Metallic ground state in an ion-gated two-dimensional superconductor

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Science  23 Oct 2015:
Vol. 350, Issue 6259, pp. 409-413
DOI: 10.1126/science.1259440

A 3D approach to make 2D superconductors

When the thickness of a superconducting film becomes comparable to the typical size of its electron pairs, its superconductivity enters a two-dimensional (2D) regime. Thinner films usually have higher amounts of disorder, making it difficult to isolate the 2D effects. To circumvent this limitation, Saito et al. induced charge carriers on the surface of the 3D insulator ZrNCl. This approach produced a clean superconducting layer thinner than the unit cell of the crystal. The superconducting state was extremely sensitive to the application of a perpendicular magnetic field, as expected for clean systems.

Science, this issue p. 409


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 an ion-gated zirconium nitride chloride surface, exhibiting a dome-shaped phase diagram with a maximum critical temperature of 14.8 kelvin, 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 kelvin is occupied by a metallic state with a finite resistance, owing to the quantum creep of vortices caused by extremely weak pinning and disorder. Our findings highlight the potential of electric-field–induced superconductivity, establishing a new platform for accessing quantum phases in clean 2D superconductors.

Recent technological advances of materials fabrication have led to discoveries of a variety of superconductors at heterogeneous 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 opportunities for searching for superconductivity at higher temperatures, 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 necessary to achieve zero electrical resistance under magnetic fields, may be too weak. To address this question, superconductivity 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 increases disorder. In such thin films, a direct superconductor-to-insulator transition (SIT) is observed in most cases when the system is disordered (8). This SIT has been understood in the framework of the so-called “dirty boson model” (9); however, this simple picture needed to be modified because an intervening metallic phase between the superconducting (SC) and insulating phases under magnetic fields was observed in less-disordered systems (8, 10). Therefore, investigating 2D superconductivity in even cleaner systems is desirable.

In contrast to the conventional metallic films, the recently discovered 2D superconductors are highly crystalline, displaying lower normal state sheet resistance. The electric-double-layer transistor (EDLT), which is composed of the interface between crystalline solids and electrolytes, can be a good candidate to realize such a clean system, because 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 applicability to a wide range of materials, as exemplified by gate-induced superconductivity in 3D SrTiO3 (3, 11, 12), KTaO3 (13), quasi-2D layered ZrNCl (14), transition metal dichalcogenides (1517), and cuprates (1822). Here, we report comprehensive transport studies on a ZrNCl-EDLT, which provide evidence of 2D superconductivity in this system based on several types of analyses. In particular, we found that the zero-resistance state is immediately destroyed 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 comprises 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 (2528). 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, demonstrating a typical n-type field-effect transistor behavior. As shown in the temperature dependence of the sheet resistance, 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 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 state driven by the binding of vortex-antivortex pairs. To determine the BKT transition temperature, we used 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 gradual 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 (3234) for the 2D fluctuation conductivities into account (fig. S4) (29). These results suggest that 2D superconductivity is achieved at zero magnetic field.

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 to 6.5 V. The device was cooled down to low temperatures after applying VG gate voltages at 220 K. (D) Resistive transition at zero magnetic field and VG = 6.5 V, plotted on a semilog scale (linear scale in the inset). The black solid line represents the BKT transition using the Halperin-Nelson equation (30), Embedded Image, 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 both 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).

Figure 2, A and B, display temperature-dependent Rsheet(T) values at VG = 6.5 V for magnetic fields applied perpendicular and parallel to the surface of ZrNCl, respectively. For the out-of-plane magnetic fields, Tc is dramatically suppressed 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 large contribution of the vortex motion in the out-of-plane magnetic field geometry. Figure 2C shows the angular dependence of the upper critical field, μ0Hc2 (θ) (θ represents the angle between the c axis of ZrNCl and applied magnetic field directions), at 13.8 K, which is just below 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 3D 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 temperature dependence of μ0Hc2 at θ = 90° (Embedded Image) and at θ = 0° (Embedded Image), which exhibits a good agreement with the phenomenological Ginzburg-Landau (GL) expressions for 2D SC films. Embedded Image(1)Embedded Image(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 temperature-independent SC thickness. As a result of the fit, we obtained ξGL(0) Embedded Image 12.8 nm and dsc Embedded Image 1.8 nm. The latter parameter 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 extreme 2D limit. The dsc for this system is much smaller than the reported value of ~11 nm for the interface superconductivity on SrTiO3 (1, 36), which is presumably 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 layer (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 because of the paramagnetic effect as compared with the orbital limit, leading to an estimated dsc thicker than the real value.

