Inhomogeneous and nonlocal optical response in magic-angle twisted trilayer graphene

The response of traditional two-dimensional (2D) materials to electromagnetic fields is typically homogeneous and local, as the wavelength of the electromagnetic field is much longer than the lattice constant of 2D materials. In contrast, plasmons in moir\'e flatband systems enable the coupling of electromagnetic fields and electrons at extremely small length scales. In this paper, we demonstrate that the plasmons in magic-angle twisted trilayer graphene (TTG) exhibit significant inhomogeneity and nonlocality, along with violation of in-plane wave-vector conservation. The exceptional optical scenarios arising from inhomogeneous response can be characterized by the 2D distribution patterns of the plasmonic electric fields. Our findings provide additional means for detecting the electronic states of materials by near-field optical experiments, as well as an innovative approach for advancing the development of optoelectronic devices.