The electronic structure of the lightly hole-doped triangular-lattice moiré Hubbard model is studied within cluster perturbation theory (CPT) using 13-site clusters for a fixed doping concentration $p=1/13$ varying the Coulomb parameter $U$ and the hopping phase parameter $\varphi$ related to the spin-orbital interaction. We have also developed a rather simple generalized mean-field approximation (GMFA) containing the amplitude of the spin correlations as a free parameter to fit the CPT data. The evolution of the Fermi surface and the pseudogap with the parameters $\varphi$ and $U$ is explained from the viewpoint of the short-range magnetic order. The geometric frustration and the additional model parameter related to the spin-orbital interaction result in a more rich physics of the pseudogap state compared to the case of a more conventional square lattice.

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• Electronic structure
• Fermi surface
• Spin-orbit coupling
• Strongly correlated systems
• Transition metal dichalcogenides
• Triangular lattice
• Cluster methods
• Hubbard model
• Mean field theory