Anomalous enhancement of large-momentum scattering by electron-electron interaction in moir\'e superlattices

TL;DR

This paper reveals that electron-electron interactions in moiré superlattices exhibit anomalous large-momentum scattering enhancements near certain twist angles, with nontrivial modifications indicating complex interaction effects beyond simple models.

Contribution

The study introduces a microscopic model showing significant deviations from Coulomb interactions, highlighting non-monotonic and angle-dependent large-momentum scattering in moiré graphene.

Findings

Large-momentum scattering is enhanced near θ ≲ 4°

Non-monotonic momentum dependence appears near the magic angle

Interaction modifications differ from simple Wannier orbital explanations

Abstract

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 $\theta\lesssim4^\circ$, 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 $\theta\lesssim1.2^\circ$, 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 moir\'e graphene.