Recently, twisted moiré systems have attracted intense attention, where the emergence of the moiré potential is experimentally observed as an effective way to regulate the electron and exploit novel properties. Various theoretical models have been proposed and attributed the moiré potential as a result from interlayer electrical polarization or atomic relaxation effects. To date, the moiré potential is not yet directly calculated via an exact first-principles method and the universal mechanism in different systems is still unclear. Here, we obtain and analyze the surface superlattice potential by directly using first-principles calculations. We demonstrate that the moiré potential is a widely existing phenomenon in twisted systems with or without interlayer electrical polarization and is generally determined by the local work function. Specifically, the surface moiré potential is positively proportional to the local work function in single-atom-thick materials and negatively in multi-atom-thick ones due to a compensation effect. Interestingly, the surface potential amplitude of an unpolarized phosphorene system ($\sim 430$ meV) is much larger than that of the polarized $h$-BN system ($\sim 170$ meV). Our work directly reveals the universal moiré potential via fully first-principles calculations and provides a different angle in the study of moiré systems and twistronics.

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• Electronic structure
• First-principles calculations
• Structural properties
• 2-dimensional systems
• Interfaces
• Layered crystals
• Phosphorene
• Surfaces
• Transition metal dichalcogenides
• Twisted heterostructures
• Two-dimensional electron system