Superconducting Dome in a Gate-Tuned Band Insulator

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Science  30 Nov 2012:
Vol. 338, Issue 6111, pp. 1193-1196
DOI: 10.1126/science.1228006


A dome-shaped superconducting region appears in the phase diagrams of many unconventional superconductors. In doped band insulators, however, reaching optimal superconductivity by the fine-tuning of carriers has seldom been seen. We report the observation of a superconducting dome in the temperature–carrier density phase diagram of MoS2, an archetypal band insulator. By quasi-continuous electrostatic carrier doping achieved through a combination of liquid and solid gating, we revealed a large enhancement in the transition temperatureTc occurring at optimal doping in the chemically inaccessible low–carrier density regime. This observation indicates that the superconducting dome may arise even in doped band insulators.

In many unconventional superconductors (13), the transition temperature Tc has a maximum as a function of external parameters such as chemical doping or pressure; in cuprate families, this so-called superconducting dome arises upon the chemical doping of the parent Mott insulator (1). In band insulators, similar behavior was observed at low carrier densities (4) where superconductivity is usually not favorable because of the low density of states (DOS) (4, 5). Except in certain cases (4, 6), however, using chemical doping to achieve low carrier densities results in nonuniformity or phase separation. Other systems exhibiting optimal doping of the superconducting state include two-dimensional (2D) electron systems at surfaces and interfaces, whose phase diagrams may be explored by applying electric fields (79). In recent years, this electrostatic carrier doping has been effectively implemented by using ionic liquids to form an electrical double layer (EDL) of high capacitance (1012). This method has produced carrier densities that span the superconducting dome in high-Tc cuprates (13, 14) and may be an effective tool to access exotic superconducting states in other materials.

We chose a typical band insulator, MoS2, because the high mobility found in its solid-state transistor operations (15) suggests that interesting basic physical properties may be revealed by using the EDL dielectrics (11, 1618). To make our devices, we isolated thin flakes of MoS2 from a bulk 2H-type single crystal (Fig. 1A) by the Scotch tape method widely used in graphene research (19, 20) and transferred them onto the surface of HfO2 grown by atomic layer deposition on a Nb-doped SrTiO3 substrate. We selected atomically flat thin flakes by examining their optical micrographs (21) and patterned them into a Hall bar configuration (Fig. 1B), which acts as a transistor channel (11, 16). A droplet of ionic liquid (DEME-TSFI) (21) was applied onto the surface of the thin flake covering the side gate electrode (Fig. 1C). A voltage applied between the thus formed liquid gate (LG) and the channel drives either anions or cations onto the channel surface under positive or negative bias, respectively. The ions and induced carriers (~1014 cm−2) right beneath form an equivalent capacitance of ~10 μF/cm2, large enough for inducing superconductivity at the interface (1014). In addition, we were able to modulate the carrier density (to ~1013 cm−2) using a high-k dielectric (HfO2) back gate (BG), which remains effective after the freezing of the ion motion at a temperature below ~200 K. For carriers induced at the top surface of the MoS2 flake by the LG, the effective BG capacitance is affected by two layers of dielectrics: HfO2 and the bulk of MoS2 flake. Using this double gating method, we could access a large range of carrier densities n2D quasi-continuously and precisely, thereby avoiding the staging effect (22), even in the low-density regime where chemical doping is plagued by nonuniformity.

Fig. 1

MoS2-based EDLT device and its transistor properties. (A) Ball-and-stick model of the layered 2H-type MoS2 single crystal. (B) Optical micrograph of a typical MoS2 device under transmission light illumination. (C) Double-gate device and measurement configuration. (D) Transfer curve of transistor operations by accumulating carriers by EDL top liquid gate (red: ramping VLG up; blue: ramping VLG down) and HfO2 bottom solid gate (green), both at 220 K. (E) Output curve of the thin-flake MoS2 EDLT with both electron (0 < VLG < 1 V) and hole (–0.6 < VLG < –0.2 V) channel. Well-behaved saturation at large VDS was found in the dominating electron transport. For each VLG, we measured the two overlapping IDS curves with forward and backward scans of VDS.

