Earth - Topological Insulator! Quantum Physics Reveals a Whole New Perspective
While most of the air and oceans on our planet are stirred up with the onset of storms, some phenomena are very regular. At the equator, for example, waves thousands of kilometers long persist in the chaos.
In the oceans and the atmosphere, these giant waves, called Kelvin waves, are always moving eastward. They fuel oscillating weather patterns such as El Niño, a cyclical warming of ocean temperatures that occurs every few years.
Since the 1960s, geophysicists have relied on a mathematical explanation of equatorial Kelvin waves that, for some, is not entirely satisfactory. These scientists wanted a more intuitive physical explanation for the existence of Kelvin waves; they wanted to understand the phenomenon in terms of its fundamentals and answer the following questions:
- What is special about equatorial Kelvin waves?
- What is special about the equator that permits the Kelvin wave to circulate there?
- Why does it always propagate eastward?
Earth's ocean currents twist and turn as they take on different colors depending on their temperature. Some of these currents appear turbulent and chaotic, but others are orderly and stable, and they fuel large-scale cyclical weather patterns.
In 2017, three physicists thought about this differently. They began by imagining our planet as a quantum system, and eventually they made a connection between meteorology and quantum physics. It turns out that the Earth's rotation deflects the flow of fluids in a way similar to the way a magnetic field distorts the trajectory of electrons in a quantum material like a topological insulator.
If the Earth is visualized as a giant topological insulator, they say, it explains the origin of the equatorial Kelvin waves.
But while this theory works, it is still only theoretical. No one has ever verified it directly with observations. Now, in a new preprint paper, a team of scientists describes direct measurements of distorted atmospheric waves - just the kind of evidence needed to support topological theory. This work has already helped scientists use the language of topology to describe other systems, and it could lead to new insights about waves and weather patterns on Earth.
"Topological Signature of Stratospheric Poincare - Gravity Waves"
This new result is a major advance that will provide a foundational understanding of the Earth's fluid system. Brown University physicist Brad Marston is one of the authors of this new paper, and of this result, he states, "We actually live in a topological insulator."
The origin of this concept has been described in two ways.
William Thomson, whose observations of tides in the English Channel led to the discovery of Kelvin waves.
The first story is about water, and begins with William Thomson (who was also known as Lord Kelvin), who in 1879 noticed that the tides in the English Channel were stronger along the French coastline than along the English coastline.Thomson realized that the rotation of the Earth could explain this phenomenon: when the Earth rotates, it generates a force called the Coriolis force ( Coriolis force), which causes fluids in each hemisphere to rotate in different directions: clockwise in the north and counterclockwise in the south.
This phenomenon pushes the waters of the English Channel towards the French coastline, forcing waves to flow along the French coast. These waves flow clockwise around the land in the northern hemisphere (the coastline is to the right of the waves) and counterclockwise in the southern hemisphere.
But scientists waited nearly a century to discover the larger equatorial ripple and link it to coastal Kelvin waves.
This happened in 1966, when meteorologist Taroh Matsuno was mathematically modeling the behavior of fluids (air and water) near the Earth's equator. Through his calculations, Matsuno realized that Kelvin waves should also exist at the equator. In the ocean, instead of pushing toward the shoreline, Kelvin waves collide with water from the opposite hemisphere - which rotates in the opposite direction of the Kelvin waves. According to Matsuno's math, the resulting equatorial waves should flow eastward and should be huge: thousands of kilometers long.
In 1968, scientists first observed huge equatorial Kelvin waves, confirming Matsuno's prediction. Thus, the math worked; as predicted, equatorial waves existed.
However, Matsuno's equations do not explain everything about equatorial waves.
The reason is hidden in the quantum realm, which geophysicists rarely venture into. Likewise, most quantum physicists don't usually look into the mysteries of geophysical fluids.
But Marston is an exception. He began his career in condensed matter physics, but he is also curious about climate physics and the behavior of fluids in Earth's oceans and atmosphere.
Marston suspected a connection between geophysical waves and electrons moving in magnetic fields, but he didn't know where to find it until his colleague Antoine Venaille suggested that he look at the equator, and Marston then noticed that the dispersion relation of waves along the equator (which Kiladis had measured) was remarkably similar to that of electrons in topological insulators. similar to that of electrons in topological insulators.
This is where the story begins a second time: with the recent discovery of the quantum behavior of electrons in topological insulators.
In 1980, a quantum physicist named Klaus von Klitzing wondered what the behavior of electrons was when they were frozen in a magnetic field long enough for their quantum properties to be revealed. The electrons would deviate from their direction of motion as they tried to traverse the magnetic field and end up moving in circles; but he didn't know how things would change when he introduced a quantum component.
Von Klitzing froze the electrons to almost absolute zero. As he suspected, at the edges of the material, the electrons completed only half of their circular motion before entering the edge. Then they migrated along the edge, moving in a single direction - their movement along the edge created an edge current.
Von Klitzing found that at ultracold temperatures, when the quantum nature of the electrons becomes relevant, the fringe current is surprisingly robust: it is immune to variations in the applied magnetic field, the disorder of the quantum material, and any other imperfections in the experiment. As a result, he also discovered a phenomenon called the quantum Hall effect.
Over the next few years, physicists realized that the immunity of fringe currents hinted at a now widely accepted concept in physics. An object is said to be "topologically insulating" when it is stretched or squeezed (or otherwise deformed without being destroyed) and its characteristics remain unchanged.
