Magic Angle: Unlocking Extraordinary Properties in Twisted 2D Materials

What is the Magic Angle?

The magic angle refers to a specific angle of rotation between two stacked layers of two-dimensional (2D) materials, such as graphene, transition metal dichalcogenides (TMDs), and hexagonal boron nitride (hBN). When these layers are twisted relative to each other at the magic angle, the resulting twisted bilayer structures exhibit extraordinary electronic properties, including superconductivity, correlated insulating states, and flat electronic bands. The discovery of magic angle phenomena has opened up a new field of research called twistronics, which explores the electronic properties of twisted 2D materials.
Schematic representation of twisted bilayer graphene at the magic angle
Illustration of a moiré pattern that emerges upon stacking and rotating two sheets of bilayer graphene. Correlated electronic states with magnetic ordering emerge in twisted double bilayer graphene over a small range of twist angles, and can be tuned with gating and electric field. (Image: Matthew Yankowitz)

Moiré Superlattices in Twisted 2D Materials

When two layers of a 2D material are twisted at the magic angle, a moiré superlattice emerges due to the interference between the two lattices. The moiré superlattice has a much larger periodicity compared to the individual layers, typically on the order of several nanometers. The formation of the moiré superlattice is crucial for the emergence of the unique electronic properties observed in magic-angle twisted 2D materials.

Multiple Magic Angles

While the magic angle of approximately 1.1° in twisted bilayer graphene has garnered significant attention, it is important to note that there are multiple magic angles at which interesting electronic properties emerge. Theoretical calculations and experimental observations have revealed the presence of several magic angles in twisted bilayer graphene, each associated with distinct electronic properties.
In addition to the well-known magic angle of 1.1°, other magic angles in twisted bilayer graphene have been predicted and observed at slightly higher values. For example, a second magic angle has been reported at around 1.3°, which is close to the primary magic angle. At this angle, the electronic structure of the twisted bilayer graphene exhibits similar flat electronic bands and correlated electronic states as those observed at 1.1°.
Furthermore, theoretical studies have predicted the existence of additional magic angles at higher twist angles, such as around 2.0° and 3.0°. These higher-order magic angles are associated with the formation of multiple flat electronic bands and the emergence of novel quantum phenomena. However, experimental observations of these higher-order magic angles remain challenging due to the increased sensitivity to structural disorder and the difficulty in achieving precise control over larger twist angles.
In twisted bilayer TMDs, multiple magic angles have also been theoretically predicted and experimentally observed. The specific values of these magic angles depend on the material properties, such as the lattice constant and the strength of the interlayer coupling. For instance, in twisted bilayer Molybdenum Disulfide (MoS2), magic angles have been reported at around 2°, 3°, and 5°, each associated with distinct electronic properties and correlated states.
The existence of multiple magic angles adds an extra dimension to the tunability of twisted 2D materials, as each magic angle offers a unique set of electronic properties that can be accessed by precisely controlling the twist angle. This tunability enables the exploration of a rich phase space of quantum phenomena and the potential for designing novel electronic devices with tailored properties.
As research in this field continues to progress, a deeper understanding of the underlying mechanisms and the interplay between different magic angles is expected to emerge. The discovery of multiple magic angles in twisted 2D materials highlights the complexity and richness of the electronic properties in these systems and paves the way for the rational design of twisted 2D materials with desired electronic properties.

Synthesis and Fabrication of Twisted 2D Materials

The synthesis and fabrication of twisted 2D materials require precise control over the twist angle and the alignment of the layers. Several methods have been developed to achieve this control, including:
  • Mechanical Stacking: In this method, individual layers of 2D materials are mechanically exfoliated from bulk crystals and then stacked on top of each other with a controlled twist angle using a transfer setup. This method allows for the fabrication of high-quality twisted bilayer structures with clean interfaces, but it is limited in terms of scalability and throughput.
  • Chemical Vapor Deposition (CVD): Chemical Vapor Deposition has been used to grow twisted bilayer graphene and TMDs directly on a substrate. By controlling the growth conditions, such as temperature, pressure, and precursor flow rates, it is possible to obtain twisted bilayer structures with specific twist angles. CVD-grown twisted 2D materials have the advantage of larger sample sizes and potential for scalability, but achieving precise control over the twist angle remains a challenge.
  • Nanomechanical Manipulation: Nanomechanical manipulation techniques, such as atomic force microscopy (AFM) and scanning tunneling microscopy (STM), have been employed to locally twist 2D materials with nanometer-scale precision. This method allows for the creation of twisted structures with well-defined twist angles and the ability to study local electronic properties, but it is limited to small sample sizes.

Experimental Techniques for Studying Magic Angle Phenomena

Various experimental techniques have been used to investigate the electronic properties of magic-angle twisted 2D materials, including:
  • Transport Measurements: Electrical transport measurements, such as resistance and Hall effect measurements, are commonly used to probe the electronic properties of twisted 2D materials. These measurements can reveal the presence of superconductivity, correlated insulating states, and other quantum phenomena. Low-temperature measurements are often necessary to observe these effects, as they typically occur at temperatures below a few Kelvin.
  • Scanning Probe Microscopy: Scanning probe techniques, such as STM and scanning tunneling spectroscopy (STS), provide local information about the electronic structure and density of states in twisted 2D materials. These techniques can map out the moiré superlattice, visualize the flat electronic bands, and study the spatial distribution of electronic states with atomic resolution.
  • Angle-Resolved Photoemission Spectroscopy (ARPES): ARPES is a powerful technique for directly measuring the electronic band structure of materials. In twisted 2D materials, ARPES can reveal the presence of flat electronic bands near the Fermi level, which are a signature of the magic angle phenomena. ARPES measurements require high-quality samples with clean surfaces and are typically performed at synchrotron facilities.
  • Optical Spectroscopy: Optical spectroscopy techniques, such as Raman spectroscopy and photoluminescence, can provide information about the vibrational and electronic properties of twisted 2D materials. These techniques are sensitive to the interlayer coupling and can be used to characterize the twist angle and the quality of the samples.

Potential Applications and Future Directions

The discovery of magic angle phenomena in twisted 2D materials has opened up new avenues for both fundamental research and potential applications. From a fundamental perspective, twisted 2D materials provide a unique platform for studying strongly correlated electron systems, topology, and unconventional superconductivity. The ability to tune the electronic properties by varying the twist angle and applying external fields offers a rich playground for exploring novel quantum phenomena.
In terms of applications, the extraordinary properties of magic-angle twisted 2D materials could lead to the development of novel electronic devices, such as high-temperature superconductors, quantum sensors, and nanoscale electronic circuits. The flat electronic bands and strong electronic correlations in these materials could enable the realization of low-power, high-speed electronic devices and quantum computing architectures.
However, several challenges need to be addressed for the practical realization and application of magic-angle twisted 2D materials. These challenges include the precise control and stabilization of the twist angle, the scalable fabrication of high-quality devices, and the understanding of the underlying mechanisms governing the observed phenomena.
Future research directions in this field include the exploration of new 2D materials and heterostructures that exhibit magic angle phenomena, the investigation of the interplay between superconductivity, magnetism, and topology, and the development of advanced characterization techniques to probe the local electronic properties with higher resolution. As the field of twistronics continues to evolve, magic-angle twisted 2D materials are expected to play a central role in unraveling new quantum phenomena and enabling novel electronic applications.

Further Reading