Figure 1D shows the transfer curves of a typical double-gate device at 220 K with a source-drain voltage VDS = 10 mV. For the n-channel conduction, an on/off ratio of >104 was reached for biasing with either the liquid ionic gate (VLG) or the high-k back gate (VBG), with a channel resistance RDS > 1 gigohm in the off state. Compared with the BG, the LG not only had 10 times the gate efficiency (the change of channel current versus gate voltage ΔIDSΔVG), but also created an additional p-channel when a negative VG was applied. This ambipolar transport indicates that the LG is effective in shifting the Fermi level EF to access both the valence and conduction bands (16). An enhanced p-channel with more balanced ambipolar transport could be found in flakes with less intrinsic electron doping (sulfur deficiency), where the barely metallic state in the p-channel was still far from reaching hole superconductivity (16). To confirm the electrostatic operation of LG, we performed a transfer curve measurement with fast gate bias cycles (fig. S1). The possibility of a chemical reaction was ruled out by repeatability and a negligible (~1 nA) leak current IG, as well as a persistent off state (> 1 gigohm). The IDS versus VDS characteristic in the output operation (Fig. 1E) of a typical MoS2 EDL transistor (EDLT) corroborates the more pronounced n-channel (0 < VLG < 1 V) than p-channel operation (–0.6 < VLG < –0.2V), consistent with the transfer characteristics. Compared with the n-channel operation observed in monolayer devices (15), the more pronounced saturation at high VDS indicates well-behaved transistor operation.

After introducing carriers onto the channel surface at 220 K with different liquid-gate biases VLG, we measured the four-terminal sheet resistance Rs as a function of temperature T when the device was being cooled down to 2 K (Fig. 2A). At gate biases VLG < 1 V, we observed a negative temperature derivative of Rs (dRs/dT) for insulating states. The increase of dRs/dT with VLG indicates the gradual formation of degenerate carriers and enhanced mobility at low temperatures. The channel surface shows metallic transport (positive dRs/dT) at VLG ≥ 1 V. The enhancement of metallicity continues with further increase of VLG, and superconductivity emerges at VLG = 4 V. The transition temperature Tc shows clear VLG dependence until VLG reaches 6 V, the maximum voltage used in our experiment. Similar field-induced superconductivity was reported recently by Taniguchi et al. (23).

Fig. 2

Transport properties of the thin-flake MoS2 EDLT. (A) Temperature dependence of the channel sheet resistance Rs at different VLG gate biases ranging from 0 to 6 V (indicated on the right). (B) Temperature dependence of the channel sheet resistance Rs at VLG = 1 V and different VBG’s showing a metal-insulator transition at n2D = 6.7 × 1012 cm−2. For each VBG, we marked the corresponding n2D measured by the Hall effect at 20 K. (C) Phase diagram showing the evolution of different electronic phases as a function of carrier density n2D. The phase diagram shows an insulating (n2D < 6.7 × 1012 cm−2), a metallic (6.7 × 1012 < n2D < 6.8 × 1013 cm−2), and a dome-like superconducting phase (n2D > 6.8 × 1013 cm−2), where the color corresponds to the logarithm of the sheet resistance Rs (Ω). (D) Normalized superconducting transition Rs/Rs (15K) as a function of temperature for different gate voltages. The Tc is marked as a circle at 90% of the total transition. Both VLG and VBG are varied; for a given VLG, we show the evolution of the transition with increasing VBG. All data corresponding to the same VLG are shown with the same color. The dashed arrows indicate the order of increasing VBG from –4 to 2 V in ∆VBG = 2 V. (Upper panel) For VLG between 4 and 5.5 V, Tc increased with increasing VBG; (bottom panel) for VLG = 6 V, Tc decreased with increasing VBG because the corresponding n2D had reached the peak of the superconducting dome.

For the metallic states at VLG = 1 V, we switched on the solid back gate to study the metal insulator transition (MIT) by a precise control of the transport with 18 different n2D values (7.3 × 1011 < n2D < 8.7 × 1012 cm−2) measured by the Hall effect at 20 K (Fig. 2B). A transition between the insulating (blue) and metallic (red) transport was clearly separated by a critical resistance Rc = 21.7 kilohm (separatrix, black line) at nc = 6.7 × 1012 cm−2, close to the quantum resistance h/e2, consistent with MITs found in other 2D systems (24). A Hall mobility of μH ~ 240 cm2/V s at n2D = 8.7 × 1012 cm−2 is comparable to the bulk value (25), supporting our choice of (~20 nm thick) flakes instead of monolayers, where ripples might lower the mobility (26, 27). After the formation of metallic states, increasing the gate bias also creates a growing perpendicular surface electric field Es, inducing spin-orbit interaction, which corroborates the 2D nature of MoS2 interface (21, 28). Varying both VLG and VBG, we quasi-continuously mapped log Rs in the n2D and T plane (Fig. 2C). This enables a detailed study of the full superconducting phase induced by the field effect in a pristine compound, avoiding a nonuniform dopant distribution or phase separation. At several fixed values of VLG, we manipulated Tc by varying VBG (Fig. 2D).

