www.sciencemag.org/cgi/content/full/338/6111/1193/DC1

Supplementary Materials for

Superconducting Dome in a Gate-Tuned Band Insulator

J. T. Ye,* Y. J. Zhang, R. Akashi, M. S. Bahramy, R. Arita, Y. Iwasa*

*To whom correspondence should be addressed. E-mail: yejianting@ap.t.u-tokyo.ac.jp (J.T.Y.);

iwasa@ap.t.u-tokyo.ac.jp (Y.I.)

Published 30 November 2012, Science 338, 1193 (2012) DOI: 10.1126/science.1228006

This PDF file includes:

Materials and Methods Figs. S1 to S5 References (34–47)

2

Materials and Methods

1. Sample Fabrication

We fabricated thin flakes of MoS2 by micro-mechanically cleaving a single crystal

of 2H-MoS2. Flakes with the proper thickness (~20 nm) were roughly classified by

analyzing the intensity shifts in the red, green and blue (RGB) channels of optical

micrographs. Based on previous measurements of the transmission intensities, I and I0, at

positions on the flake and bare transparent substrates, respectively, a relationship between

the transmittance,

I / I0, with the true thickness of the thin flake, d, measured by atomic

force microscope (AFM) was established as

I / I0 ed for each RGB channel (16). Here,

is the absorption coefficient for each color channel. This rapid estimation of the flake

thickness is especially effective for thick and highly absorptive flakes when the reflection

contrast is less effective for determining their thickness. The actual thickness of the flakes

was then determined by measuring the height profile from an AFM image. Atomically

flat, high-quality MoS2 flakes were subsequently selected.

To enhance the tunability beyond the conventional SiO2/Si substrate, which is

widely used in graphene research, we replaced the SiO2 dielectrics with HfO2 (30 nm,

dielectric constant of ~24), which was deposited by atomic layer deposition onto a Nb-

doped SrTiO3 substrate. The HfO2 layer was carefully optimized for flat morphology in

conformity with the layered structure of MoS2. With this high-k dielectric, the carrier

density could be tuned on the order of ~1013

cm-2

and is effective at low temperatures,

which is important for tuning the carrier density because the liquid gate would lose its

control on the carrier density after the motion of ions stops at temperatures below 200 K.

3

Electrodes were attached with a Hall bar configuration on the flakes selected for the

experiments using conventional micro-fabrication techniques (electron-beam lithography,

electron-beam evaporation, and lift-off). The electrodes are composed of a multilayered

structure of SiO2/Au/Ti (30/60/10 nm), where Ti provides good electrical contacts to

MoS2 and SiO2 seals the electrodes from direct contact with the ionic liquids (Figs. 1B

and C). Transport measurements were performed by applying a small AC (10 mV)

voltage between the source and drain electrodes. Lock-in amplifiers were used to

simultaneously measure the transverse (Vxy) and longitudinal voltage (Vxx) drops along

the Hall bar devices as a function of varied parameters, such as the gate voltage (VG),

temperature (T), or magnetic field (H). Owing to the very high concentration of ions in

ionic liquids, the thickness of the electric double layer (EDL) is considerably less than

that of common polymer electrolytes. We also took care in designing a large surface ratio

between the gate and channel (> 102:1). With these efforts, virtually all of the voltage

drops occur at the liquid/flake interface throughout the complete range of applied gate

voltages, as shown in previous measurements (17).

For all of the liquid gating measurements, we used the ionic liquid: N, N-diethyl-N-

(2-methoxyethyl)-N-methylammonium bis-(trifluoromethylsulfonyl)-imide (DEME-

TFSI). It is well-known that the performance of ionic liquids is very sensitive to the

presence of moisture (34), which prevents the reversible and reliable operation of the

devices. To remove the possibility of a chemical reaction induced by residual water

molecules, we carefully degased the ionic liquid and performed all of the measurements

under high vacuum (< 10-6

mbar). To confirm the electrostatic accumulation of charge

during the operation of the device and to ensure the reproducibility of our results, we

4

performed extensive control experiments. Figure S1 presents continuous gating cycles

that were performed with a very fast scan speed of ~ 40 mV/sec at 220 K under a small

AC source-drain bias (VDS = 10 mV). Typical transfer curves were measured on a time

scale of 3 minutes from the maximum positive to the minimum negative gate voltage.

Despite the hysteresis observed due to the slow motion of ions at 220 K, the transfer

curve is reversible, as shown in Fig. S1A. The possibility of a chemical reaction was

excluded based on the repeatability of the transfer curves, the negligible (~1 nA) leak

current (IG) (Fig. S1B), and the persistent OFF state (RDS > 1 GΩ).

