Using a microscopic model, we show that the large-momentum scattering of electrons in flat bands deviates significantly from that of the Coulomb scattering. In particular, we find that large-momentum scattering is enhanced at $\theta \lesssim 4^{\circ }$, with a nonmonotonic momentum dependence appearing near the magic angle. For $\theta \gtrsim 1.2^{\circ }$, the enhanced large-momentum scattering can be attributed to the compact Wannier function. On the other hand, for $\theta \lesssim 1.2^{\circ }$, the nonmonotonic momentum dependence of the interaction matrix cannot be explained by a simple Wannier orbital, indicating a nontrivial modification of the electron-electron scattering. Notably, the range of angles $\theta$ where the large-momentum scattering is enhanced differs from the magic angles at which nearly flat bands emerge, suggesting that the angle dependence of material properties provides information about the effect of the interaction. The results highlight unusual features of the interaction in moiré graphene.

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• Twistronics
• Twisted bilayer graphene
• Materials modeling
• Tight-binding model
• Wannier function methods