M-point Twist

Researchers introduce a new class of twistable materials, unlocking unprecedented quantum possibilities

Twisted materials—known as moiré structures—have revolutionized modern physics, emerging as today's "alchemy" by creating entirely new phases of matter through simple geometric manipulation. The term "moiré" may sound familiar—it describes the strange rippling patterns you sometimes see when photographing striped shirts or screens; in physics, the same underlying principle applies at the atomic scale.  Imagine taking two atomically thin sheets of either the same or different materials, stacking them up together, and rotating one layer slightly relative to the other. Remarkably, this simple twist fundamentally transforms the resulting material, enabling it to exhibit exotic properties vastly different from its individual layers. By carefully controlling the twist angle, physicists can engineer entirely new quantum states, opening doors previously closed to experimental science. These moiré structures promise a future rich with fundamental science and technological applications, from quantum simulators—specialized systems that help scientists study complex quantum phenomena—to ultrasensitive terahertz sensors and single-photon detectors.

When two layers are twisted, electrons from each layer interfere strongly, reshaping their combined quantum landscape. A striking example of this effect is twisted bilayer graphene, where superconductivity—a state in which electrons flow without resistance—unexpectedly emerges, even though graphene layers individually cannot become superconducting.

Electrons in materials have a quantum number called momentum, which essentially describes their quantum mechanical state of motion. Until now, the focus has predominantly been on hexagonal lattices twisted around what are known as K-points—special points of electronic momentum symmetric under 120-degree rotations. Only a handful of materials such as graphene, MoTe₂, MoSe₂, and WSe₂ have been explored experimentally. However, in new research published in Nature, a team of international researchers introduces an entirely new twisting paradigm based on the M-point of the electron momentum, significantly expanding the moiré landscape.

“So far, all twisting has been around the K points, limiting us to a small corner of the material universe,” explains Dumitru Călugăru (PhD 2024, Princeton), a Leverhulme-Peierls fellow at the University of Oxford. “By shifting our focus to the M points, we unlock a completely new class of twisted quantum materials with entirely new quantum behavior. The position of the electronic band minimum is key," says Călugăru.

The paper represents a significant international collaboration across multiple continents and institutions, including Princeton University (USA), Donostia International Physics Center (Spain), University of Oxford (UK), the Max Planck Society (Germany), Cornell University (USA), Ludwig Maximilian University of Munich (Germany), University of Sherbrooke (Canada), and University of Florida (USA).

The research team—which includes theoretical physicists, computational physicists, and an international group of materials scientists and chemists who have begun synthesizing and exfoliating the proposed materials—began by identifying hundreds of candidate materials suitable for this novel type of twisting. These materials were systematically classified based on the position of their electronic band minimum, a critical feature controlling the resulting quantum properties of the twisted layers. Out of these materials, two (SnSe₂ and ZrS₂) – with band minimum at the M point - were chosen for the in-depth current study.  

"Unlike K-point twisting, where moiré bands typically exhibit topological characteristics, we found the M-point twisted bands to be topologically trivial yet remarkably flat," explained Haoyu Hu, a postdoctoral researcher at Princeton. “However, the bands at the M-point possess a previously unnoticed type of symmetry, rendering them highly unusual and sometimes even one-dimensional. This fundamentally alters their quantum behavior," added Hu.

Through extensive microscopic ab initio calculations—requiring over six months of computational effort—Yi Jiang and Hanqi Pi (Donostia International Physics Center) demonstrated that the electron bands become significantly flattened at low twist angles of about three degrees. Flattening electron bands effectively slows down electrons, enhancing their mutual interactions, and giving rise to novel quantum phenomena.

"This flattening can localize electrons in either a hexagonal lattice or a kagome lattice arrangement," Jiang noted. Pi further elaborated, "Such localization means we can now experimentally realize diverse quantum states, potentially including quantum spin liquids."

Quantum spin liquids, elusive states that have fascinated physicists, promise exciting applications including possible pathways to high-temperature superconductivity. However, they have never been conclusively observed experimentally in bulk materials, largely because of extreme difficulties in precisely controlling doping (adding or removing electrons) and other essential material properties. Twisted materials, however, offer greater experimental controllability due to their tunable structure and the possibility of electrostatic gating – a technique which allows the doping of electrons without degrading the material, overcoming many of these historical hurdles.

The team's theoretical predictions and detailed electronic models represent a major step toward observing these states in realistic materials. Other phases of matter identified, such as unidirectional spin liquids and orthonormal dimer valence bond phases, are entirely new and unique to the M-point system.

Yet, this research transcends theory. Collaborators in quantum materials chemistry—Leslie Schoop (Princeton University) and Claudia Felser (Max Planck Institute, Dresden)—have already successfully synthesized bulk crystals of several predicted candidate materials, providing the critical first step toward practical realization. World-leading experts in 2D materials—including Dmitri Efetov (Ludwig Maximilian University of Munich), Jie Shan, and Kin Fai Mak (both at Cornell University)—then are exfoliating these bulk crystals into single-layer sheets, clearly to demonstrate the experimental feasibility of the proposed platform.

"The experimental realization of these materials is critical. Once twisted, gated, and measured, these new quantum states may become tangible realities.

Every new twist we perform seems to yield surprises. Fundamentally, these materials offer a gateway to quantum states of matter nobody has envisioned. Because they are so experimentally controllable, the possibilities truly are limitless" - B. Andrei Bernevig