Quantum confinement and interference via Fabry-Pérot-like resonators in rhombohedral trilayer graphene on graphite

Rhombohedral trilayer graphene (rTG) has recently emerged as a new playground for exploring flatband-induced exotic quantum phenomena and sparked considerable concern. However, the experimental accessing of local quantum behaviors such as the quantum confinement of flatband electrons in rTG has been highly limited so far. Here, using scanning tunneling microscopy and spectroscopy, we study the quantum confinement and interference of quasiparticles in rTG via Fabry-P\'erot-like resonators. The resonators are formed by narrow rTG terraces with different geometries. In a narrow rectangular terrace (\ensuremath{\sim}50-nm width) made by two parallel step edges, we observe quantum confined states, which can be accurately replicated by the Fabry-P\'erot model. These confined states are highly governed by the transmission and scattering from the electronic states of adjacent graphene layers, leading to significant broadening and suppression of the flatband peak in rTG. The effective length of the flatband suppression is determined to be \ensuremath{\sim}15--30 nm for different step edges. Furthermore, we reveal the quasiparticle interference around two intersecting step edges, whose features can be well simulated by a developed Fabry-P\'erot model. These findings not only uncover the fundamental properties of quasiparticle interference in confined rTG systems, but also provide important insight into the interactions between the flatband electrons of rTG and their surrounding environments.