90-degree twist creates tunable quantum simulators

17 December 2025

Photo: Xian et al.

Schematic illustration of the quantum simulation of square lattice Hubbard model using 90˚ twisted bilayer rectangular two-dimensional materials.

Researchers at the Max-Planck-Institute for the Structure and Dynamics of Matter (MPSD) and partner institutes have developed a general and experimentally realistic method to create square-lattice moiré materials by twisting two-dimensional semiconductors with rectangular unit cells by 90 degrees. This simple geometric recipe produces moiré patterns with square symmetry and flat, isolated electronic bands that map onto a tunable square-lattice Hubbard model—the theoretical framework underpinning magnetism and high-temperature superconductivity. The approach works across a broad class of materials and offers powerful knobs to explore correlated-electron phases in a clean, gate-tunable platform.

A new study introduces a broad and practical scheme for engineering square-lattice moiré systems—a long-sought goal. While moiré physics has been widely explored in triangular and honeycomb materials, square lattices have been rare because few naturally square 2D crystals exist. The researchers propose a simple alternative: take two or more rectangular-lattice two-dimensional materials—such as GeX and SnX monochalcogenides—and rotate them by exactly 90 degrees.

A nearly ideal square lattice

This rotation creates a predictable lattice mismatch along both in-plane directions. When the two lattice vectors differ slightly, they form a long-wavelength moiré pattern that is nearly an ideal square lattice. Using large-scale first-principles simulations on twisted GeS, GeSe, SnS and multilayer variants, the team shows that the spatially varying interlayer registry generates narrow, isolated flat bands at the conduction-band edge. These bands are well captured by a square-lattice Hubbard model with tunable parameters—including nearest-neighbor and next-nearest-neighbor hopping—providing a clean platform to study correlated-electron behavior.

Because the bands are so flat, electron–electron interactions dominate. With ab-initio-derived interaction parameters, the half-filled flat band can form a Mott insulator with Néel antiferromagnetic order, where the magnetic moments reside not on atoms but on moiré-scale orbitals.nThe platform offers exceptional control: material choice and layer number tune magnetic frustration, while electric displacement fields continuously adjust band anisotropy. This flexibility enables systematic exploration of antiferromagnetism, stripe order, pseudogap behavior and unconventional superconductivity. 

A powerful playground for strongly interacting electrons

This excites the co-author and MPSD Director Angel Rubio, who is a researcher in the Cluster of Excellence "CUI: Advanced Imaging of Matter": “The surprising thing is how simple the idea turned out to be. By twisting two rectangular layers by 90 degrees, a clean square lattice appears almost automatically. Once we saw how robust this mechanism was, we realized it could open a large new direction in moiré research.”

Lede Xian, co-author, hopes fellow researchers will use their result in their future work:“We hope this work encourages the community to look more widely at two dimensional materials. Rectangular lattices are more common, and with a simple 90 degree twist they can become a powerful playground for strongly interacting electrons.”

The study was performed by the Max-Planck-Institute for the Structure and Dynamics of Matter together with colleagues from the RWTH Aachen, the Tsientang Institute for Advanced Study and University of Pennsilvania. Text: MPSD, ed.

Citation

Q. Xu, A. Fischer, N. Tancogne-Dejean, T. Zhang, E. Viñas Boström, M. Claassen, D. M. Kennes, A. Rubio, L. Xian

Engineering 2D Square Lattice Hubbard Models in 90° Twisted GeX/SnX (X = S, Se) Moiré Superlattices

Physical Review X 15, 041049 (2025)

DOI: 10.1103/wcbz-lbr1