KEY CONCEPTS
• Magic-angle twisted graphene exhibits a superconducting phase at temperatures near absolute zero.
• Spin-orbit coupling in twisted graphene bilayers was achieved by placing magic-angle twisted graphene in close proximity to tungsten diselenide. 
• This phenomenon enabled the researchers to determine that magic-angle twisted graphene also can exhibit ferromagnetism. 

Energy dissipation due to friction and resistance continues to be one of the biggest challenges to develop machines that operate at high performance levels. To increase the efficiency of mechanical systems, tribologists strive to overcome this overheating by minimizing friction formation.

On the other hand, physicists have long been studying a phenomenon called superconductivity as a potential solution to reducing the energy consumption associated with electron flows in electrical systems. A wide variety of metallic materials become superconducting at low temperature, where electrons can flow without resistance or friction. While this offers an ideal solution for dissipationless electrical energy transport, the requirement of a low temperature environment places a substantial limit on its application. Creating a superconducting phase that is stable at room temperature has been a central focus for superconducting research.

One of the most interesting superconducting materials is the so-called magic-angle twisted bilayer graphene. Jia Li, assistant professor of physics at Brown University in Providence, R.I., says, “Graphene has a lattice structure that contains one layer of atoms and exhibits a thickness of 0.3 nanometers. But graphene, a semi-metallic material, remained relatively boring to study from a quantum phenomenon perspective until recently.”

In 2018, researchers reported that stacking two sheets of graphene with a rotational misalignment that is 1.1 degrees produces an interesting superconducting phase at temperatures near absolute zero. Li says, “The interaction of the twisted graphene bilayer is modified by rotational misalignment. The fact that superconductivity is stabilized by the rotational misalignment between two graphene layers is a surprising breakthrough.”

This superconducting phase may hold the key to potentially addressing the challenge associated with realizing dissipationless in electron flow. At the same time, a system of twisted graphene can be further engineered to explore novel topological phases, which can unlock a host of exciting future applications.

An interesting aspect of magic-angle twisted bilayer graphene is its ability to host superconductivity and ferromagnetism. Superconductive materials rarely show the ability to exhibit ferromagnetism because the two phenomena are usually not compatible. Li explains, “To form superconductivity, the spins between a pair of electrons are required to point in different directions, which is completely opposite to that of ferromagnetism, where electron spins are often aligned in the same direction.”

Li and his colleagues have now found a new approach to realize a new topological ferromagnetic order in a magic-angle twisted graphene bilayer.

Spin-orbit coupling
In two-dimensional materials, ferromagnetism is often accompanied by unusual topological properties. It has been recognized that spin-orbit coupling is an essential ingredient to stabilize topological phrases. Li says, “Spin-orbit coupling refers to a material property where the motion of an electron is coupled to the orientation of its spin. For example, if an electron moves from left to right in its orbit, the spin will be up. Changing the direction of electron movement from right to left leads to the spin being down.”

However, carbon has very weak spin-orbit coupling, which prompted researchers to introduce a new material that induces this interaction when placed in proximity. Li says, “We decided to place magic-angle twisted graphene near tungsten diselenide, which is a compound known to exhibit spin-orbit coupling and is readily available.”

To introduce spin-orbit coupling in twisted graphene bilayers, the researchers first identified a segment of graphene that is roughly 50 microns in size and cut it in half using an atomic force microscope. Combining the initial piece of graphene with a second sheet led to the formation of magic-angle twisted graphene. A few layers of tungsten diselenide were then stacked above the graphene. Optimal sample quality was achieved through encapsulation of the graphene and tungsten diselenide with dual boron nitride and graphite crystals placed above and below them.

Figure 3 shows a schematic of magic-angle graphene (blue and red atoms on the bottom) and tungsten diselenide (blue and yellow atoms on top). Li says, “The presence of tungsten diselenide induces spin-orbit coupling in magic-angle twisted graphene due to the electron wavefunction overlap across the interface between the two materials.”


Figure 3. Spin-orbit coupling between magic-angle twisted graphene on the bottom (red and blue atoms) and tungsten diselenide on the top (blue and yellow atoms) produces a ferromagnetic effect. This finding shows that magic-angle twisted graphene now demonstrates both superconductive and ferromagnetic properties. Figure courtesy of Brown University.

The temperature of the experimental setup was reduced to near absolute zero. Application of an in-plane magnetic field identifies the presence of spin-orbit coupling. By tuning an in-plane magnetic field, the researchers were able to observe a reversal in the magnetic order, suggesting that spin and orbital degrees of freedom are linked together. In addition, a perpendicular electric field controls the strength of the spin-orbit coupling. Adjustment of the electric field can reduce the strength of the spin-orbit coupling, which allowed the researchers to verify that the ferromagnetic order is indeed stabilized by the engineered atomic interface.

Li says, “Our work shows that ferromagnetism and superconductivity can be achieved within the same material platform but under different empirical conditions. Future work has the goal of finding empirical conditions where magic-angle twisted graphene and tungsten diselenide can exhibit both ferromagnetism and superconductivity at the same time.”

The outcome of this work is to open up additional pathways to develop materials that exhibit superconductivity and also may act as ferromagnets. Additional information can be found in a recent article¹ or by contacting Li at jia_li@brown.edu.

REFERENCE
1. Lin, J., Zhang, Y., Morissette, E., Wang, Z., Liu, S., Rhodes, D., Watanabe K., Taniguchi, T., Hone, J. and Li, J. (2022), “Spin-orbit-driven ferromagnetism at half moiré filling in magic-angle twisted bilayer graphene,” Science, 375 (6579), pp. 43-44.