Back to the experiment. When the electrons inside von Klitzing's ultracold material are rotated in a magnetic field, their wave function (a quantum description of their wave nature) is distorted into a shape similar to a Möbius loop. By some trick of physics, the internal topological distortion is transformed into a fringe current that flows without dissipating. In other words, the immunity of the fringe current is a topologically protective property resulting from the internal electronic distortion. Materials like von Klitzing's ultracold samples are now called topological insulators because, although they are insulators on the inside, the topology allows current to flow at their edges.
And when Marston and his colleagues looked at Earth's equatorial Kelvin waves, they saw a regularity that led them to wonder if these waves were analogous to edge currents in topological insulators.
In 2017, Marston, along with physicists Pierre Delplace and Venaille of the Ecole Normale Supérieure in Lyon, France, observed that the Coriolis force rotates fluids on Earth in the same way that a magnetic field rotates the electrons in von Klitzing. In the planetary version of a topological insulator, equatorial Kelvin waves are like currents at the edges of quantum materials.
These huge Kelvin waves propagate around the equator because the equator is the boundary between two insulators (hemispheres). They flow eastward because in the Northern Hemisphere, the Earth's rotation causes the fluid to rotate clockwise; in the Southern Hemisphere, the oceans rotate in the other direction.
Of this achievement, Biello says, "This is the first time that anyone has given a non-trivial answer as to why Kelvin waves exist. In his view, the trio explained the phenomenon using a broad range of fundamental principles, rather than simply balancing terms in mathematical equations."
Venaille even argues that the topological description explains why Kelvin waves at the Earth's equator seem surprisingly powerful, even in the face of turbulence and the planet's erratic weather. "Kelvin waves withstand perturbations just as currents at the edges of topological insulators don't dissipate as they flow, and don't take impurities in the material into account."
El Niño-Southern Oscillation
Despite theoretical studies, the connection between topological systems and Earth's equatorial waves remains indirect. Scientists have seen waves flowing eastward. But they have yet to see anything similar to the internal electron vortex that would be the original source of boundary wave robustness in a quantum system. To confirm that on the largest scales, Earth's fluids behave like electrons in a topological insulator, the team needed to find topological twisting waves farther from the equator.
In 2021, Marston, along with Weixuan Xu, then a student at Brown University, and their colleagues set out to find these distorted waves. To do so, they looked to the Earth's atmosphere, where the Coriolis force churns up pressure waves in the same way it churns up seawater. To find such waves, the team targeted a particular type of wave - Poincaré-gravity waves - that exist in the stratosphere (a region of the atmosphere about 10 kilometers high).
If their theory is correct, the experimental team says, then these distorted topological waves should exist throughout the atmosphere and on the surface of the oceans; it's just that they're most likely to be found in the relatively calm environment of the stratosphere.
They began by combing through the European Center for Medium-Range Weather Forecasts' ERA5 dataset: a collection of atmospheric data from satellites, ground-based sensors, and weather balloons, combined with weather models. From these datasets, the team identified Pangaea-gravity waves. They then compared the height of the waves to the speed of their horizontal motion. When they calculated the offset between the ups and downs of these waves (i.e., the phase between wave oscillations), the scientists found that this 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" (often used in quantum physics, but not often in Earth sciences), they found that the phase spiraled and formed a vortex: the distortion of the wave phase was similar to the wave function of a spiral in a topological insulator - a bit of an abstraction, but that's how it works. -is a bit abstract, but it's exactly the sign they've been looking for.
Theoretical calculations at (a)-(b) low frequencies (Rossby waves) and (c)-(d) high frequencies (Poincaré-gravity waves).
ERA5 data analysis for different cases.
These waves have never been analyzed in this way before and this study is certainly a major breakthrough. It will provide a different perspective on atmospheric waves and will likely lead to new insights.
Now, other scientists are looking for connections between particle motion on the smallest scales and fluid motion on planetary and even larger scales. Researchers are studying topology in fluids ranging from magnetized plasmas to collections of self-propelled particles; Delplace and Venaille are pondering whether the dynamics of stellar plasmas might also resemble those of topological insulators. While these insights may one day help geophysicists better predict the emergence of large-scale weather patterns on Earth, this work is already helping to better understand the role topological structure plays in a variety of systems.
Last December, David Tong, a quantum theorist at the University of Cambridge, studied the same fluid equations as Thomson. This time, however, he examined it from a topological perspective; he ended up linking fluids on Earth to the quantum Hall effect once again, but in a different way - namely, using the language of quantum field theory. Through his work, David Tong was able to explain the existence of the coastal Kelvin waves originally discovered by Thomson.
Together, these ideas, which range from condensed matter to the liquid flowing on Earth, highlight the ubiquity of topology in our physical world.
It is not yet clear whether viewing the Earth as a topological insulator in the big picture will unravel the mysteries of large-scale weather patterns and may even lead to new geophysical discoveries. For now, this is a simple reinterpretation of Earth phenomena. Decades ago, the application of topology to condensed matter was also a reinterpretation of phenomena; von Klitzing discovered the elasticity of fringe currents in quantum materials without realizing that it was related to topology; later, other physicists reinterpreted his discovery as a topological explanation, which eventually revealed a series of new quantum phenomena and phases of matter.
We look forward to more significant advances from similar reinterpretations.
[1]https://www.quantamagazine.org/how-quantum-physics-describes-earths-weather-patterns-20230718/
[2]https://arxiv.org/abs/2306.12191
