Quasiparticles do the twist

Physics often involves hidden surprises in how matter behaves at the smallest scales. A fundamental property in physics is angular momentum, which describes how things spin or rotate, from planets all the way down to particles. Angular momentum is involved in many important effects like magnetism and quantum states that could one day be used in quantum computers.

When atoms vibrate inside crystals, the vibrational energy they release is often found in multiples of discrete values, i.e. they resemble fixed packets of energy. Physicists liken these packets to particles of vibrational energy that they call phonons.

More particularly, a phonon is a kind of emergent particle called a quasiparticle. In 2017, Vijay B. Shenoy, an associate professor at the Centre for Condensed Matter Theory at the Indian Institute of Science, Bengaluru, explained the concept to me in a way I’ve always liked to return to:

The idea of a ‘quasiparticle’ is a very subtle one. At the risk of being technical, let me try this: An excitation is called a particle if, for a given momentum of the excitation, there is a well-defined energy. Quite remarkably, this definition of a particle embodies what we conventionally think of as a particle: small hard things that move about.

Now, to an example. Consider a system made of atoms at a very low density. It will be in a gaseous state. Due to their kinetic energy, the atoms will be freely moving about. Such a system has particle-like excitations. These particle-like excitations correspond to the behaviour of individual atoms.

Now consider the system at a higher density. The atoms will be strongly interacting with each other and, therefore, make up a solid. You will never “see” these atoms as low-energy excitations. There will now be new types of excitations that are made of the collective motion of atoms and which will be particle-like (since there is a well-defined energy for a given momentum). These particle-like excitations are called phonons. Note that the phonon excitation is very different from the atom that makes up the solid. For example, phonons carry sound within a solid – but when the sound propagates, you don’t have atoms being carried from place to place!

A ‘quasiparticle’ excitation is one that is very nearly a particle-like excitation: for the given momentum, it is a small spread of energy about some average value. The manifestation is such that, for practical purposes, if you watch this excitation over longer durations, it will behave like a particle in an experiment…

Recently, physicists predicted that phonons can themselves carry angular momentum the way physical particles like electrons do. They were predicted to do so in materials called chiral crystals, where the atoms are arranged in a spiral structure. However, in spite of the exciting prediction, nobody had directly observed this phonon angular momentum before. Proof was missing in part because measuring something so small and subtle isn’t easy. A new study in Nature Physics finally appears to have fixed this gap, reporting the first direct evidence of the effect using a well-known chiral crystal.

Researchers from Germany and the US designed an experiment with tellurium, an element whose crystals grow in spiral shapes that wind either to the left or to the right. Since phonons are the vibrations inside a crystal, their angular momentum as they travel in curved paths through the crystal can’t be recorded directly. Instead, the researchers surmised that if all the phonons in the chiral crystal added up, they might twist the whole crystal ever so slightly, like a wind-up toy.

So in their experiment, they heated a crystal in an uneven way in order to throw the left‑ and right‑handed phonons off balance, leaving behind a net phonon angular momentum that the whole crystal would have to offset by twisting in the opposite direction.

To test this, the team started by growing small, pure tellurium crystals in the lab, making sure some were single crystals — i.e. with all atoms lining up the same way — and others were polycrystals, consisting of atoms lining up in random orientations. The team assumed that only the pure chiral crystals would show the new effect whereas the polycrystals wouldn’t.

Team members then attached the crystals to minuscule cantilevers. If the crystal twisted even a small amount, the cantilever would bend, and an electrical circuit would detect and amplify the signal. Finally, they created a temperature difference between the two ends of the crystals by shining a small, focused laser light on it. This thermal gradient was expected to allow a net angular momentum to build up, if it was there.

The team ran its tests on both types of crystals, changing the direction of the temperature gradient and running the experiment at different temperatures. In the process the team also ruled out the effects of other forces acting on the crystals, such as expansion due to heating.

When the laser was switched on, the single-crystal tellurium samples showed a clear torque on the cantilevers while the polycrystalline samples didn’t. The torque flipped direction if the temperature gradient was reversed — a smoking gun that it was related to the handedness of the vibrations — and disappeared altogether when the laser was turned off.

The team measured the torque to be an extremely slight 10^-11 N·m, which matched theoretical predictions.

At higher temperatures, even the pure crystals stopped displaying a torque, in keeping with the expectation that the effect only appeared below the Debye temperature — which is the temperature at which a crystal lattice has its highest vibrational quantum energy.

More than the recent theoretical predictions, the research team’s motivation also traced back to an experiment that Albert Einstein and the Dutch physicist Wander Johannes de Haas conducted in 1915. It showed that flipping a magnetic field also made a tiny iron rod twist. Einstein and de Haas explained that this happened because the rod’s electrons had to conserve angular momentum, thus confirming that these particles had this property, an important moment in the history of physics. The researchers behind the new study similarly called what they observed the phonon Einstein-de Haas effect.

Shenoy, however was more measured in his assessment of the new study:

It is, in general, not unusual to have quasiparticles possessing properties of physical particles. Condensed matter physics is replete with examples, such as phonons (discussed here), magnons, density excitations in low dimensions, etc.

What is not usual is the discussion of angular momentum in the context of phonons. As the authors emphasise, this is possible due to the noncentrosymmetric nature of tellurium. The system does not have centrosymmetry (or inversion symmetry): that is, roughly, if you flip [the crystal] ‘inside out’ it looks like an inside out image' rather than itself. An instructive illustration is a mirror image: the mirror image of a circle is a circle (mirror-symmetric), but the mirror image of a right hand is not a right hand. Centrosymmetry is a three-dimensional version of mirror reflection. Broadly speaking, the whole report is not super surprising, but it is interesting that the scientists can measure this.

Many of these physics papers reporting very specialised results make it a point to mention potential future applications of the underlying science. Admittedly, the pursuit of these applications, as and when they come to pass, and the commercial opportunities they create may help to fund the research. However, such speculation in papers also reinforces the idea that studies at the cutting edge are indebted (especially financially) to the future. I don’t agree with that position although I understand its grounding.

For example, this is what the researchers behind the new study wrote in their paper (emphasis added; AM stands for ‘angular momentum’):

… our measurements firmly establish the existence of phonon-AM in chiral crystals. Phonon-AM is the theoretical basis of chiral and topological phonons that may interact with topological fermions to create unique topological quantum states. Phonons can also transfer AM to other fundamental particles and elementary excitations allowing for novel quantum transduction mechanisms, thermal manipulation of spin, and detection of hidden quantum fields. This discovery provides a solid foundation for emergent chiral quantum states and opens a new avenue for phonon-AM enabled quantum information science and microelectronic applications.

And this is what Shenoy had to say about that:

I am not sure that [the finding] will have an immediate technological impact, particularly since this is a very subtle effect that requires very expensive single crystals; my guess is that this will be useful in some very specialised sensor application of some sort in the future. The authors also mention some microelectronics stuff, not sure about that. At this stage, this is firmly in the basic sciences column!