Anomalous enhancement of large-momentum scattering by electron-electron interaction in moiré superlattices

Using a microscopic model, we show that the electron-electron interaction of flat bands deviates significantly from the Coulomb interaction. In particular, we find that large-momentum scattering is enhanced at $\theta \lesssim 4^{\circ }$, with a non-monotonic 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 to the el-el interaction. 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 interaction. The results highlight unusual features of the interaction in moiré graphene.