2. Spin-orbit interaction

Inducing carriers through electrostatic doping is highly expected to enrich the

superconducting phase diagram by accessing carrier density region where chemical

methods are not able to or have difficulty reaching. However, in addition to inducing

carriers, gate tuning can also introduce a concomitant external electric field. This non-

centrosymmetric field perpendicular to the channel surface is the origin of the Rashba-

type spin-orbit interaction (SOI) that is observed in many semiconductor heterojunctions

(35-38). Furthermore, a SOI was observed in the LaAlO3/SrTiO3 interfaces, which

enriched the superconducting phase diagram (28). Electric field control of the SOI

manifested itself in the transport measurement as a crossover between weak localization

(WL) and anti-localization (WAL) in the low temperature magnetoresistance as a

function of the applied gate voltage (28, 36). In 2D superconducting LaAlO3/SrTiO3

interfaces, this SOI was observed at a temperature higher than that for the emergence of

superconductivity and was expected to contribute to the 2D superconducting properties

5

due to the significant spin-orbit splitting, which was even larger than the energy of the

superconducting gap (28).

In liquid gating, this surface electric field, Es = VG/d (~10 MV/cm), is especially

strong due to the closely attached ions above the channel surface in the sub-nanometer

distance, d. This perpendicular field breaks the inversion symmetry and adds a Rashba

Hamiltonian as an additional term for describing the electronic properties of interface

carriers (39). As shown in Fig. S2A, we observed a clear crossover from WL to WAL as

a function of increasing VG, which corroborates the 2D nature of the MoS2 interface with

a clear effect from an increasing surface electric field, Es. The magnetoresistance at VG =

3.5 V reveals a diminishing WAL with increasing temperature up to 10 K (Fig. S2B),

which is also consistent with the temperature dependence of a WAL. Under higher VG > 4

V, the onset of superconductivity prevents us from further distinguishing a WAL feature.

On the MoS2 interface, we confirmed that, as a function of the induced carrier density

n2D, the contribution from the SOI was observed to emerge after the creation of a metallic

state before the appearance of superconducting states. Because the SOI contribution is

expected to increase with the increase of electric field at higher gate voltages, the SOI

should also contribute even in the superconducting state, although this weak transport

signature is overwhelmed by the appearance of superconducting transitions. As shown in

Fig. S4, pinning down the SOI interaction in the phase diagram indicates that the SOI

might also contribute to the superconductivity observed in MoS2. Furthermore, this

observation provides an example to the issue of specifically locating where the SOI

appears in the phase diagram of interface systems (8, 12, 28).

6

3. Superconducting properties

Alkali metals can be introduced into the van der Waals gap of pristine MoS2 and

induce superconductivity with a Tc up to ~ 7 K (29, 30). The superconducting transitions

observed in these alkali-doped AxMoS2 compounds are summarized in Fig. 3A.

Compared to chemically intercalated compounds, electrostatic doping will not introduce

an impurity, which is especially important for low carrier density electronic phases where

chemical doping is hampered by non-uniformity. In addition, the chemically doped

system also suffers from structural instability. In the alkali-doped MoS2 compound, a

doping-induced change from a hexagonal to tetragonal structure was observed in

compounds doped with Na and Li at high doping concentrations, which might limit the Tc

because of the chemically introduced randomness (30). The structural change in the

EDLT is avoided due to the accumulation of surface charge without the chemical process

of introducing an alkali metal followed by annealing at elevated temperatures (29, 30, 33,

40). Chemical doping in layered materials have additional problems due to the staging

effect, which causes problems in obtaining continuous control of the carrier density (22).

To characterize the electric field induced superconductivity in MoS2, the

magnetoresistance was measured at different VG values with a magnetic field of up to 9 T

applied parallel to the c-axis of the MoS2 flake. As shown in Fig. S3A, the sheet

resistance (Rs) recovered to the normal state value (at T=15 K), although the

superconductivities close to the optimal doping level at 2 K were not fully suppressed,

even at 9 T. Here, Hc2 is defined as the magnetic field required for recovering half of the

value of Rs.

7

A large Hc2 has not been reported in bulk compounds. For instance, the Hc2 value of

potassium-doped MoS2 is ~ 1 T for the same field orientation (41). As shown in Fig.

S3B, from the magnetoresistance as a function of VG at 2 K, we plotted the extracted Hc2

value at each VG as a function of corresponding carrier density, n2D. This plot also formed

a dome-like change similar to the Tc dependence on n2D shown in the superconducting

phase diagram (Fig. 3A). The higher Hc2 observed in the superconductivity induced by

EDLT corresponds to more robust superconducting states with a higher Tc at the optimal

doping level. As compared to the Tc dependence on n2D shown in Fig. 3B, the Hc2

dependence on n2D follows a similar trend.

As shown in Fig. S4, individual electronic phases were labeled at different doping

carrier concentrations that cover the range of field-induced superconductivity in a linear

scale of n2D. Due to the limitation of the lowest obtainable temperature (2 K), the present

experiment is still far from accessing the true quantum critical point defined at zero

temperature. For the sharp switch-on of the superconductivity, the data can be fitted by a

dashed line according to the theoretical prediction from the 3D-XY model

T (n2D n0 )zv (42). We obtained

zv 0.6, which is consistent with the 2D nature of

superconductivity in MoS2.

