Electric skyrmion bubbles can be viewed as small regions whose electric polarization (pink in the figure) opposes the electric polarization of the surrounding matrix (green). We have known for a while how to stabilize these "objects", e.g. by considering a ferroelectric material in a multidomain configuration (50% pink, 50% green) and applying an electric field that favors one "color" over the other. Then, about 5 years ago, it was theoretically predicted -- and experimentally demonstrated! -- that these electric bubbles can display non-trivial topologies akin to magnetic skyrmions. This discovery attracted a lot of attention, among other things because it suggested that electric skyrmions could be used in the many applications envisioned for their magnetic counterparts -- from energy-efficient memories to ultra-low-power devices for unconventional computing -- but with one key advantage: in principle, we should be able to control the electric bubbles using electric fields, easier to apply than the electric currents necessary to manipulate magnetic skyrmions. Exciting indeed! However, for electric bubbles to fulfill their promise, we still lack one key element: their mobility. So far, experiments have only reported on static electric skyrmions, an observation that might well be related to pinning by defects, which in turn might be a by-product of the (aggressive) sample preparation needed for advanced microscope imaging of such nanostructures. (Electric bubbles can be only a few nanometers in diameter!) In this context, Hugo Aramberri and I started a project to investigate the (possible) mobility of electric bubbles in samples free of defects, using the same computer simulation methods that allowed us to predict their topological character five years ago. Strikingly, we found that in suitable regimes thermal noise is enough to induce deformations and drifts of the bubble boundaries, often resulting in a net drift of the bubble center. Indeed, we predicted that electric bubbles can behave as stable Brownian particles, following a random walk through the sample for as long as we can simulate (several nanoseconds). Such regimes where spontaneous bubble motion occurs should also provide the ideal conditions to induce bubble currents, a possibility we are now exploring with very promising preliminary results. We hope our predictions will encourage efforts to demonstrate diffusing electric bubbles in the lab, a major challenge for our experimental colleagues. The prize is big: this will really establish the quasiparticle nature of electric bubbles, reinforcing the analogy with magnetic skyrmions and opening the door to countless possibilities for further development and application. To learn more, have a look at our 2024 paper in Physical Review Letters, where you can find some incredible videos of wandering bubbles!

Ferroelectric compounds reduce their energy by polarizing spontaneously, that is, by displacing their negative ions with respect to the positive ones. However, such ionic displacements ultimately result in an accumulation of electric charge at their interfaces with other compounds. For good or bad, when ferroelectrics are surrounded by media that does not enjoy such charge build-ups and the attendant electric fields (e.g., stiff dielectrics), the development of a polarization is energetically penalized. Nevertheless, ferroelectrics usually make do by breaking into regions (domains) of opposing polarization, so that the interfacial charges associated to different domains compensate each other and the energy penalty is minimized. The ferroelectric is frustrated in this state, though, as the boundaries (walls) between domains are energetically costly themselves. In fact, if we now apply an external electric bias that favors a particular polarization orientation, the ferroelectric readily forms bigger domains and minimizes the walls, thus approaching its preferred configuration and reducing its energy. This peculiar behavior (all but impossible among non-ferroelectrics) is characterized by a "negative capacitance". The energy released by the ferroelectric becomes available to do work in the surrounding materials, which effectively experience a bias that is larger than the one actually applied. This magic sounding "voltage amplification" has created a lot of technological excitement, as it may be a route towards the development of low-voltage (low-power) electronic devices. While waiting for those to come (which may not happen soon, because of many scientific and technical difficulties involved), we moved to the next obvious question: How large can this voltage amplification be? What can we do to maximize it? With Mónica Graf and others, we used second-principles simulation to predict viable strategies, based on sound physical mechanisms, that yield very large amplifications above 10-fold! Our results explain trends and point at directions for further improvement, suggesting that the intrinsic amplification (in ideal but not outlandish conditions) can indeed be very large. Admittedly, our job as theorists is probably quite easy compared to the device implementation of these concepts. But the important message is this: there is hope, and probably a big prize awaiting! To know more about our voltage-amplification treasure map, please read the freely available Graf et al., Nature Materials 21, 1252 (2022).