Insulators are materials in which electrons cannot move freely. Past theoretical studies predicted the existence of an unusual insulating state dubbed obstructed atomic insulator (OAI), in which electrons are localized inside a crystal, while their centers of charge lie in empty spaces between atoms, rather than on the atoms themselves.
Two independent research teams, one at Princeton University and Donostia International Physics Center (DIPC), and the other at Columbia University recently observed signatures of this long-theorized quantum state in two different transition metal dichalcogenides, niobium diselenide (NbSe₂) and tungsten diselenide (WSe₂). Their papers, both of which were published in Nature Physics, could open new possibilities for the study of topological quantum phenomena.
The study by researchers at Princeton and DIPC
The researchers at Princeton University and DIPC set out to closely study 1H-NbSe₂, a two-dimensional quantum material made up of the transition metal niobium (Nb) sandwiched between two selenium (Se) layers. This material has been investigated for decades, as it has been found to be a promising platform for studying quantum phenomena.
“NbSe₂ superconducts, forms a charge-density wave, and is widely used as a building block in van der Waals devices,” Dr. Dumitru Călugăru, co-author of the first paper, told Phys.org. “Our project grew out of a basic question about this familiar material: where do the electrons responsible for its low-energy physics actually live?”
Typically, electrons are assumed to be associated with the atoms in a crystal. Modern physical theories, however, showed that a material’s symmetry and topology (i.e., properties that remain unchanged when a material is deformed) can sometimes force the electronic orbitals of an electron’s band to be centered not on atoms, but on empty positions in the crystal lattice. This phenomenon is known as an “obstructed atomic band.”
“Obstructed atomic bands had been predicted theoretically in several materials, but direct experimental evidence was still lacking,” said Dr. Yi Jiang, co-author of the paper. “Our main goal was to determine whether such a band could be observed directly in a real quantum material, and whether one could image its unusual real-space structure.”
As part of their study, Dr. Călugăru, Dr. Jiang and their colleagues studied a monolayer NbSe₂ sample using a technique known as scanning tunneling microscopy (STM). STM allows researchers to image and study the surface of materials at an individual-atom scale. Previous STM work focusing on the kagome metal CoSn showed that spectral weight associated with this material’s flat bands can be concentrated at empty positions of the kagome lattice.
“STM does not directly image the atomic nuclei,” said Dr. Haojie Guo, co-author of the paper. “Instead, it maps the electronic states near the surface with atomic-scale resolution.”
Notably, the samples examined by the researchers contained a small number of impurities. While physicists and materials scientists typically try to synthesize materials with no or very few impurities, in this case these imperfections helped them to locate the sites where atoms were in STM images.
“This gave us a reference frame for comparing the electronic density to the actual crystal lattice,” explained Prof. Miguel M. Ugeda, co-author of the paper. “We then combined the STM images with first-principles calculations and symmetry-based theoretical modeling. This allowed us to reconstruct where the relevant electronic orbital is centered. The result was very clear: the electronic weight associated with this band is concentrated at an empty position in the lattice, rather than on one of the atoms. That is the defining fingerprint of an obstructed atomic band.”
The team at Columbia’s study
The second research team based at Columbia University carried out a very similar study focusing on another transition metal dichalcogenide, WSe₂. This is another 2D material comprised of a central layer of tungsten (W) in between two selenium (Se) layers.
“For a long time, my group has been thinking about the quantum geometry of transition metal dichalcogenide semiconductors,” Raquel Queiroz, co-senior author of the second paper, told Phys.org. “They are the simplest example of an obstructed atomic insulator, and I am confident many of their amazing features are enabled by this geometric origin. The valence band of WSe₂ is dominated by the d-character on the tungsten atoms at the band edge, and yet its Wannier center sits between the W atoms, at the hollow site of the lattice.”
This team’s recent paper emerged from conversations between Queiroz and others within her department at Columbia. Specifically, her colleague Madisen Holbrook had collected STM images of WSe₂ that did not match theoretical predictions, as they exhibited defects between the bright spots in the topograph, rather than on them.
“By chatting in the hallways, it became clear that this was precisely a consequence of topological obstruction and we quickly worked it out on the board drawing orbitals, which is always very fun,” said Queiroz.
“The Wannier center sits between the metal atoms, so the orbital interference and charge density are highly dependent on the probed point in momentum space. The proof would be to see the charge density jump—and Madisen went on to do more measurements (which were very challenging because the lattice position needed to be tracked through the bias sweep) and saw exactly that. It was very satisfying.”
Queiroz and her collaborators also studied their samples using STM, as this technique can map the spatial distribution of electrons at a given energy with sub-atomic resolution. This is particularly advantageous when trying to uncover topological quantum phases, including the obstructed atomic insulator phase.
“Two things make reading topology of an STM image of a 1H-TMD extremely non-trivial,” explained Queiroz. “First, the metal sites, the chalcogen sites, and the hollow site of the lattice all share the same triangular symmetry. From a clean image alone, you cannot tell which bright spot corresponds to which atom; this has caused decades of debate in the literature. Second, even if you do identify the location of the maximum density, that is not enough to know where the Wannier center is located there! All topological information lives in the phase of the wavefunctions, which is not what STM directly measures. We thus needed to go beyond a single STM image.”
To locate peaks of electron density inside their sample, the researchers slightly doped crystals. Each of the dopants they used lit up a specific symmetry-defined location inside a crystal (i.e., a Wyckoff position), thus acting as references and allowing them to map the position of electronic states.
“The second part of our study is where the theory came in handy, and much of the heavy lifting came from Julian Ingham on the phenomenology side and Daniel Kaplan with ab initio simulations,” said Queiroz.