4. Band Calculation

We calculated the partial density of states (DOS) for each Mo d-orbital using the

full-potential linearized augmented plane wave code WIEN2k (43). As shown in Fig S5,

the calculation was performed for the bilayer configuration with the crystal structural

parameters for bulk states (44) and the repeating slab of MoS2 to mimic the electrostatic

8

doping by EDLT in the topmost monolayer of the MoS2 channel (45). The generalized-

gradient approximation for the exchange-correlation functional (46) was used with the

scalar-relativistic correction (47). The muffin-tin radii RMT were set to 2.41 for Mo and

2.14 for S, respectively, and the maximum modulus for the reciprocal vectors Kmax was

chosen. The RMT Kmax =7.00 and a 16161 k-mesh was employed.

Doping the bilayer configuration (Fig. S5A) mimics the chemically doped

compound. Electrostatic doping could be more properly represented by the monolayer

configuration (Fig. S5B) because the applied electric field is well screened in the bulk

material, and the doped carriers only reside at the outermost MoS2 layer. In this situation,

the carriers are effectively isolated from the other layers, and the interlayer hopping

becomes irrelevant.

As shown in Fig. S5, we observe two notable differences between the results for the

two configurations. For the superconducting phases, the total DOS is ≤ 1 [ /(eV f. u.)] in

the slab model when Tc reaches the maximum that corresponds to a shift of the Fermi

level (EF) of 0.25 eV from the conduction band edge. In the bulk configuration, to reach

the highest Tc observed in K0.3MoS2, the shift of EF is larger than 0.5 eV to a DOS of ≥2.0

[/(eV f. u.)]. In the primarily contributing Mo 4d orbitals, the conduction states are almost

entirely formed by the Mo dz2 orbital in the monolayer EDLT charge accumulation (slab

configuration). However, for the bulk configuration (bilayer configuration), the

conduction states are formed by almost equal contributions from both the Mo dz2 and dx

2-

y2 + dxy orbitals.

9

Fig. S1. (A) Reversible transfer curves measured with a small AC source-drain bias (VDS

= 10 mV) under a rapid gate sweep (VLG ~ 40 mV/sec). The MoS2 thin flake device was

gated only by the top liquid gate using DEME-TFSI at 220 K. The black arrows show the

scanning direction of the gate voltage (VG); one directional full scale voltage scan from

the maximum positive voltage to the minimum negative voltage required ~3 minutes. (B)

The corresponding leak currents, ILG, (< 1 nA) measured for the transfer curves are

shown in panel (A).

10

Fig. S2. (A) The magnetoresistance (∆Rs=Rs(B)–Rs(0)) at 2 K of the MoS2 channel, which

exhibits a clear crossover from weak localization to weak anti-localization as a function

of the liquid gate voltage, VLG. (B) The weak anti-localization at VLG = 3.5 V as a

function of temperature from 2 to 10 K.

11

Fig. S3. (A) The magnetoresistance measured at different carrier densities, n2D, inside the

superconducting dome. Magnetic fields of up to H = 9 T were applied along the c-axis of

the crystal at T = 2 K. The arrows in the figure indicate the change of the

magnetoresistances as a function of n2D. (B) The dependence of Hc2 at T = 2 K as a

function of the carrier density, n2D. From 6.8<n2D<121013

cm-2

, the extracted Hc2 values

increase with the increase of n2D. Whereas, Hc2 decreases in the range of 12<

n2D<151013

cm-2

. Here, Hc2 is defined as the magnetic field required for recovering half

the value of the sheet resistance at 15 K. The corresponding superconducting dome from

Fig. S4 was overlaid as a guide to the eye.

12

Fig. S4. Phase diagram of superconductivity of electrostatically doped MoS2. The

colored areas indicate different ground states that cover different carrier densities, n2D

(red: insulating, blue: metallic, and green: superconducting). The data from 4 samples

contained are listed in the caption of Fig. 3A. The dashed line corresponds to a fit based

on

T (n2D n0)zv where

zv 0.6.

13

Fig. S5. Theoretical calculation of the band structure of the bulk and monolayer MoS2

where three 4d states of Mo, dx2-y

2, dxy and dz

2, primarily contribute in accommodating

the doped carriers. (A) Density of states (DOS) and band structure of bulk MoS2, where

the shaded area corresponds to the carrier density covered by the alkali-doped MoS2

compound in the superconducting phase. (B) DOS and band structure of the monolayer

MoS2 isolated by field effect carrier accumulation. The shaded area in the DOS

corresponds to the carrier density range spanned by the superconducting phase resulting

from the electrostatic doping.

14

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