Strong evidence of unconventional superconductivity has been very recently reported experimentally in twisted transition metal dichalcogenide bilayer and gathered a significant amount of interest. Here we consider the Hubbard model on a triangular lattice describing the hole-doped moiré superlattice emerging in ${\mathrm{WSe}}_2/{\mathrm{WSe}}_2$ twisted homobilayer in the moderately correlated regime. By applying the density matrix renormalization group, we diagonalize the spin-valley-polarized Hamiltonian and show signatures of coexisting singlet and triplet pairings in the range of hole dopings and displacement fields reported in the experiments. In this view, we show that the superconductivity in the ${\mathrm{WSe}}_2/{\mathrm{WSe}}_2$ twisted homobilayer is likely to be induced by electronic correlations and has a mixed-symmetry character. These predictions can shed light on the nature of the superconducting state observed in the twisted homobilayer of ${\mathrm{WSe}}_2/{\mathrm{WSe}}_2$. We also identify the emerging superconducting orders, which are $d_{xy}(d_{x^2-y^2}\pm i{d}_{xy})$ and $p_y(p_x\mp i{p}_y)$ for the singlet and triplet channels in the cylinder of width three (four), respectively.

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• Spin-singlet pairing
• Spin-triplet pairing
• Superconductivity
• Strongly correlated systems
• Two-dimensional electron system
• Unconventional superconductors
• Density matrix renormalization group
• Hubbard model