Higher-dimensional Fermiology Reveals Tunable Moiré Superlattices in Equilibrium Van Der Waals Crystals

Moiré patterns, traditionally used to engineer and control materials, now extend into three dimensions thanks to research led by Kevin P. Nuckolls, Nisarga Paul, and Alan Chen, all from the Massachusetts Institute of Technology, alongside colleagues including Avi Auslender from Harvard University. This team reports the creation of a new family of layered crystals, (SrTaS2)(TaS2), which exhibit moiré patterns throughout their bulk structure, unlike previous work focused on surface effects. These naturally occurring, tunable patterns allow scientists to map the complex behaviour of electrons within the material, revealing an exceptionally intricate Fermi surface comprised of over 40 distinct cross-sectional areas, the most ever observed in a material to date. This discovery demonstrates a new pathway for designing materials with tailored electronic properties and suggests that three-dimensional moiré structures can encode and realise physical phenomena predicted in higher-dimensional physics, potentially paving the way for advanced electronic devices.

Moiré Materials Exhibit Synthetic Quantum Dimension

This research investigates moiré metals, layered materials where the interaction between layers creates a distinctive moiré pattern, and proposes that these patterns effectively introduce a synthetic dimension to the material’s electronic structure. Scientists propose that these materials can be understood as having a higher-dimensional electronic structure, despite being physically two-dimensional or quasi-two-dimensional, opening up possibilities for new quantum phenomena and a richer understanding of quantum oscillations. The study explains how moiré patterns arise when two periodic structures are overlaid with a slight twist or mismatch, modifying the electronic band structure and leading to phenomena like correlated insulating states, superconductivity, and unconventional magnetism. Scientists focused on quantum oscillations as a powerful tool to probe the Fermi surface and understand the electronic structure of these materials, but found traditional interpretations break down due to the complex, aperiodic nature of the moiré pattern.

The team investigated layered materials created by stacking transition metal dichalcogenides with a controlled twist angle, performing high-field magnetotransport measurements at very low temperatures to look for quantum oscillations. Torque magnetometry precisely measured the angular dependence of these oscillations, providing information about the shape and orientation of the Fermi surface, and Fourier transform analysis extracted the frequencies of the quantum oscillations from the experimental data. The most striking result is the observation of a dense, linearly spaced series of quantum oscillation frequencies, an unusual finding that cannot be explained by simple models of the Fermi surface. These frequencies form what the authors call frequency combs, a series of evenly spaced frequencies, and the spacing between them is sensitive to the twist angle between the layers.

STS(3,90°) is identified as a relatively simple case where the moiré pattern is one-dimensional, making it easier to understand the underlying physics. Comparing the quantum oscillations in STS(8,81°) and STS(8,90°), scientists observed that STS(8,81°) exhibits more complex and less evenly spaced frequencies, while STS(8,90°) exhibits a clearer frequency comb. The authors propose that the observed frequency combs arise from the merging and splitting of Fermi pockets as the layers shear against one another, breaking the translational symmetry of the material. This framework provides a new way to understand strongly correlated electron systems and offers insights into the relationship between the synthetic dimension and other physical properties of the materials.

Aperiodic Crystals Synthesise Moiré Material Properties

Scientists pioneered a new approach to synthesizing high-mobility moiré materials, moving beyond traditional methods to create mechanically exfoliatable van der Waals crystals. This work centers on a new family of aperiodic composite crystals, (Sr6TaS8)1+δ(TaS2) for δ ≈0. 1, designed to emulate the essential properties of lattice-mismatched heterobilayer moiré materials, and leverages principles of solid-state chemistry to establish a potentially scalable route for producing high-quality moiré materials suitable for next-generation electronics. This innovative synthesis contrasts with existing methods and offers a pathway towards large-area production.

The research involved designing materials based on the intergrowth of layered compounds with differing crystal systems, hexagonal and monoclinic, to create a foliated superlattice structure. Scientists hypothesized that accommodating interlayer lattice frustration could partially satisfy symmetry constraints, allowing the formation of a new material with a tunable moiré superlattice. The resulting crystals exhibit a unique structural arrangement, enabling the exploration of novel electronic properties. Quantum oscillation measurements mapped the complex Fermiology and demonstrated tunability via the moiré superlattice structure, revealing a dense spectrum of quantum oscillation frequencies inconsistent with previously proposed mechanisms.

Instead, the measurements indicated the presence of extremal Fermi-surface orbits propagating into a synthetic superspace dimension. This interpretation draws inspiration from higher-dimensional superspace models of incommensurate crystallography, suggesting that the moiré superlattice encodes electronic properties in a manner analogous to higher-dimensional crystals. The study’s findings establish a framework for utilizing bulk moiré materials as platforms for accessing theoretical proposals in higher dimensions, paving the way for exploring new physical phenomena and designing advanced electronic devices.

Bulk Moiré Crystals Grown Directly From Solution

Scientists have achieved a breakthrough in creating and controlling moiré materials, moving beyond two-dimensional layered structures to synthesize bulk crystals with tunable properties. This work introduces a new family of foliated superlattice materials, (Sr6TaS8)1+δ(TaS2)8, which are naturally exfoliating van der Waals crystals exhibiting atomically incommensurate lattices, and circumvents the need for manual alignment of layers by generating moiré superlattices directly during crystal growth. The team demonstrated that lattice mismatches between alternating layers naturally form moiré superlattices, analogous to those observed in 2D materials, but coherent throughout the bulk of the crystals. Detailed X-ray diffraction measurements revealed two key signatures of these aperiodic composite lattices: a superposition of diffraction patterns from each layer and a modulation of a moiré superlattice near zero momentum transfer, confirming minimal structural disorder within millimeter-sized crystals.

Further experiments revealed an exceptionally complex electronic structure within these moiré metals. High-field oscillation measurements mapped the Fermi surface, revealing over 40 distinct cross-sectional areas, the highest number observed in any material to date, and mirroring concepts from higher-dimensional superspace crystallography. The team postulates that new oscillation frequencies stem from extremal Fermi-surface orbits propagating into a synthetic superspace dimension generated by the moiré pattern, offering a new understanding of the relationship between material structure and electronic behaviour.