Observation of topological superconductivity in a stoichiometric transition metal dichalcogenide 2M-WS2

Topological superconductors (TSCs) are unconventional superconductors with bulk superconducting gap and in-gap Majorana states on the boundary that may be used as topological qubits for quantum computation. Despite their importance in both fundamental research and applications, natural TSCs are very rare. Here, combining state of the art synchrotron and laser-based angle-resolved photoemission spectroscopy, we investigated a stoichiometric transition metal dichalcogenide (TMD), 2M-WS2 with a superconducting transition temperature of 8.8 K (the highest among all TMDs in the natural form up to date) and observed distinctive topological surface states (TSSs). Furthermore, in the superconducting state, we found that the TSSs acquired a nodeless superconducting gap with similar magnitude as that of the bulk states. These discoveries not only evidence 2M-WS2 as an intrinsic TSC without the need of sensitive composition tuning or sophisticated heterostructures fabrication, but also provide an ideal platform for device applications thanks to its van der Waals layered structure.


Supplementary Note 3: Ab initio calculation on the charge density from the topmost Satom layer
Ab initio calculation on the charge density distribution in the bilayer 2M-WS2 is detailed in Supplementary Fig. 3. The energy range is selected to be 300~350 meV above the Fermi level, which corresponds to the bias voltage of +340 mV applied in the STM measurement. The side view of the charge density ( Supplementary Fig. 3b) can be easily matched with the crystal structure in Supplementary Fig. 3a. The charge distribution on the topmost S atom layer ( Supplementary Fig. 3c) and middle W atom layer ( Supplementary Fig. 3d) is extracted. As illustrated in Fig. 1e in the main text, the STM topography shows a consistent pattern with the charge density distribution on the topmost S atom layer, which indicates a defect-free S-termination.

Supplementary Note 5: dependence of the bulk electronic states
During the photoemission process, the in-plane momentum ( ∥ ) of electrons in the sample is obtained directly from the photoelectrons' inplane momentum component due to the momentum conservation.
However, the out of plane momentum perpendicular to the crystal surface ( ) is not conserved due to the surface electric field. Under the free-electron final state approximation and use a potential parameter 0 (also known as the inner potential), we can derive the as: where is the emission angle, is the effective electron mass and is the kinetic energy of the photoelectron, which satisfies: where ℎ is the photon energy, is the work function and is the electron binding energy.
As 0 is a material-dependent parameter, we typically perform photon energy dependent ARPES measurement to cover enough range (ideally more than one Brillouin zone). By comparison with corresponding calculation, we can estimate the value of the ARPES spectrum under specific photon

Dirac point
Since the surface Dirac point is slightly above the Fermi level ( − ≈ 10 ), we managed to access the upper Dirac cone via surface potassium doping, as shown in Supplementary Figs. 4b and 4e.
Although the spectra are broadened due to the surface disorders introduced by this process, the surface and bulk bands near the surface Dirac point can be resolved by careful analysis of the momentum distribution curves (MDCs), as shown in Supplementary Fig. 6.

Supplementary Note 7: Extraction of the superconducting gap by the spectral function
Superconducting gap magnitude was quantitatively determined by the spectral function at kF  and  are the real and imaginary part of the self energy , which has the form 4 : Here  is a single-particle scattering rate (here we assume it as energy-independent for simplicity). The second term is the BCS self-energy (corresponding to the diagonal term of the Nambu-Gorkov propagator), where  is the superconducting gap and gamma is a small real positive quantity to avoid the divergence when E = 0.
For the EDCs extracted at the Fermi momentum kF, the spectral intensity can be described as the ARPES Supplementary Fig. 7a presents the temperature evolution of the deconvoluted ARPES EDCs, which are obtained by Ideconv = deconvlucy (I, R). R is the energy resolution function -Gaussian function (normal distribution) with standard deviation  = 0.9 meV, extracted from the Au spectra (see Supplementary Fig. 7b). The deconvlucy algorithm is based on maximizing the likelihood that the deconvoluted data Ideconv is an instance of the original data I under Poisson statistics. The deconvolution is performed using the built-in function deconvlucy in MATLAB. The fitted temperature-dependent superconducting gap  exhibits a rapid decrease to zero whereas the scattering rate  shows significant