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A twisting mystery of electrons, vibrations and heat

Scientists have observed the thermal Hall effect in insulators, leading to an important open question in condensed-matter physics.

January 22, 2023 09:57 am | Updated January 26, 2023 10:11 am IST - Chennai

Representative illustration.

Representative illustration. | Photo Credit: PIRO4D/Pixabay

High-school physics: When charged particles enter an area where there is a magnetic field, a force deflects them away from their path.

This is how the thermal Hall effect emerges in an electrical conductor: when you apply a temperature gradient in the material in one direction, another temperature gradient appears in a perpendicular direction in the presence of a magnetic field. The electrons in the material carry both electric charges and thermal energy, and the magnetic field deflects them, giving rise to the perpendicular gradient.

But scientists have observed the thermal Hall effect in insulators as well, especially terbium oxides, strontium titanate and twokinds of cuprates. Electrons in insulators aren’t involved in transferring heat or electricity, so what could explain this? This is an important open question in condensed-matter physics.

A leading candidate for an answer involves a particle called the phonon, and a paper published on December 21 advances a new idea: while phonons can’t be deflected by the magnetic field – they have no electric charge – they are affected by the electrons that are deflected by the magnetic field.

Subroto Mukerjee, an associate professor in the Department of Physics, Indian Institute of Science, called the study a “solid piece of work, for sure”. (He wasn’t involved in the study.)

What are phonons?

Technically, phonons aren’t particles; they’re quasiparticles – packets of energy that behave like particles in a system. A phonon is a quasiparticle of vibrational energy. When the grid of atoms that make up the material vibrates, it releases this energy, and physicists encapsulate it in the form of phonons.

In the presence of a magnetic field, electrons are deflected from their paths in a perpendicular direction. The phonons aren’t directly affected by the magnetic field, but when they scatter off the deflected electrons, they are deflected in a perpendicular direction as well.

“The thermal Hall effect arises when the particles carrying energy have chirality, in that they are deviated more clockwise than anticlockwise, or vice versa, in some circumstances,” Léo Mangeolle, a postdoctoral scholar at ENS de Lyon, France, and a coauthor of the new study, told The Hindu.

This lateral scattering mechanism is called skew-scattering. “To see the thermal Hall effect, phonons need to be deflected perpendicular to their direction of motion, so skew-scattering is important,” Dr. Mukerjee said.

The study offers a way to generalise its findings. “Phonons don’t have to be directly deflected by individual electrons; they can also be deflected by the collective properties of electrons, or another kind of organisation of electrons,” Dr Mukerjee explained.

Collective excitations

Mangeolle et al. collected these possibilities as a set of Q fields. These fields are collective excitation fields: “they describe any physical property of a material that is defined at every point in space” – such as electric charge, polarisation, magnetisation, etc. – and which can move around, Dr. Mangeolle explained.

Phonons are an example of collective excitations: “they are essentially a well-defined wave packet” of vibrational energy.

And by working with Q fields, Dr. Mangeolle said, “you can [replace Q] with your favourite object to deduce results in specific materials of interest.”

A potential explanation of the thermal Hall effect in insulators is a notable feat. It will need to be independently confirmed by a different group of researchers. This said, the mechanism proposed in the paper isn’t the only one of its kind and that physicists already know of other ways it’s possible, according to Dr. Mukerjee.

He also said the paper is “probably too technical, too hard” for scientists outside the condensed-matter community “to appreciate what has been done”. He added: “It would have been nice if there had been a couple more physical examples of the actual consequences of their calculations.”

Implications for superconductors

Although the new study doesn’t address superconductivity per se, its point of focus – the way electrons interact with phonons – is bound to trigger some collective excitations in that community.

A material is said to be a superconductor when it offers no resistance to the flow of electric currents. They are sought after for applications in a variety of things, from medical diagnostics to particle accelerators, from sophisticated microscopes to nuclear fusion reactors.

One type of superconductor is the conventional superconductor. It can be explained by the concepts of Bardeen-Cooper-Schrieffer (BCS) theory. In this theory, the phonons in a material nudge the electrons to team up and form pairs, which ‘flow’ smoothly, conducting electricity without any resistance, through the material.

Does this mean electron-phonon interactions could give us insights into the emergence of superconductivity, and lead to the discovery of new superconducting materials?

“Our study shows that the thermal Hall resistivity of the phonons provides quite unobscured access to the magnitude of these couplings, which could provide quantitative insights [into the] mechanisms leading to superconductivity,” Dr. Mangeolle said.

But he stressed on a caveat: “The phonon Hall effect may be dominant only in insulating materials, where electrons are not mobile”. As a result, physicists need to “extrapolate the knowledge about electron-phonon coupling gained in insulators” to “different materials of the same family” that are superconductors.

“This will require some more work.”

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