (D) Temperature dependence of μ0Hc2

perpendicular and parallel to the surface, 0 c2 ( )H T⊥µ and ||

0 c2 ( )H Tµ . Solid black curves are theoretical

curves obtained from the 2D Ginzburg–Landau equation.

/ sciencemag.org/content/early/recent / 1 October 2015 / Page 7 / 10.1126/science.1259440

on April 26, 2020

http://science.sciencem

ag.org/D

ownloaded from

Fig. 3. Electronic phase diagram of electric-field-induced and bulk superconductivity in ZrNCl. The SC transition temperatures, Tc (defined as the temperature at which Rsheet reaches half the value of RN at 30 K), for ZrNCl-EDLTs were measured in seven different devices, indicated by the colored circles. The data for Li-intercalated ZrNCl was taken from (28), and the thickness of a bilayer was used to calculate n2D from the 3D carrier density. The sheet carrier density for ZrNCl-EDLTs was determined by Hall-effect measurements at 60 K (fig. S6) (29).

/ sciencemag.org/content/early/recent / 1 October 2015 / Page 8 / 10.1126/science.1259440

on April 26, 2020

http://science.sciencem

ag.org/D

ownloaded from

Fig. 4. Vortex dynamics in ion-gated ZrNCl. (A) Arrhenius plot of the sheet resistance of a ZrNCl-EDLT at VG = 6.5 V for different magnetic fields perpendicular to the surface of ZrNCl. The black dashed lines demonstrate the activated behavior described by

( )sheet B'exp ( )R R U H k T= − . The arrows separate the thermally activated state in the high-

temperature limit and the saturated state at lower temperatures. (B) Activation energy, U(H) /kB, which is derived from the slopes of the dashed lines in Fig. 4A, is shown on a semi-logarithmic plot as a function of magnetic field. The solid line is a fit by using the equation,

0 0( ) ln( / )U H U H H= . The inset shows the same data plotted as lnR′ versus U/kBTc. These plots

indicate that the resistance is governed by the thermally activated motion of dislocations of the 2D vortex lattice (2D thermal collective creep). (C) Low-temperature saturated values of the resistance as a function of magnetic field at 2 K. The red solid line is a fit using Eq. 3, which gives C ≅ 4.8 × 10−3. The inset shows H-linear dependence of Rsheet above 1.3 T (black solid line). (D) Vortex phase diagram of the ZrNCl-EDLT. The boundary between the thermally-assisted vortex-creep regime and the quantum regime, Tcross, is determined from the Arrhenius plot as shown by the arrows in Fig. 4A. TBKT and Tc0 are the BKT transition temperature and the temperature obtained by analyses of the superconducting amplitude fluctuation, respectively (fig. S4) (29).

/ sciencemag.org/content/early/recent / 1 October 2015 / Page 9 / 10.1126/science.1259440

on April 26, 2020

http://science.sciencem

ag.org/D

ownloaded from

Metallic ground state in an ion-gated two-dimensional superconductorYu Saito, Yuichi Kasahara, Jianting Ye, Yoshihiro Iwasa and Tsutomu Nojima

published online October 1, 2015

ARTICLE TOOLS http://science.sciencemag.org/content/early/2015/09/30/science.1259440

MATERIALSSUPPLEMENTARY http://science.sciencemag.org/content/suppl/2015/09/30/science.1259440.DC1

REFERENCES

http://science.sciencemag.org/content/early/2015/09/30/science.1259440#BIBLThis article cites 47 articles, 3 of which you can access for free

PERMISSIONS http://www.sciencemag.org/help/reprints-and-permissions

Terms of ServiceUse of this article is subject to the

is a registered trademark of AAAS.ScienceScience, 1200 New York Avenue NW, Washington, DC 20005. The title (print ISSN 0036-8075; online ISSN 1095-9203) is published by the American Association for the Advancement ofScience

Copyright © 2015, American Association for the Advancement of Science

on April 26, 2020

http://science.sciencem

ag.org/D

ownloaded from