“Different tunneling bias voltages select different parts of the valence band. Near the top of the band (the K point of the Brillouin zone) the bright pattern sits between the W atoms. Deeper in the band (near the Γ point), the bright pattern moves onto the W atoms. This shift has the topological information. At K, the Bloch states transform under threefold rotation with a non-trivial phase; at Γ they transform trivially. That mismatch in the symmetry eigenvalues at different momenta is the hallmark of a symmetry indicator of a topological obstruction.”
Queiroz and their colleagues were also able to visualize the true location of electronic charge centers in their WSe₂ samples. The measurements they collected confirmed the presence of a topologically obstructed electronic band.
“Earlier diagnostics of topological obstructions rely on what happens at boundaries: edge states, corner charges, all consequences of bulk-boundary correspondence. Here we see the obstruction in the bulk itself,” said Queiroz. “Where the electrons live inside the unit cell is being directly observed, not inferred from a boundary.
Main achievements of these studies
These two research groups were the first to directly observe obstructed atomic bands experimentally. Their findings confirm that in some materials, electrons do not always reside where one would expect them to.
“More broadly, our work connects a rather abstract idea from modern band theory to an intuitive real-space picture,” said Prof. B. Andrei Bernevig, co-author of the paper. “We are literally seeing electronic weight concentrated at empty positions in the crystal lattice. That makes the concept much more tangible.”
Prof. Bernevig and his colleagues at Princeton and DIPC also introduced a promising approach to interpret the real-space structure of electronic bands in materials with high precision. In the future, their approach could be used to study various other quantum materials.
“Our results may also have implications for the broader physics of NbSe₂,” said Prof. Fernando de Juan. “This material is famous for its superconductivity and charge-density-wave order. Our work shows that, before one even includes strong many-body effects, the electrons already have a highly nontrivial real-space structure. A natural next question is whether this hidden electronic geometry helps shape the collective phases that emerge at low temperature.”
The concentration of electronic charges at empty crystal sites could eventually also prove useful for the engineering of materials. For instance, it could allow researchers to create chemically active regions in materials that are not located on atoms.
Queiroz and her colleagues also introduced a promising methodology to study the band topology of materials, which combines STM with symmetry-related measurements. The researchers are now planning to refine their approach and turn it into a tool that can be systematically used to characterize the topology of materials.
“On the experimental side, our work resolves a long-standing ambiguity,” said Queiroz. “People have been reassigning what the bright spots in STM images of MX₂ correspond to for almost forty years. The answer is that at the band edge the bright spots are not on the atoms; they are at the bond center between the metals. A number of defect identifications in this material family will have to be revisited. And I expect the same to be true in many other materials.”
The two recent studies offer direct experimental proof that transition metal dichalcogenides exhibit a topological obstruction. While these materials have been widely studied over the past few decades, the researchers’ findings suggest that many of their unique and advantageous features are associated with their underlying quantum geometry and topology.
“Our study sheds new light on a class of materials we thought we already understood and makes us think about designing material properties in new ways,” said Queiroz. “The same geometric feature we are imaging controls several seemingly unrelated observables. It enhances the dielectric constant of TMDs, orbital magnetization, and binding energy of excitons, which are some of the reasons they are so useful in optics and photonics and, more recently, have even been shown to host fractionalized quantum phases when twisted. TMDs are fascinating and understanding their band geometry is absolutely crucial to keep studying them.”
Future research directions
The two research groups aim to conduct further studies exploring the structure of electronic states in quantum materials. The researchers at Princeton and DIPC plan to apply the approach they developed to other materials that exhibit quantum behavior.
“We also hope to understand what the obstructed atomic band in NbSe₂ means for the material’s many-body physics,” said Prof. Bernevig. “In this work, we measured the first essential ingredient: the real-space structure of the electronic wave function. The next question is whether this structure influences the charge-density wave, superconductivity, or other collective phases of the material. In that sense, this paper is not the end of the story, but the beginning of a broader program.”
The second research group at Columbia is currently working on generalizing their newly proposed methodology. They hope that this will eventually allow them to extend their exploration to a wide range of other materials.
“Other space groups, other point groups, will involve different combinations of symmetry-protected eigenvalues, different orbital interferences, and different kinds of obstructions,” added Queiroz. “We want to write the recipe down: given a band representation, which real-space STM measurements can pin down the topology of the band? Done well, it becomes a standard to explore and interpret the density variations of STM with bias.”
Written for you by our author Ingrid Fadelli, edited by Gaby Clark, and fact-checked and reviewed by Robert Egan—this article is the result of careful human work. We rely on readers like you to keep independent science journalism alive.
If this reporting matters to you, please consider a donation (especially monthly). You’ll get an ad-free account as a thank-you.
Publication details
Dumitru Călugăru et al, Observation of an obstructed atomic band in a transition metal dichalcogenide, Nature Physics (2026). DOI: 10.1038/s41567-026-03196-5.
Madisen Holbrook et al, Real-space imaging of the band topology of transition metal dichalcogenides, Nature Physics (2026). DOI: 10.1038/s41567-026-03197-4.
© 2026 Science X Network
Citation:
Atomic bands in two transition metal dichalcogenides hint at long-theorized quantum state (2026, May 13)
retrieved 13 May 2026
from https://phys.org/news/2026-05-atomic-bands-transition-metal-dichalcogenides.html
This document is subject to copyright. Apart from any fair dealing for the purpose of private study or research, no
part may be reproduced without the written permission. The content is provided for information purposes only.