Ruthenium dioxide (RuO2) is a metal oxide that commonly serves as an important metallic conductor, quantum material and industrial electrocatalyst. While there have been debates surrounding the magnetic properties of RuO2, it is generally thought to be nonmagnetic in its bulk form. But now, a new study, published in Science Advances, has found that very thin layers of RuO2 can become magnetic when its lattice is placed under strain.

One of the most striking discoveries in condensed matter physics over the past few years is that simply rotating one atomically thin crystal on top of an identical layer can create entirely new electronic behavior. This idea became famous in 2018, when physicists found that graphene sheets stacked at a very particular “magic angle” could turn into a superconductor, even though a single sheet of graphene is not. That discovery launched an entire field, sometimes called twistronics, built around moiré patterns: the large-scale interference patterns that appear when two crystal lattices are laid on top of each other with a slight mismatch in angle or spacing. In many materials, these patterns reshape how electrons move, sometimes producing superconductivity or other exotic collective states.

Moiré collapse

Most of this research has focused on materials whose crystal structure looks roughly the same in every direction, such as graphene, where the interesting physics shows up only at very small twist angles, close to perfect alignment. Now, a team of researchers instead looks at a strongly directional material: bilayer black phosphorus, whose atomic structure behaves very differently along two perpendicular directions in the plane, somewhat like a fabric that stretches easily one way but not the other. That built-in directionality turns out to change the whole logic of moiré physics, producing an effect the authors call moiré collapse. ¹

In black phosphorus, the two layers start out rotated 90 degrees relative to each other. As that angle is dialed away from 90 degrees, the moiré pattern does something unusual. Rather than staying a two-dimensional pattern, like a slowly shifting checkerboard, it stretches more and more along one direction until, at a specific angle that depends only on the material’s own geometry, it effectively stops repeating in the other direction altogether. What remains behaves like a one-dimensional crystal, even though the material is still built from ordinary two-dimensional atomic sheets. For twisted bilayer black phosphorus, the calculations place this collapse at a twist of about 71.6 degrees, or equivalently about 18.4 degrees away from the initial 90-degree arrangement.

Pure geometry

This transformation has nothing to do with how electrons repel or attract each other; it is pure geometry. The mathematical description of the moiré pattern, expressed in terms of the directions in which its periodicity repeats, is squeezed from two independent directions down to one. In ordinary space, this means the pattern keeps a well-defined repeat distance along one axis while stretching out indefinitely along the other, with no repeating pattern left in that direction at all.

Such a dramatic structural change reshapes the electrons riding on top of it. At the untwisted 90-degree configuration, the anisotropy of one layer happens to cancel out the anisotropy of the other, so electrons move about equally well in every in-plane direction. As the twist angle approaches the collapse point, that cancellation breaks down. The electron energy bands become sharply directional, and electrons increasingly travel along one preferred line rather than spreading across the plane. Their energy spectrum starts to show the telltale fingerprints of one-dimensional systems, including sharp spikes in the density of available electron states known as one-dimensional van Hove singularities.

Luttinger liquid physics

One-dimensional conductors behave very differently from ordinary metals. In a three-dimensional metal, electrons can mostly be treated as independent particles that only weakly notice one another. Confine them to a single dimension, however, and that picture stops working: electrons cannot slip past each other, so they are forced to move collectively, in a coordinated wave-like fashion. The framework that describes this collective behavior, called Luttinger liquid theory, traces back to work by Sin-Itiro Tomonaga in 1950 and Joaquin Luttinger in 1963, and it has since been confirmed experimentally in systems such as carbon nanotubes. In a Luttinger liquid, the basic excitations are not single electrons at all, but collective ripples of charge and spin, and this leads to electrical transport properties that look qualitatively different from those of a normal metal.

The calculations in this study show that moiré collapse naturally sets up the conditions Luttinger liquid physics requires. As the collapse angle is approached, the one-dimensional electronic channels that form become progressively less coupled to their neighbors, making the correlated, wave-like behavior increasingly favorable. The analysis estimates a Luttinger parameter of about 0.3 for the collapsed black phosphorus system, a value indicating strong electron-electron interactions, and it predicts distinctive collective charge oscillations and unusual, non-metallic patterns in electrical conduction that could, in principle, be measured in the laboratory.

A notable feature of this mechanism is that the electron bands stay quite dispersive even at collapse, with electron speeds exceeding 100 kilometers per second. This sets it apart from most previously studied moiré systems, including twisted graphene, where strong correlations usually arise because the electronic bands become extremely flat and electrons effectively slow to a crawl. Here, the correlated behavior instead comes from the geometric collapse of the moiré lattice itself, with fast-moving electrons confined to one dimension rather than slow ones spread over two.

