## A monolayer of many talents

Superconductors with a topologically nontrivial band structure have been predicted to exhibit exotic properties. However, such materials are few and far between. Now, two groups show that the monolayer of the material tungsten ditelluride (WTe_{2})—already known to be a two-dimensional topological insulator—can also go superconducting. Fatemi *et al.* and Sajadi *et al.* varied the carrier density in the monolayer by applying a gate voltage and observed a transition from a topological to a superconducting phase. The findings may lead to the fabrication of devices in which local gating enables topological and superconducting phases to exist in the same material.

## Abstract

The layered semimetal tungsten ditelluride (WTe_{2}) has recently been found to be a two-dimensional topological insulator (2D TI) when thinned down to a single monolayer, with conducting helical edge channels. We found that intrinsic superconductivity can be induced in this monolayer 2D TI by mild electrostatic doping at temperatures below 1 kelvin. The 2D TI–superconductor transition can be driven by applying a small gate voltage. This discovery offers possibilities for gate-controlled devices combining superconductivity and nontrivial topological properties, and could provide a basis for quantum information schemes based on topological protection.

Many of the most important phenomena in condensed matter emerge from the quantum mechanics of electrons in a lattice. The periodic potential of the lattice gives rise to Bloch energy bands of independent fermions; on the more exotic side, electrons in a lattice can pair up into bosons and condense into a superconducting macroscopic quantum state, which conducts electricity with zero resistance. Relatively recently, it was realized that Bloch wave functions can have a nontrivial topology, leading to the discovery of topological insulators—materials that are electrically insulating in their interior but have conducting boundary modes (*1*). The first of these to be studied was the so-called 2D topological insulator (2D TI), in which 1D helical edge modes (spin locked to momentum) give rise to the quantum spin Hall effect (*2*–*4*).

Materials that combine nontrivial topology with superconductivity have been the subject of active investigation in recent years (*5*–*7*). Here, we report that monolayer WTe_{2}, recently shown (*8*–*13*) to be an intrinsic 2D TI, turns superconducting under moderate electrostatic gating. Several other nontopological layered materials superconduct in the monolayer limit, either intrinsically or under heavy doping using ionic liquid gates (*14*–*22*). In monolayer WTe_{2}, however, the phase transition to a superconducting state is from a 2D topological insulator, and it occurs at such a low carrier density that it can be readily induced by a simple electrostatic gate. The discovery may lead to gateable superconducting circuitry and may enable the development of topological superconducting devices in a single material, as opposed to the hybrid constructions currently required (*5*).

We present data from two monolayer WTe_{2} devices, M1 and M2, with consistent superconducting characteristics. Each contains a monolayer flake of WTe_{2} encapsulated along with thin platinum electrical contacts between hexagonal boron nitride (hBN) dielectric layers. Figure 1A shows an image of M1, which has seven contacts along one edge, together with a side view and a schematic showing the configuration used to measure the linear four-probe resistance, *R _{xx}* =

*dV/dI*. Top and bottom gates—at voltages

*V*

_{t}and

*V*

_{b}and with areal capacitances

*c*

_{t}and

*c*

_{b}, respectively—can be used to induce negative or positive charge in the monolayer WTe

_{2}, producing an areal doping density given by

*n*= (

_{e}*c*

_{t}

*V*

_{t}+

*c*

_{b}

*V*

_{b})/

*e*, where

*e*is the electron charge. Note that we do not interpret this as a carrier density because the insulating state may be of correlated nature (as in, for example, an excitonic insulator); in addition, Hall density measurements are challenging because of the 2D TI edge conduction. See (

*23*) for details about gating, contact resistances, and capacitances.

