Spectroscopic visualization of flat bands in magic-angle twisted monolayer-bilayer graphene: localization-delocalization coexisting electronic states

Recent transport studies have demonstrated the great potential of twisted monolayer-bilayer graphene (tMBG) as a new platform to host moir\'e flat bands with a higher tunability than twisted bilayer graphene (tBG). However, a direct visualization of the flat bands in tMBG and its comparison with the ones in tBG remain unexplored. Here, via fabricating on a single sample with exactly the same twist angle of ~1.13{\deg}, we present a direct comparative study between tMBG and tBG using scanning tunneling microscopy/spectroscopy. We observe a sharp density of states peak near the Fermi energy in tunneling spectroscopy, confirming unambiguously the existence of flat electronic bands in tMBG. The bandwidth of this flat-band peak is found to be slightly narrower than that of the tBG, validating previous theoretical predictions. Remarkably, by measuring spatially resolved spectroscopy, combined with continuum model calculation, we show that the flat-band states in tMBG exhibit a unique layer-resolved localization-delocalization coexisting feature, which offers an unprecedented possibility to utilize their cooperation on exploring novel correlation phenomena. Our work provides important microscopic insight of flat-band states for better understanding the emergent physics in graphene moir\'e systems.