Mapping the twist angle and unconventional Landau levels in magic angle graphene (1908.04595v1)

Abstract: The emergence of flat electronic bands and of the recently discovered strongly correlated and superconducting phases in twisted bilayer graphene crucially depends on the interlayer twist angle upon approaching the magic angle $\theta_M \approx 1.1\deg$. Although advanced fabrication methods allow alignment of graphene layers with global twist angle control of about 0.1$\deg$, little information is currently available on the distribution of the local twist angles in actual magic angle twisted bilayer graphene (MATBG) transport devices. Here we map the local $\theta$ variations in hBN encapsulated devices with relative precision better than 0.002$\deg$ and spatial resolution of a few moir$\'e$ periods. Utilizing a scanning nanoSQUID-on-tip, we attain tomographic imaging of the Landau levels in the quantum Hall state in MATBG, which provides a highly sensitive probe of the charge disorder and of the local band structure determined by the local $\theta$. We find that even state-of-the-art devices, exhibiting high-quality global MATBG features including superconductivity, display significant variations in the local $\theta$ with a span close to 0.1$\deg$. Devices may even have substantial areas where no local MATBG behavior is detected, yet still display global MATBG characteristics in transport, highlighting the importance of percolation physics. The derived $\theta$ 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.

• The paper demonstrates that advanced nanoSQUID imaging can map twist angle variations in MATBG with relative accuracies better than 0.002°.
• It shows that twist angle gradients generate unscreened electric fields (~0.4 kV/m) which significantly modify Landau levels and impact quantum Hall states.
• The findings pave the way for band structure engineering in graphene devices, offering novel insights into controlling superconductivity and correlated insulator states.

Magic Angle Graphene and Its Impact on Landau Levels and Correlated Phenomena

The investigation presented in "Mapping the twist angle and unconventional Landau levels in magic angle graphene" provides crucial insights into the role of twist angles in magic angle twisted bilayer graphene (MATBG) and their impact on the material's electronic properties. By employing advanced imaging techniques, the researchers achieve unparalleled precision in mapping local variations of twist angles, consequently connecting these with the transport properties and quantum phases exhibited by MATBG.

Overview of Findings

The paper primarily focuses on resolving the local twist angle variations in MATBG devices encapsulated within hexagonal boron nitride (hBN), achieving high spatial resolution and precision. This is executed using a scanning nanoSQUID-on-tip, an innovative technique that facilitates tomographic imaging of Landau levels in the quantum Hall (QH) state. The paper discovers significant local variations in the twist angle that can span up to 0.1°, affecting the transport characteristics of MATBG devices even when global MATBG features remain evident.

The local variations and structure of the Landau levels, which are crucial in the formation of unconventional QH states, reveal that twist angle gradients generate substantial unscreened electric fields. These fields can drastically alter the QH state, a finding that illuminates how such gradients can form edge states within the bulk of the sample. Additionally, the paper links the twist angle disorder to observed variations in correlated insulator states and superconductivity, emphasizing the material's sensitivity to local variations in structure.

Significant Numerical Results and Observations

The precision achieved in mapping the twist angle is noteworthy, with relative accuracies better than 0.002° and absolute accuracies of ±0.005°. Such fine measurements allow for a detailed understanding of the spatial inhomogeneities and their influence on the electronic properties of MATBG. The detection of narrow incompressible strips, approximately 50 nm wide, using the nanoSQUID-on-tip reflects the technique's capability to discern features critical to electronic behavior in MATBG.

The derived spatial maps of the twist angle exhibit significant gradients and a network of jumps, highlighting how electronic properties can be varied spatially with a high degree of control. The gradients not only modify the electronic band structure but also induce symmetry breaking, potentially leading to new electronic phases that were previously not considered. The unscreened electric fields generated by twist angle gradients, measured to be approximately 0.4 kV/m, have the potential to influence the phase diagram significantly, which could lead to novel correlated phenomena and device applications.

Implications and Future Directions

The findings in this paper underline the complexity and precision required to manipulate MATBG for practical applications. The exploration of band structure engineering, facilitated by twist angle gradients and tunable electric fields, presents a promising avenue for discovering new correlated phenomena and expanding the capabilities of quantum materials.

Practically, this work suggests pathways for the advancement of MATBG-based devices in electronics, particularly where control over electronic phases, such as superconductivity and correlated insulators, is pivotal. The intricate relationship between local twist angle variations and global transport properties underpins the necessity for careful material fabrication and experimentation.

Theoretically, the insights gained from this paper indicate that further exploration into heterostructures with controlled twist angle distributions could yield unexpected electronic behaviors, contributing to a broader understanding of correlated materials. Future research may focus on systematically investigating how various twist angle configurations affect the quantum phases in MATBG and other two-dimensional heterostructures.

Overall, the research provides a detailed examination of the interplay between twist angle variation and quantum phenomena in MATBG, setting the stage for future exploration and technological innovation in the domain of two-dimensional materials.