Figure 1B illustrates the electrostatic tuning of M1 from p-doped conducting behavior at negative gate voltage, through an insulating state, to an n-doped highly conducting state at positive gate voltage. M1 is the same device whose insulating state was investigated in (*9*) and was demonstrated to be a 2D TI (*9*, *13*); at *n _{e}* = 0,

*R*is more than 10

_{xx}^{7}ohms, owing to a meV-scale gap that blocks edge conduction below 1 K [see below and (

*23*)]. For

*n*above

_{e}*n*

_{crit}≈ +5 × 10

^{12}cm

^{–2}, however, the resistance drops drastically when the sample is cooled, reaching the noise floor of the experiment (~0.3 ohms) for

*n*> +7 × 10

_{e}^{12}cm

^{–2}at 20 mK, indicating the appearance of superconductivity. Figure 1C is a phase diagram constructed from these and similar measurements discussed below. The emergence of a superconducting phase in direct proximity to a 2D TI phase, and at a doping level achievable with a single electrostatic gate, is the primary result of our work.

The transition from an insulating to a metallic/superconducting *T* dependence—the crossing of *R _{xx}* lines in Fig. 1B—occurs at 2.4 kilohms. This corresponds to a square resistivity ρ ≈ 20 kilohms, with a substantial uncertainty because the precise distribution of current in the device is not known (

*23*). The evolution of the

*T*dependence with

*n*is illustrated in Fig. 2A. For all densities shown, the collapse of

_{e}*R*with temperature is gradual, as expected for materials where the normal-state 2D conductivity is not much greater than

_{xx}*e*

^{2}/

*h*(where

*h*is the Planck constant). We define a characteristic temperature,

*T*

_{1/2}, at which

*R*falls to half of its 1 K value. Although this specific definition is somewhat arbitrary, it is typical in the literature (

_{xx}*15*,

*21*,

*22*) and does not affect any of our conclusions (

*23*). Measured values of

*T*

_{1/2}are shown as red dots on the phase diagram in Fig. 1C to indicate the boundary of superconducting behavior.

The superconductivity is suppressed by a perpendicular (*B*_{⊥}) or in-plane (*B*_{||}) magnetic field (Fig. 2, B and C). For a perpendicular field, orbital effects are expected to dominate (*24*–*26*). The dependence of *T*_{1/2} on *B*_{⊥} (Fig. 2B, inset) in the low-field limit is consistent with the linear expected from Ginzburg-Landau theory. The characteristic perpendicular field in the low-temperature limit, based on the measurements in Fig. 2B (inset), is , where is the magnetic field where *R _{xx}* falls to half its normal-state resistance. Estimates for the superconducting coherence length can be obtained either from the slope of near

*T*

_{1/2}or from , yielding ξ

_{meas}= 100 ± 30 nm in both cases (

*23*).

The fact that ξ_{meas} is much larger than the estimated mean free path ≈ 8 nm suggests that the system is in the dirty limit (λ << ξ). To calculate λ, we use spin and valley degeneracies *g*_{s} = *g*_{v} = 2, as well as density and normal-state resistivity reflecting the conditions for Fig. 2B: *n _{e}* = 20 × 10

^{12}cm

^{–2}and ρ ≈ 2 kilohms, respectively. The coherence length expected in the dirty limit is , for zero-temperature gap Δ

_{0}= 1.76

*k*

_{B}

*T*

_{c}and diffusion constant

*D*, where

*ħ*is the reduced Planck constant and

*k*

_{B}is the Boltzmann constant. Indeed, if we use

*T*

_{1/2}= 700 mK for

*T*

_{c}, and if

*D*= 2π

*ħ*

^{2}/

*g*

_{s}

*g*

_{v}

*m**

*e*

^{2}ρ ≈ 12 cm

^{2}s

^{–1}(from the Einstein relation) with effective mass

*m** = 0.3

*m*[where

_{e}*m*is the electron mass (

_{e}*27*)], the result is ξ ≈ 90 nm, consistent with ξ

_{meas}.

For the in-plane magnetic field, the atomic thinness of the monolayer makes orbital effects small. In the absence of spin scattering, superconductivity is then suppressed when the energy associated with Pauli paramagnetism in the normal state overcomes the superconducting condensation energy. This is referred to as the Pauli (Chandrasekar-Clogston) limit (*28*) and gives a critical field *B*_{P} = 1.76*k*_{B}*T*_{c}/*g*^{1/2}μ_{B}, where μ_{B} is the Bohr magneton. Assuming an electron g-factor of *g* = 2 and taking *T*_{c} = 700 mK gives *B*_{P} ≈ 1.3 T. However, the data in Fig. 2, C and F, indicate superconductivity persisting to .

