Enhanced superconductivity in atomically thin TaS2

The ability to exfoliate layered materials down to the single layer limit has presented the opportunity to understand how a gradual reduction in dimensionality affects the properties of bulk materials. Here we use this top–down approach to address the problem of superconductivity in the two-dimensional limit. The transport properties of electronic devices based on 2H tantalum disulfide flakes of different thicknesses are presented. We observe that superconductivity persists down to the thinnest layer investigated (3.5 nm), and interestingly, we find a pronounced enhancement in the critical temperature from 0.5 to 2.2 K as the layers are thinned down. In addition, we propose a tight-binding model, which allows us to attribute this phenomenon to an enhancement of the effective electron–phonon coupling constant. This work provides evidence that reducing the dimensionality can strengthen superconductivity as opposed to the weakening effect that has been reported in other 2D materials so far.

The RRR is calculated as the ratio between the room temperature (297 K) resistance and the low temperature resistance at 4 K (RRR = R(297K)/R(4K)). High RRR values (~10) are still maintained below the bulk limit thickness of 10 nm indicating pristine flakes and absence of strong substrate interaction.  7 We found a significant agreement between the measured optical contrast for thin flakes and that obtained from the model using the refractive index of bulk TaS 2 . It is remarkable that the optical contrast is strongly dependent on the illumination wavelength and even changes its sign for flakes thinner than 20 nm. This behaviour makes white light illumination inappropriate for the identification of the thinnest flakes by optical microscopy. Oppositely, illumination under certain wavelengths enhances the optical contrast of the thinnest TaS 2 crystals, which allowed the optical identification of layers as thin as 1.2 nm.

Supplementary Note 2: Raman spectroscopy of 2H-TaS 2 .
The potential relationship between the flake thickness and the Raman scattering intensity was explored. For this reason a µ-Raman probe was used to explore different thickness flakes.
Supplementary Figure 4 shows the thickness dependence of a selection of Raman features.
Whereas the frequency shift and the full-width-at-half-maximum (FWHM) of the A 1g and E 2g Raman modes do not seem to be at all related to the number of layers, it may be clearly appreciated how the ratio between the intensity of the Si peak (at 521 cm -1 ) and the A 1g and E 2g peaks both increase upon decreasing the number of layers of the probed flake. The frequency difference between the A 1g and E 2g Raman modes also exhibit a linear proportionality with the number of layers present in the flakes. It is important to highlight that as for other TMDCs, some sensitivity to the Raman laser beam was also exhibited by the TaS 2 flakes. In this way, upon performing experiments with long exposure times or high irradiation powers, the flakes were irreversibly damaged as seen by a change in the optical contrast in the focus spot of the laser beam. Yet, no apparent change in the height profile as measured by AFM could be detected. By contrast, the appearance of a strong photoluminescence emission band around 555 nm suggested that some oxidation to Ta 2 O 5 had occurred. 8 On a final note, it has been previously observed in other transition metal dichalcogenides how the intensity of the distinct Raman modes may vary as the angle between the linearly polarized incident beam and the scattered signal is modified. 9 This can be used to confirm the origin of the Raman peaks. In the TaS 2 case, it could be observed that while the intensity of the E 2g mode does not depend on the angle between the excitation and detection, the A 1g mode presents its maximum intensity for parallel excitation and detection and it vanishes for cross polarized excitation and detection in agreement with that reported for other TMDC flakes, 10 confirming that the Raman signal comes from an analogous crystal (see Supplementary Figure 5).

Supplementary Note 3. Berezinskii-Kosterlitz-Thouless (BKT) fits to selected devices.
I-V curves were fit to a power law of the form V α I -α , where α spans from 1 for temperatures above T BKT , reaching a value of α = 3 at the BKT transition, and monotonically increasing as

Supplementary Note 4. Charge density wave (CDW) considerations in 2H-TaS 2 .
The experimentally observed charge density wave in 2H-TaS 2 has a periodicity of 3 x 3 unit cell in the layer plane. We consider an effective one-orbital tight-binding model and simulate the CDW at mean field level as an onsite potential that locally shift the onsite energy.
The effect of the CDW is seen in the DOS at an energy of 0. where we have defined the following integrals, tanh /2 tanh /2 with /2 0 . As we have seen by the DFT simulations and the tight-binding model, the total DOS normalized by the number of layer is featureless close to the Fermi level, so that the integral is performed in the usual way and it gives ln 1.14 / .
At the same time, the DOS displays van Hove singularities at higher energies, that become more and more pronounced as we lower the number of layers. In the limit / ≪ 1, the integral can be approximated as