Split Electron States on Bismuth Surface Offer New Window on Magnetic Monopole Physics

For nearly a century, the magnetic monopole has occupied one of the most tantalizing positions in theoretical physics: a particle that behaves as a single, isolated north or south magnetic pole. Ordinary magnets never behave this way. Slice a bar magnet in two and each fragment immediately develops its own pair of poles, so that no amount of division ever yields an isolated pole. Electric charges, by contrast, exist freely as positive or negative entities, and this asymmetry between electricity and magnetism has long bothered physicists. In 1931, Paul Dirac demonstrated that if magnetic monopoles exist anywhere in the universe, their mere presence could explain why electric charge is quantized, appearing only in discrete multiples of a fundamental unit. That argument elevated the monopole from curiosity to cornerstone, embedding it in quantum field theory and grand unified theories of particle physics. Yet despite decades of searches in cosmic rays, particle accelerators and ancient minerals, an elementary magnetic monopole has never been directly observed, leaving the idea mathematically compelling but experimentally unconfirmed.

Condensed-matter physics has now opened a different route into this territory, one that does not require finding a fundamental particle at all. Topological magnetoelectric theory predicts that the surface electrons of a topological insulator respond to an electric field in a remarkable way: when an active electric field is applied near the boundary between a topological insulator and a topologically trivial material such as vacuum, the electrons generate a magnetic response that can be mathematically described as an image magnetic monopole. In effect, the surface behaves as though a magnetic monopole were lurking just beneath it, mirroring the applied electric field the way an ordinary image charge mirrors an electric charge. The prediction is elegant, but realizing it in the laboratory demands two difficult things at once: a way to create an electric field that is intense and localized on nanometre scales, and a way to detect the faint magnetic response it induces. A new experimental study suggests that both requirements can be met with a single, well-established instrument.

Scanning tunnelling microscopy, or STM, turns out to be a natural engine for this kind of physics. When a sufficiently large bias voltage is applied between the microscope’s metallic tip and the sample, the instrument enters the field-emission regime: electrons are torn from the tip apex and travel across the tunnelling junction toward the sample surface. This process produces an intense, highly localized active electric field confined to the tiny gap between tip and surface, exactly the kind of field that topological magnetoelectric theory calls for. Crucially, the field in the junction has more structure than a simple perpendicular pull. It comprises the tip-induced field together with a transient field generated by the moving, field-emitted electrons themselves, and the tip-induced field possesses a radial component, Er, that points outward from the junction axis. The strength of this radial component depends inversely on the dielectric constant of the substrate and on the tip-sample distance, a dependence that would soon prove decisive in interpreting the experiment.

The same field-emission conditions create a second phenomenon that serves as the experiment’s readout mechanism. An electron that has been emitted but has not yet joined the sample remains outside the surface, where it is attracted by the image charge it induces in the material beneath it. This attractive potential can briefly trap the electron just outside the surface, binding it into a ladder of Rydberg-like electronic states known as image potential states, or IPSs. These states hover nanometres above the surface, exquisitely sensitive to anything that perturbs the electrostatic landscape there, including the active electric field produced by the tip. On ordinary, topologically trivial surfaces, IPSs form a conventional, predictable series of spectroscopic peaks. That predictability is precisely what makes them powerful: any deviation from the expected pattern signals that something unusual is happening at the surface, and the details of the deviation encode what that something might be.

A research team led by Lan Chen at the Institute of Physics of the Chinese Academy of Sciences exploited this sensitivity to examine IPSs on Bi(111), the (111) surface of bismuth, which possesses higher-order topological character. Higher-order topological insulators, or HOTIs, are materials whose unusual topology manifests not in conducting edge channels on every boundary, as in conventional topological insulators, but in more subtle surface electronic structure that emerges under specific conditions. Using low-temperature STM, the researchers first established a baseline: on topologically trivial reference surfaces, the spectra displayed the conventional series of IPS peaks, exactly as textbook physics predicts. When they turned to Bi(111), however, the spectra revealed a strikingly unexpected splitting of the IPS features, an anomaly with no place in the standard description of image-potential states and an immediate hint that the higher-order topology of the surface was somehow involved.

