Visualizing the Local Twist Angle Variation within and between Domains of Twisted Bilayer Graphene

Moire superlattices in twisted two-dimensional materials have emerged as ideal platforms for engineering quantum phenomena, which are highly sensitive to twist angles, including both the global value and the spatial inhomogeneity. However, only a few methods provide spatial-resolved information for characterizing local twist angle distribution. Here we directly visualize the variations of local twist angles and angle-dependent evolutions of the quantum states in twisted bilayer graphene by scanning microwave impedance microscopy (sMIM). Spatially resolved sMIM measurements reveal a pronounced alteration in the local twist angle, approximately 0.3 degrees over several micrometers in some cases. The variation occurs not only when crossing domain boundaries but also occasionally within individual domains. Additionally, the full-filling density of the flat band experiences a change of over 2 x 1011 cm-2 when crossing domain boundaries, aligning consistently with the twist angle inhomogeneity. Moreover, the correlated Chern insulators undergo variations in accordance with the twist angle, gradually weakening and eventually disappearing as the deviation from the magic angle increases. Our findings signify the crucial role of twist angles in shaping the distribution and existence of quantum states, establishing a foundational cornerstone for advancing the study of twisted two-dimensional materials.