An “obstructed” electronic band in a two-dimensional quantum material observed for the first time

An international team led by Donostia International Physics Center (DIPC) has managed to experimentally confirm the existence of an “obstructed” electronic band in a monolayer of niobium diselenide (NbSe2), a two-dimensional material known for its collective electronic phases, such as superconductivity and the charge density wave (CDW). The result, published in the journal Nature Physics, quantitatively demonstrates a concept that has remained theoretical until now.

“The presence of obstructed or non-obstructed bands serves as a key feature in the modern topological classification of solids. Specifically, an obstructed band is one whose electronic charge is “anchored” by symmetry in the gaps of the crystal lattice, rather than on the atoms themselves”, says Miguel Moreno Ugeda, Ikerbasque Research Professor at DIPC. Although it may sound paradoxical, “this “shift” is not a mere geometric detail but a robust signature of how symmetry and topology determine the electronic structure of a crystal”, adds Ugeda. In crystalline materials, atoms form an ordered lattice and the electrons do not move at any energy level, but rather in electronic bands like authorized traffic lanes. In many cases, the charge associated with the electrons remains concentrated in the positions of the atoms themselves. However, “something counterintuitive happens in an “obstructed” band: the symmetry of the crystal forces the “centre of gravity” of that electronic distribution to shift to an empty point in the atomic lattice”, explains Andrei Bernevig, Ikerbasque Research Professor at DIPC.

To demonstrate this phenomenon, the DIPC team combined scanning tunnelling microscopy (STM), a technique that allows the electronic distribution to be mapped with atomic resolution, with first-principles calculations. In this way, a method was developed enabling quantitative information about how electronic states combine with each other to be extracted from experimental images. The methodology was applied to NbSe₂, thus confirming that the charge of the band studied, linked to the superconductivity and CDW in the material, centres on an empty site in the lattice.

“Although the concept of band obstruction had become hugely significant in the modern theory of electronic structure and band topology, it has not been possible to observe it directly in actual materials until now”, says Miguel Moreno Ugeda. What is more, the fact that the band studied is directly related to the physics that governs quantum properties and superconductivity in NbSe2 poses new questions about how the phenomenon of “obstruction” may influence these electronic phases.

Both agree that “beyond the experimental results, a novel and potentially generalizable methodology emerges from the study”. The combined team of experimentalists and theorists at DIPC has developed a strategy that allows electron maps with atomic resolution to be directly linked to detailed theoretical descriptions of electronic states, thus opening the door to applying it in a wide variety of quantum materials.

The work reflects the close collaboration between theoretical and experimental physicists at DIPC, and the significance of this approach. The constant exchange between both approaches was key to designing the method, interpreting the data and confirming the observed phenomenon, thus enabling the problem to be addressed from a comprehensive perspective, in which theoretical predictions and experimental measurements reinforced each other.