Mapping the twist-angle disorder and unconventional Landau levels in magic angle graphene

The emergence of flat electronic bands and of the strongly correlated and superconducting phases in twisted bilayer graphene crucially depends on the interlayer twist angle upon approaching the magic angle 1.1°. Although advanced fabrication methods allow alignment of graphene layers with global twist angle control of about 0.1°, little information is currently available on the distribution of the local twist angles in actual magic angle graphene (MAG) transport devices. Here we map the local variations in hBN encapsulated devices with relative precision better than 0.002° and spatial resolution of a few moiré periods. Utilizing a scanning nanoSQUID-on-tip, we attain tomographic imaging of the Landau levels in the quantum Hall state in MAG, which provides a highly sensitive probe of the charge disorder and of the local band structure determined by the local [1]. We find a correlation between the degree of twist angle disorder and the quality of the MAG transport characteristics. However, even state-of-the-art transport devices, exhibiting pronounced global MAG features, such as multiple correlated insulator states, high-quality Landau fan diagrams, and superconductivity, display significant variations in the local with a span that can be close to 0.1°. Devices may even have substantial areas where no local MAG behavior is detected, yet still display global MAG characteristics in transport. The derived maps reveal substantial gradients and a network of jumps. We show that the twist angle gradients generate large unscreened electric fields that drastically change the quantum Hall state by forming edge states in the bulk of the sample, and may also significantly affect the phase diagram of correlated and superconducting states. The findings call for exploration of band structure engineering utilizing twist-angle gradients and gate-tunable built-in planar electric fields for novel correlated phenomena and applications.
[1] A. Uri et al., arXiv:1908.04595