Twists and Swirls

The why, it turned out, was hiding in the quantum realm — a place geophysicists rarely tread. Likewise, most quantum physicists don’t generally tackle the mysteries of geophysical fluids. But Marston was an exception. He began his career in condensed matter physics, but he was also curious about climate physics and the behavior of fluids in Earth’s oceans and atmosphere. Marston suspected there was a connection between geophysical waves and electrons moving through a magnetic field, but he didn’t know where to find it — until his colleague Antoine Venaille suggested looking at the equator. Marston then noticed that the dispersion relation of the waves along the equator (which Kiladis had measured) looked remarkably similar to the dispersion relation of electrons in a topological insulator. Any condensed matter physicist “would immediately recognize it,” Marston said. “If I had been paying attention to the equatorial regions of the Earth, I would have realized this much sooner.”

And here’s where the story begins for the second time, with the relatively recent discovery of the quantum behavior of electrons in topological insulators.

In 1980, a quantum physicist named Klaus von Klitzing wanted to know how electrons behaved in a magnetic field when they were chilled enough for their quantum nature to become apparent. He already knew that an electron attempting to traverse a magnetic field is deflected from its direction of motion and ends up moving in circles. But he didn’t know how that might change when he introduced the quantum component.

Von Klitzing chilled his electrons almost to absolute zero. As he suspected, at the edge of a material, the electrons only complete half their circle before running into the edge. They then migrate along that boundary, moving in a single direction. Their motion along the boundary creates an edge current. Von Klitzing found that at super-cold temperatures, when the quantum nature of electrons becomes relevant, the edge current is surprisingly robust: It’s immune to variations in the applied magnetic field, disorder in the quantum material, and any other imperfections in the experiment. He had discovered a phenomenon called the quantum Hall effect.

Over the next few years, physicists realized that the edge current’s immunity hinted at a now widely recognized concept in physics. When an object is stretched or squashed — or otherwise deformed without being broken — and its features stay the same, the object is said to be “topologically protected.” For example, if you make a Möbius strip by twisting a strip of paper once and attaching the two ends, the number of twists doesn’t change no matter how the shape is stretched. The only way to modify the twist is to cut the Möbius strip. So the strip’s winding number, 1, is a topologically protected feature.

Back to the experiment. As the electrons in the interior of von Klitzing’s super-chilled material swirled around in the magnetic field, their wave functions (a quantum description of their wavelike nature) twisted into something like a Möbius strip. By some trick of physics, the topological twists in the interior translated into an edge current that flowed without dissipating. In other words, the edge current’s immunity was a topologically protected property created by the twisting interior electrons. Materials like von Klitzing’s super-chilled samples are now referred to as topological insulators, because even though their interiors are insulators, topology allows current to flow around their edges.

When Marston and his colleagues looked at Earth’s equatorial Kelvin waves, they saw a regularity that made them wonder if the waves were analogous to the edge current in a topological insulator.

In 2017, along with Pierre Delplace and Venaille, both physicists at the École Normale Supérieure in Lyon, France, Marston observed that the Coriolis force swirls fluids on Earth the way the magnetic field spins von Klitzing’s electrons. In the planetary version of a topological insulator, equatorial Kelvin waves are like the current flowing at a quantum material’s edge. These immense waves propagate around the equator because it is the boundary between two insulators, the hemispheres. And they flow east because in the northern hemisphere, Earth’s rotation swirls fluids clockwise, and in the southern hemisphere, the ocean swirls in the other direction.

“This was the first nontrivial answer anybody provided to why the Kelvin wave should exist,” Biello said. To him, the trio had explained the phenomenon using broad, fundamental principles, rather than simply balancing terms in mathematical equations.

Venaille even thinks the topological description might explain why Earth’s equatorial Kelvin waves seem surprisingly strong, even in the face of turbulence and chaos — our planet’s erratic weather. They stand up to perturbations, he explained, in the same way that the edge current of a topological insulator flows without dissipating and with no regard for impurities in the material.

The Shape of Air

Despite the theoretical work, the connection between topological systems and Earth’s equatorial waves was still indirect. Scientists had seen the eastward-flowing waves. But they hadn’t yet seen anything analogous to the swirling interior electrons, which in a quantum system would be the original source of the boundary waves’ robustness. To confirm that on the largest scale, Earth’s fluids behave like electrons in a topological insulator, the team needed to find topologically twisted waves somewhere farther from the equator.

In 2021, Marston set out to find those twisted waves, along with Weixuan Xu, then at Brown University, and their colleagues. To do that, they looked to Earth’s atmosphere, where the Coriolis force stirs pressure waves in the same way it stirs ocean water. For their search, the team targeted a specific type of wave — called a Poincaré-gravity wave — that exists in the stratosphere, a region of the atmosphere about 10 kilometers up. (If their theory was correct, Marston said, these twisted topological waves should exist throughout the atmosphere and on the ocean’s surface. It’s just that they had the best chance of actually finding them in the relatively calm milieu of the stratosphere.)

They started by combing through the ERA5 data set from the European Center for Medium-Range Weather Forecasts, which takes atmospheric data from satellites, ground-based sensors and weather balloons and combines it with meteorological models. The team identified the Poincaré-gravity waves in those data sets. They then compared the height of the waves to the velocity of their horizontal motion. When they calculated the offset between those undulations — referred to as the phase between wave oscillations — the scientists saw that the ratio was not always the same. It depended on the exact length of the wave. When they plotted the phase in an abstract “wave vector space” — something that’s done in quantum physics all the time, but not often in earth science — they saw that the phase spiraled around and formed a vortex: The twisting in the waves’ phases resembled the spiraling wave functions in a topological insulator. Although a bit abstracted, it was the hallmark they had been searching for. “We actually proved the theory to be true,” Xu said.