To trace the origin of the splitting, the researchers systematically varied two experimental parameters: the thickness of the Bi(111) films and the dielectric properties of the substrate supporting them. The results were revealing. In the thinnest Bi(111) films, the anomalous splitting was entirely absent; it appeared only as the films grew thick enough for the characteristic Bi(111) surface electronic structure to develop. This thickness dependence tied the anomaly directly to the emergence of the topological surface states rather than to any bulk property of bismuth or to a generic artifact of the measurement. The surface electronic structure, in other words, was not a bystander but an active participant in producing the splitting, consistent with the idea that the effect involves the special response of topological surface electrons to the local field environment created by the STM junction.

The substrate experiments delivered the second, and arguably most telling, clue. When Bi(111) was supported on semiconducting Si(111), which screens electric fields only weakly, the splitting grew as the tunnelling current was raised and the STM tip moved closer to the surface, intensifying the field in the junction. When Bi(111) rested instead on metallic Sb(111), a far more effective screening substrate, the splitting remained nearly unchanged regardless of tip approach. This contrast indicates that the anomalous splitting is governed not by the perpendicular electric field in the junction, the component one might naively expect to dominate, but by the radial component of the active electric field, the component whose strength is controlled by substrate screening. A purely electrostatic explanation tied to the perpendicular field could not account for this behavior, pointing instead toward a coupling between the radial field and the surface’s electronic structure that carries magnetic-response character.

Building on these observations, the researchers proposed a phenomenological picture that connects all the pieces. In their interpretation, the radial active electric field couples to the Bi(111) surface electronic structure and induces an effective magnetic-response-like perturbation, one that is compatible with the monopole-like topological magnetoelectric response predicted by theory. Such a perturbation would lift the degeneracy of the orbital-like sublevels of the image potential states, splitting what should be a single peak into the multiple components observed in the spectra. The thickness dependence enters because the surface states that participate in this coupling only exist once the film is thick enough; the substrate dependence enters because screening controls the radial field strength. Within this framework, every experimental observation finds a natural place, and the anomalous splitting becomes a candidate spectroscopic fingerprint of a phenomenon that has otherwise been accessible only through theoretical formalism.

The broader significance of the work lies in the experimental method itself. Field-emission IPS spectroscopy, as demonstrated here, accomplishes in a single measurement what previously required separate capabilities: it simultaneously creates a highly localized active electric field through the STM tip and sensitively probes the surface’s response to that field through the trapped image-potential states. This dual role transforms the STM from a passive imaging tool into an active probe of magnetoelectric coupling at higher-order topological surfaces. For a field in which the central prediction, the image magnetic monopole, has remained a theoretical construct awaiting a practical detection strategy, the demonstration that a splitting of Rydberg-like surface states can serve as its signature represents a genuine methodological advance, opening a new experimental route for investigating active-field responses in topological materials.

Much work remains before the interpretation is settled. The study, published in National Science Review with DOI 10.1093/nsr/nwag548, reports an experimental observation together with a phenomenological framework, and the proposed connection between the splitting and a monopole-like magnetoelectric response is presented as a possible, physically consistent explanation rather than a definitive proof. Nevertheless, the findings give physicists something they have rarely had in this area: a reproducible, tunable spectroscopic anomaly whose dependence on film thickness, substrate screening and tip-sample distance can be systematically mapped, and whose theoretical meaning can be sharpened with each new measurement. If subsequent studies confirm the monopole-like interpretation, the humble image-potential states that have hovered above surfaces since the early days of surface physics will have become the medium through which one of Dirac’s most enduring ideas finally meets a laboratory analogue, not in the cosmos or a collider, but in the nanometre-scale gap beneath a scanning tunnelling microscope tip.

Subject of Research: Anomalous image-potential state splitting on higher-order topological insulator Bi(111) as a spectroscopic probe of monopole-like topological magnetoelectric response

Article Title: Anomalous splitting of image-potential states on HOTI Bi(111) provides a new spectroscopic window into possible monopole-like topological magnetoelectric responses

Article References: Anomalous splitting of image-potential states on HOTI Bi(111) provides a new spectroscopic window into possible monopole-like topological magnetoelectric responses. (n.d.). Original publication

Image Credits: AI Generated

DOI: Not provided

Keywords: magnetic monopoles, topological insulators, bismuth, image-potential states, scanning tunnelling microscopy, magnetoelectric effect, field emission, higher-order topology, surface states, spectroscopy, condensed matter physics, National Science Review