Celebrating the treasures of topological twists.
Sometimes a scientific idea falls into obscurity as researchers turn their attention elsewhere, yet contains such mathematical beauty that it is revived again and again. Such is the story of the skyrmion: a concept that has had several makeovers since it was first formulated in the late 1950s by the British physicist Tony Hilton Royle Skyrme.
One way to visualize a skyrmion is to imagine a sphere studded with arrows pointing towards its centre. Then take away the sphere, project the arrows onto a plane while keeping their orientations fixed, and admire a twisting configuration.
This texture is best defined mathematically as a 'topological' spatial feature that, like the twist in a Möbius strip, is preserved under continuous deformation. But the skyrmion turned out to be more than pure mathematics: in 1962, Skyrme found that it could explain how subatomic particles such as neutrons and protons exist as discrete entities emerging from a continuous nuclear field. This was a problem that had been worrying some of the highest-profile physicists of the day. In the Skyrme model it was intuitively explained by imagining such particles as stable geometric twists in an otherwise flat background, much like whirlpools in a mass of water.
It was an imaginative and satisfying solution — and one that was overlooked for a decade or two. This was probably at least in part because of the advent of another big idea in particle physics in the 1960s: quarks. It may also have had something to do with Skyrme's modesty and lack of ambition to gain far-reaching acceptance for his ideas.
The Skyrme model was finally embraced by particle physicists in the 1980s, only to be overshadowed a second time by an even bolder idea: string theory. In that same decade, however, an unexpected revival of skyrmions was already brewing, thanks to the discovery of a new kind of electronic system known as a quantum Hall device — the subject of two Nobel prizes, and the basis of a revolution in condensed-matter physics. Quantum Hall devices exhibit very unusual quantum effects, which show up as ultraprecise jumps in electronic current when a magnetic field is applied.
Slowly, the understanding emerged that these quantum effects were best described in terms of topological features. This was a natural home for skyrmions and they were predicted and detected electronically in quantum Hall devices by the mid-1990s.
A flurry of activity ensued in the field. As research topics do, the phenomenon eventually went out of fashion — again. But in recent years, skyrmions have made yet another comeback. The field of condensed-matter physics is abuzz with excitement about topological states of matter in a range of systems besides quantum Hall devices. Moreover, there is an ambitious agenda to exploit these topological features for practical applications: it is thought that they hold the key to a whole new range of robust electronic and magnetic functions and possibly also to quantum computation.
In this issue, skyrmions are vividly brought to life in the stunning electron-microscope images of textures of swirling magnetization in a magnetic material (see Figures 1e and f on page 902). After re-emerging from the depths of obscurity several times over, the spotlight is back on skyrmions. And a reader can only wonder what other neglected gems of mathematical ideas are tucked away in the literature, awaiting a creative scientist to recognize their value to the physical world?