Figure 3A shows a superconducting phase diagram of MoS2 as a function of n2D measured by Hall effect at 20 K. As estimated from the Thomas-Fermi screening length for n2D ~1014 cm−2, we assumed that the carriers are accumulated in a half of one unit cell, 6.15 Å (a monolayer). Notably, this value of n2D can be regarded as the upper limit to the estimate of n2D when we unify our phase diagram with that of alkali metal–intercalated 2H-MoS2 in Fig. 3A (29, 30). The superconductivity sharply appears at n2D = 6.8 ×1013 cm−2, then saturates after reaching a maximum Tc = 10.8 K at n2D = 1.2 × 1014 cm−2, followed by a decrease in Tc at larger n2D; this results in a dome-like superconducting state. We defined Tc as the temperature at which Rs reaches 90% of its normal state value. At the onset of the superconducting phase, the critical behavior near the quantum critical point could be well fitted with T(n2Dn0)zv¯, where zv¯=0.6 (fig. S4), in a manner similar to that for LaAlO3/SrTiO3 interfaces (7). This is also consistent with zv¯=0.50.6 found in boron-doped diamond, where a comparable Tc was observed (31).

Fig. 3

Phase diagram and band calculation of electron-doped MoS2. (A) Unified phase diagram of superconductivity of both electrostatically and chemically doped MoS2 as a function of doping concentration x (upper horizontal axis) and carrier density n2D (bottom horizontal axis). The field-induced superconducting data were from four different samples, each marked with a differently shaped filled symbol. Filled circles of the same color correspond to the superconducting states at a fixed VLG but different VBG’s. Open circles show the Tc of MoS2 chemically intercalated with different alkali metal dopants. Solid bars denote the range of doping showing the same Tc. The structure of all intercalated compounds is 2H-type within the indicated carrier density region. (B) Calculated DOS of MoS2. The field-induced carriers mainly occupy the 4d state of Mo, covering the n2D region indicated by the shaded green area. The red arrow locates the n2D where the maximum Tc was observed.

In the combined phase diagram, which includes the chemically doped MoS2 (29, 30), the field-induced phase showed enhanced Tc (~40% higher than the maximum Tc found in CsxMoS2) at a much lower n2D (Fig. 3A). The maximum Tc is also well above that of NbSe2 (~7 K), which was thought to be the highest Tc in transition-metal dichalcogenides. That the field-induced phase appears with an enhanced Tc at a much lower n2D with respect to the alkali metal–doped compounds confirms the effectiveness of searching for different regions of carrier concentrations in doped semiconductors. It appears that the decrease in Tc connects smoothly to the region of bulk superconductivity for alkali metal–doped MoS2 compounds.

To understand these superconducting features found in MoS2 EDLT, we calculated its electronic structure for both monolayer and bulk (21). Figure 3B shows the DOS spectrum for the electron-doped monolayer MoS2, which mimics the gate-induced charge accumulation layer at large carrier densities of ~1014 cm−2. The conduction band edge consists predominantly of the dz2 orbital of Mo. Reflecting the 2D nature of the monolayer, the DOS is nearly flat in the region of 6.8 × 1013 < n2D < 1.2 × 1014 cm−2, where superconductivity sharply sets in and reaches the maximum Tc, corresponding to an EF shift of 0.25 eV from the band edge (21). The DOS continues to increase with n2D owing to the contribution from additional dx2-y2 and dxy orbitals, indicating that the decrease in Tc above 1.2 × 1014 cm−2 is not simply controlled by the change in the DOS.

Such a decrease in Tc with increasing carrier density was first recognized in Na-doped WO3 and was attributed to phonon softening from a structural transition observed in the vicinity of the superconducting phase (32). However, the phonon softening scenario should not apply to MoS2 because its structural transition occurs at an order of magnitude higher n2D (33). A similar superconducting dome with a quantum critical point has been recently observed in electric-field–controlled interface superconductivity such as in LaAlO3/SrTiO3 (7) and KTaO3 (12). Thus, it is possible that a more universal, non–material-specific model exists for the superconducting phase diagram in doped band insulators at dilute carrier densities.

Supplementary Materials

Materials and Methods

Figs. S1 to S5

References (3447)

References and Notes

  1. Information on materials and methods is available in the supplementary materials on Science Online.
  2. Acknowledgments: We thank Y. Takada and A. Bianconi for fruitful discussions and M. Nakano and Y. Kasahara for experimental help. This work was supported by a Grant-in-Aid for Scientific Research (S) (no. 21224009) from Japan and Strategic International Collaborative Research Program (SICORP), Japan Science and Technology Agency. M.S.B., R.A., and Y.I. were supported by the Japan Society for the Promotion of Science through its Funding Program for World-Leading Innovative R&D on Science and Technology (FIRST Program). Y.I. received additional funding from SICORP, Japan Science and Technology Agency.
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