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, Embedded Image, varying in 0.05 T steps from 0 to 0.1 T, in 0.1 T steps from 0.1 to 0.9 T, and in 0.15 T steps from 0.9 to 2.7 T, and of 3 T and 9 T, and (B) parallel magnetic fields, Embedded Image, varying in 1 T steps from 0 to 9 T, respectively. The inset of Fig. 2B is a magnified view of the region between 12 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 Embedded Image and the 3D anisotropic mass model Embedded Imagewith Embedded Image, respectively. (D) Temperature dependence of μ0Hc2 perpendicular and parallel to the surface, Embedded Image and Embedded Image. Solid black curves are theoretical curves obtained from the 2D Ginzburg-Landau equations.

In the present system, we found that the Pippard coherence length, Embedded Image, is equal to 43.4 nm, as calculated from Embedded Image by using Embedded Image Embedded Image, and the Bardeen-Cooper-Schrieffer (BCS) energy gap of Δ(0) = 1.76kBTc = 2.2 meV, where vF, kF, m*, Embedded Image, 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 Embedded Image 1.8 nm. We also note that the Embedded Imagemay exceed the Pauli limit for weak-coupling BCS superconductors, Embedded Image = 1.86Tc = 27.0 T. However, to confirm this phenomenon, it is necessary to investigate Hc2 at lower temperatures and higher magnetic fields.

Having estimated dsc, we can now compare the phase diagrams of electric-field–induced 2D and bulk superconductors (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 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 commonality among electric-field–induced superconductors.

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).

In an Arrhenius plot of Rsheet(T) for out-of-plane magnetic fields at VG = 6.5 V (Fig. 4A), Rsheet(T) exhibits an activated behavior just below Tc described by Embedded Image, where kB is Boltzmann’s constant, as shown by the dashed lines. The magnetic field dependence of the extracted activation energy U(H) (Fig. 4B), and the relation between U(H)/kBTc and Embedded Image(Fig. 4B, inset) are consistent with the thermally assisted collective vortex-creep model in two dimensions (39), Embedded Image and Embedded ImageThe activation energy becomes almost zero at μ0H Embedded Image 1.3 T, allowing the vortex flow motion above this field, as explained below.

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 Embedded Image. 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 semilogarithmic plot as a function of magnetic field. The solid line is a fit by using the equation Embedded Image. The inset shows the same data plotted as ln R′ 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 Embedded Image 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 (thermal creep) and the quantum creep 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).

At low temperatures, on the other hand, each RsheetT 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 quantum 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 resistance RQ = h/4e2 = 6.45 kΩ, where h and e are Planck’s constant and the elementary charge, respectively. The metallic ground state has been reported in MoGe (10) and Ta (40) thinfilms, where RN values (Embedded Image1 kΩ) are smaller than RQ. In the ZrNCl-EDLT, RN values at VG = 6 and 6.5 V are ~120 and ~200 Ω, respectively, which are even lower, reaching values as small as ~1/50 of RQ. This leads to kFl = Embedded Image~ 77 – 130 (for 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 Embedded Image1.1 – 2.4 l, which is far from the dirty limit Embedded Image. Indeed, the expression for ξGL(0) in the dirty limit Embedded Image 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 have 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 moderately 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 general form in the limit of the strong dissipation (41).Embedded Image(3)where C is a dimensionless constant. As seen in Fig. 4C, the RsheetH 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 (i) finite-size effects (42) or (ii) 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 the following reasons: (i) a BKT transition, and a zero resistance state (below ~0.05 Ω) are observed (see Fig. 1D); and (ii) the channel surface preserved atomically flat morphology with an 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 longitudinal 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 concentrations (VG = 6 and 6.5 V), which suggests that 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 Embedded Image 1.3 T, where U(H) for the thermal creep approaches zero (Fig. 4B), implying that the pinning or the elastic potential effectively disappears at high magnetic fields. Based on the above observations, we obtained the field-temperature phase diagram of ion-gated ZrNCl shown in Fig. 4D. A true zero-resistance state occurs only at very small magnetic fields below 0.05 T. The key parameters here are the dimensionality and RN of the system. The former enhances the quantum fluctuations, whereas the latter controls the coupling of vortices to a dissipative bath, which stabilizes the metallic region when RN is low (43). Our results indicate that the EDLT provides a model platform of clean 2D superconductors with weak pinning and disorder, which may potentially lead to realizing intrinsic quantum states of matter.

Supplementary Materials

Materials and Methods

Supplementary Text

Figs. S1 to S6

References (4449)

References and Notes

  1. See the supplementary materials on Science Online.
  2. 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. was supported by the Japan Society for the Promotion of Science (JSPS) through a research fellowship for young scientists. J.T.Y. acknowledges the funding from the European Research Council (consolidator grant no.648855 Ig-QPD). 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.

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