Onset of two-dimensional superconductivity in space charge doped few-layer molybdenum disulfide

Atomically thin films of layered materials such as molybdenum disulfide (MoS2) are of growing interest for the study of phase transitions in two-dimensions through electrostatic doping. Electrostatic doping techniques giving access to high carrier densities are needed to achieve such phase transitions. Here we develop a method of electrostatic doping which allows us to reach a maximum n-doping density of 4 × 1014 cm−2 in few-layer MoS2 on glass substrates. With increasing carrier density we first induce an insulator to metal transition and subsequently an incomplete metal to superconductor transition in MoS2 with critical temperature ≈10 K. Contrary to earlier reports, after the onset of superconductivity, the superconducting transition temperature does not depend on the carrier density. Our doping method and the results we obtain in MoS2 for samples as thin as bilayers indicates the potential of this approach.

Supplementary Figure 1: Raman spectroscopy. a, Raman spectra of the three samples before measurement. Inset : zoom on the E 1 2g and A1g lines. An offset was added for clarity. b, c, d, Raman spectra of each sample before and after doping and transport measurements.  Raman spectra in these few-layer samples. Degradation through ambient pollution is clearly seen in Raman spectra of 2D samples of III-VI layered semi-conductors for example [1].The question is if crystalline quality alteration through defects would be seen. Even though there is no dedicated defect mode, Raman lines in MoS 2 are altered by the presence of defects through an increase in linewidths as in most other materials [2]. We see strictly no such change in our samples.
The energy difference between the two Raman active modes E 1 2g and A 1g varies monotonically with the number of layers and has been proposed as a measure of MoS 2 thickness for very thin samples [3][4][5]. This energy difference for the 2 nm sample is compatible with bilayer samples reported in literature.

Supplementary Note 2. Variable range hopping in the insulating regime
As shown in the paper, space charge doping gives access to an extended range of carrier density and to explore both sides of the metal-insulator transition. On the insulating side of the transition (i.e. at low carrier density), the resistivity of the sample increases dramatically at low temperature, and may become non-Ohmic. This insulating behaviour can be analysed to get informations about properties like dimensionality or the conduction mechanism.
At a carrier density of 4.5 × 10 12 cm −2 the 4.5 nm sample displayed insulating behaviour reaching 270 kΩ. −1 (measured with a current of 1 µA) at 4 K. The temperature behaviour is well described by variable range hopping (VRH) as shown in Supplementary Figure 2. As the name implies, VRH describes conductivity in insulating samples mediated by thermal or electric field activation of carrier hopping between localized states near the Fermi level. VRH manifests itself in the conductivity at low electric fields as a function of temperature in the form: where p is either 1/(D + 1) in a D dimensional system with negligible Coulomb interaction between charged localized states (Mott-VRH [6]) or 1/2 in all dimensions in systems with substantial Coulomb gap (Efros Shklovskii-VRH [7]).
As shown in Supplementary Figure 2  At high electric field and low temperature, the field activation of conductivity becomes dominant over thermal activation, thus the current density becomes temperature independent and behaves as: with the same p as above, and F being the electric field.
As shown in Supplementary Figure 3, the high electric field dependence of conductivity in the 2 nm sample display Mott-VRH with p = 3 characteristic of 2D transport.
As mentioned in the literature [8], it is difficult to distinguish between the possible exponents of VRH. A linear dependence of the conductivity with T −1/4 will also appear nearly linear with T −1/3 or T −1/2 . Accordingly we have shown here the results that present the most extended linear behaviour in temperature or electric field.