Similar examples of exceeding *B*_{P} have recently been reported in other monolayer dichalcogenides, MoS_{2} and NbSe_{2}, but the Ising superconductivity mechanism (*15*, *21*) invoked in those works cannot explain an enhancement of here because WTe_{2} lacks the required in-plane mirror symmetry. One possible explanation in this case is a high spin-orbit scattering rate . Fitting the predicted form for *T*_{c} in a parallel field (*29*) to the data in the inset of Fig. 2C gives (*23*). Another possibility is that the Pauli limit is not actually exceeded but that the effective g-factor in WTe_{2} is smaller than 2 owing to the strong spin-orbit coupling.

The data in Fig. 2 display several other features worthy of mention. First, at intermediate magnetic fields, the resistance approaches a *T*-independent level as *T* → 0 that is orders of magnitude below the normal-state resistance. The data from Fig. 2B are replotted versus 1/*T* in Fig. 2D to highlight the behavior below 100 mK. Similar behavior is seen at *B* = 0 (Fig. 2A) for intermediate *n _{e}*, adding to the growing body of evidence that this is a robust phenomenon occurring in thin films close to superconductivity (

*30*). Second, even at the lowest temperature,

*R*rises smoothly from zero as a function of

_{xx}*B*

_{⊥}(Fig. 2E), whereas the onset of measurable resistance as a function of

*B*

_{||}is relatively sudden, occurring above 2 T (Fig. 2F). Third, an intermediate plateau is visible in the

*R*–

_{xx}*T*data at

*B*= 0 over a wide range of

*n*(Fig. 2A). It is extremely sensitive to

_{e}*B*

_{⊥}, almost disappearing at only 2 mT (Fig. 2B), whereas it survives in

*B*

_{||}to above 2 T (Fig. 2C and inset of Fig. 2F). A similar feature has been reported in some other quasi-2D superconductors (

*31*–

*33*), but its nature, and the role of disorder, remain unresolved.

The high tunability of this 2D superconducting system invites comparison with theoretical predictions for critical behavior close to a quantum phase transition. Figure 3 shows how *R _{xx}* depends on doping at a series of temperatures, along the dashed lines in the phase diagram (upper inset). The

*T*dependence changes sign at

*n*

_{crit}≈ 5 × 10

^{12}cm

^{–2}. In the lower inset, we show an attempt to collapse the data onto a single function of |1 –

*n*/

_{e}*n*

_{crit}|

*T*

^{–α}. The procedure is somewhat hindered by the fluctuations, which can be seen to be largely reproducible. The best-fit critical exponent α = 0.8 is similar to that reported for some insulator-superconductor transitions in thin films (

*34*), although we note that the anomalous behavior near

*n*

_{crit}mentioned above is not consistent with such a scaling.

Superconductivity induced by simple electrostatic gating in a monolayer of material that is not normally superconducting is intriguing, but perhaps even more interesting is that the ungated state is a 2D TI. This prompts the question of whether the helical edge channels remain when the superconductivity appears, and if so, how strongly they couple to it. In principle, *R _{xx}* includes contributions from edges as well as bulk. However, because in device M1 the edge conduction freezes out below 1 K, in order to investigate the combination of edge channels and superconductivity we turn to another device, M2, in which edge conduction persists to lower temperatures (

*23*).

Figure 4 shows measurements of the conductance *G* between adjacent contacts in M2 as a function of gate doping. The figure includes schematics indicating the inferred state of the edge (red for conducting), as well as the bulk state (colored to match the phase diagram). Consider first the black trace, taken at 200 mK and *B*_{⊥} = 0. At low *n _{e}*, the bulk is insulating and edge conduction dominates, albeit with large mesoscopic fluctuations. For

*n*> 2 × 10

_{e}^{12}cm

^{–2},

*G*increases as bulk conduction begins; then, once

*n*exceeds

_{e}*n*

_{crit}, it increases faster as superconductivity appears, before leveling out at ~200 μS as a result of contact resistance. This interpretation is supported by warming to 1 K (red dotted trace), which destroys the superconductivity and so reduces