Moiré collapse is not a peculiarity of one material

To test these ideas, the researchers combined simplified mathematical models with detailed first-principles calculations of the atomic and electronic structure. Beyond black phosphorus, they found the same collapse in twisted bilayer tin selenide, another layered material with strongly directional bonding. The details of the electronic structure differ somewhat because of the specific atomic orbitals involved, but the same geometric collapse into quasi-one-dimensional channels appears, suggesting the phenomenon is not a peculiarity of one material but a general consequence of twisting any sufficiently anisotropic crystal.

Taken together, the findings outline a different strategy for engineering exotic quantum matter. Instead of hunting for a special magic angle that flattens electronic bands, as in twisted graphene, this approach relies on a purely geometric collapse angle at which a two-dimensional moiré material naturally turns one-dimensional. If confirmed in experiments, it would offer a new and versatile platform for studying Luttinger liquids and other correlated electronic phases that only emerge when electrons are squeezed into moving along a single line.

 

Author: César Tomé López is a science writer and the editor of Mapping Ignorance

Disclaimer: Parts of this article may have been copied verbatim or almost verbatim from the referenced research paper/s.

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Many of today’s electronic devices — from the semiconductors in your cell phone to the photovoltaic cells in your solar panels — are built on thin-film substrates. The thin film is an electronically conductive material while the substrate is an inert material. Or is it?

Physicists and materials scientists have long assumed substrates do not react to electrical stimulus, but new research from the University of California San Diego Alex Frañó’s lab and a team of collaborators has shown that substrates are not inert after all. The discovery ¹ has the potential to help engineers build the dense, three-dimensional, brain-inspired computer chips needed for more energy-efficient computing.

In a human brain, a vast network of neurons works across different regions, enabling every thought and action we take. Yet thoughts that are quick and simple for humans — recognizing faces, differentiating a cat from a dog or solving a captcha — can be devilishly hard and energy-intensive for computers. Quantum materials may provide a solution.

It was this quest to develop new materials that led Frañó’s lab to study vanadium dioxide thin-film devices. When a voltage is applied to the thin film, an electric filament forms — something similar happens when the Earth and atmosphere create a voltage strong enough to result in lightning. The filament in the thin film drives the device’s electrical spiking, much like the signals in our neurons.

This reaction has been studied countless times in labs around the world, but Frañó’s lab was implementing a new technique, developed by graduate student Elliot Kisiel, called dark-field X-ray microscopy. Kisiel, who spent most of his graduate studies at Argonne National Laboratory and is now a Mayer Postdoctoral Fellow there, developed the tool to combine the best of two worlds: electron microscopy and X-ray diffraction.

“Dark-field X-ray microscopy gives us the ability to look at an entire device in one image, which not only greatly improves how fast we can perform these measurements, but also allows us to study the areas surrounding the devices with high fidelity,” he stated.

A changing substrate

Since the lenses for X-rays are often thick and, therefore, absorb most of the X-rays that pass through them, the team needed to look at something that provided more signal, which is why they decided to look at the substrate during some of their preliminary testing with this new technique.

What they saw was completely unexpected: not only was there a change in the thin film, but there was also a change in the substrate, showing for the first time that the two parts were sharing energy or “coupled.” This discovery went against everything scientists had assumed about substrates for decades.

 Materials for a new age of computing

Thin films are so called because they are vanishingly thin — around 100 nanometers — while the substrates they sit on can be 10,000 times thicker. Despite their lopsided sizes, in this experiment, the thin film was able to push and pull on the substrate. Frañó likened the discovery to a tree on a mountaintop being able to move the entire mountain. Furthermore, the substrate also acted on the thin film, each pushing and pulling on the other.

They spent the next four years making sure what they saw wasn’t a fluke. They not only reproduced the results doing the research exactly as they had done it the first time, but they also reproduced the results when they changed certain aspects of the sample, such as the thickness and material of the substrate. They also tested their results using different instrumentation. Much of that work was done at Argonne, which has a synchrotron facility that produces high brilliance X-rays, and at Brookhaven National Laboratory, home to the world’s only all-electric ultrafast electron microscope, which is able to capture exactly how a working device behaves under realistic operating conditions.

It wasn’t a fluke.

“The assumption that substrates are inert needs to be rethought,” Frañó stated. “Going forward, we have to assume that the substrate is undergoing changes when the film is. This is a transformational notion that counters decades of previous supposition.”

This paper is a companion to a paper that was published last year in ACS Nano ². In that paper, they used dark-field X-ray microscopy to study the thin film, while this paper focuses on the substrate. Together they illustrate how one research result leads to the next research inquiry.

In Frañó’s case, the question he now asks himself is, “What can we do with this new substrate discovery? If a tree is moving the whole mountain, let’s find a way to capitalize on that.”

One idea is that the substrate can act as a medium that can couple materials on either end of the substrate. Currently, thin film devices are connected two-dimensionally, but if researchers could build on both sides of a substrate, it would allow for three-dimensionality, opening up the possibility of denser, more interconnected computer chips, and bringing us one step closer to the next generation of computing.

 

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