Fig. 2: Topological superconductivity in hetero-bilayer TMDs.

a The phase winding of the superconducting gap in the g + ig state can be visualized by a skyrmion configuration constructed from the vector \({{{\bf{m}}}}=({{{\rm{Re}}}}{{{\Delta }}}_{{{{\bf{k}}}}},{{{\rm{Im}}}}{{{\Delta }}}_{{{{\bf{k}}}}},{\xi }_{{{{\bf{k}}}}})/{({\xi }_{{{{\bf{k}}}}}^{2}+| {{{\Delta }}}_{{{{\bf{k}}}}}{| }^{2})}^{1/2}\). m points up (down) at the highest (lowest) energies ξ_k = ϵ_k − μ and rotates \({{{\mathcal{N}}}}\) times in the plane in the vicinity of the Fermi level ξ_k = 0. The skyrmion configuration is used to calculate the winding number \({{{\mathcal{N}}}}\), which for a broad range of fillings around Van Hove filling is \(| {{{\mathcal{N}}}}| =4\), indicating an enhanced response in thermal and spin quantum Hall measurements. b Functional RG data of the irreducible two-particle correlation function V(k₁, k₂, k₃, k₄) near the instability temperature for incoming wave vectors k₁, k₂. Wave vectors are labeled by the patch points along the Fermi surface indicated in Fig. 1c. The outgoing wave vector k₃ is fixed at patch no. 1 and k₄ = k₁ + k₂ − k₃ is given by momentum conservation. The sharp diagonal features occur at k₁ = − k₂, k₃ = − k₄, indicating the formation of long-ranged superconducting correlations. c Superconducting form factors g_±(k) extracted from V(k₁, k₂, k₃, k₄) in b. They exhibit a large overlap with a linear combination of the second-nearest-neighbor lattice harmonics g₁(k), g₂(k) (solid gray lines) defined in the text, which belong to the two-dimensional irreducible representation E₂ of the lattice symmetry group C_6v. We classify them as g-wave form factors due to their eight nodes. d Absolute value and phase of the gap function on the Fermi surface. The chiral superposition Δ_k = ∣Δ∣(g₁(k) ± ig₂(k)) fully gaps the Fermi surface, thereby minimizing the energy. Such a g + ig superconducting state breaks time-reversal symmetry and is topological with a four-fold phase winding along the Fermi surface \(| {{{\mathcal{N}}}}| =4\). e Stability of the g-wave superconduting state towards inclusion of J/U for V₁/U = 0.2 at μ = 5.3075 meV. For growing values of the exchange interaction J, the nearest-neighbor harmonics d₁ and d₂ of E₂ (defined in the text) start to contribute as indicated by the colored transition. They are pure d-wave form factors with only four nodes. For J/U ≲ 0.1, the contribution from d₁ and d₂ is negligible. f Example of the extracted form factors for J/U = 0.5 where d₁, d₂ and g₁, g₂ roughly contribute by equal amounts, showing the change in the number of nodes due to the admixture.