*G*for

*n*>

_{e}*n*

_{crit}, but enhances the edge conduction at low

*n*toward the ideal value of

_{e}*e*

^{2}/

*h*= 39 μS. (We note that this

*T*dependence of the edge is associated with a gap of ~100 μeV, visible in the inset map of differential conductance versus bias and doping.) A perpendicular field

*B*

_{⊥}of 50 mT (green trace) also destroys the superconductivity, causing the conductance to fall for

*n*>

_{e}*n*

_{crit}but barely affecting it at lower

*n*. High magnetic fields have been shown (

_{e}*9*) to suppress edge conduction in the 2D TI state by breaking time-reversal symmetry. This effect can be clearly seen in the

*B*

_{⊥}= 1 T data (orange trace in Fig. 4) as

*G*falls to zero at low

*n*. Comparison of the green (

_{e}*B*

_{⊥}= 0.05 T) and orange (

*B*

_{⊥}= 1T) traces shows that

*G*falls by a similar amount at higher

*n*, consistent with a scenario in which the edge conduction supplies a parallel contribution; this implies that helical edge states persist when

_{e}*n*>

_{e}*n*

_{crit}and at temperatures below

*T*

_{c}.

This discovery raises compelling questions for future investigation. It is likely that the helical edge modes persist when the superconductivity is restored by reducing the magnetic field to zero. Other techniques, such as scanning probe microscopy, may be needed to probe the edges separately from the bulk. The measurements presented here cannot determine the degree or nature of the coupling between superconductivity and edge conduction. One key question is whether the edge states also develop a superconducting gap, in which case they could host Majorana zero modes (*5*).

Another question concerns the nature of the superconducting order. It is striking that *n*_{crit} corresponds to only ~0.5% of an electron per W atom, which is about an order of magnitude lower than the doping level needed to observe superconductivity in other transition metal dichalcogenide monolayers (*18*). Many-layer WTe_{2} is semimetallic (*35*–*38*) under ambient conditions, with near-perfect compensation of electrons and holes, but becomes superconducting as the ratio of electrons to holes increases at high pressure (*39*). Some related materials, such as TiSe_{2}, are known to switch from charge-density-wave to superconducting states at quite low doping (*40*) or under pressure (*41*). We therefore speculate that doping tips the balance in monolayer WTe_{2} in favor of superconductivity, away from a competing insulating electronic ordering. Finally, given the topological band structure and likely strong correlations in this material, it is possible that the pairing is unconventional and perhaps topologically nontrivial.

## Supplementary Materials

www.sciencemag.org/content/362/6417/922/suppl/DC1

Materials and Methods

Supplementary Text

Figs. S1 to S10

Table S1

This is an article distributed under the terms of the Science Journals Default License.

## References and Notes

**Acknowledgments:**We thank O. Agam, A. Andreev, and B. Spivak for discussions, and J. Yan for the WTe

_{2}crystals.

**Funding:**T.P., Y.F., W.Z., X.X., and D.H.C. were supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, awards DE-SC0002197 (D.H.C.) and DE-SC0018171 (X.X.); AFOSR FA9550-14-1-0277; NSF EFRI 2DARE 1433496; and NSF MRSEC 1719797. E.S., P.B., C.O., S.L., and J.A.F. were supported by the Canada Foundation for Innovation, the National Science and Engineering Research Council, CIFAR, and SBQMI.

**Author contributions:**T.P., X.X., and D.H.C. conceived of the original experiment; T.P., Z.F., and W.Z. fabricated the devices; E.S., Z.F., P.B., and C.O. carried out the measurements under the primary supervision of J.A.F. and D.H.C. in a cryostat developed by E.S., S.L., and J.A.F.; all authors contributed to the analysis of the data; E.S., J.A.F., and D.H.C. wrote the manuscript; all authors contributed to the final editing of the manuscript.

**Competing interests:**The authors declare no competing interests.

**Data and materials availability:**The data shown in the paper are available at https://github.com/EbrahimSajadi/2D_SC_TI.