Physicists from the School of Physics, Trinity College Dublin and the Universidad Complutense of Madrid have made a peculiar discovery in which energy moves from a colder to a hotter region.

They describe how a quantum effect forces current passing through a piece of matter to flow around its edges and sometimes against the typical direction of heat transfer.

The new research – just published in the prestigious journal Physical Review Letters – shows that the counterintuitive current is remarkably robust and arises in a wider class of materials than was previously believed.

This makes it easier to observe in experiments and could eventually inspire new methods for controlling the flow of energy through nanoscale structures, which could have applications in materials science and computing with better performance and sustainability in mind.

Edge currents and topological materials

Robust edge currents typically occur in so-called “topological materials”, named after the mathematical discipline of topology, which classifies shapes and surfaces according to how easily they can be deformed into one another.

For example, a football can be squished into the shape of a rugby ball with enough force (assuming it doesn’t burst), so mathematicians say that the two balls have the same topology. The topology of a ball is called “trivial” because it is so simple.

An example of non-trivial topology is a donut, which cannot be deformed into a ball without ripping it apart due to the hole in the middle. Coffee mugs and kettlebells have the same topology as a donut (because of the hole through their handle) meaning all three shapes can all be continuously deformed into one another without tearing or gluing parts together.

Inside a material, an electron can have many different energies depending on its speed and direction of motion. This landscape of possible energies forms a hypothetical surface whose topology can be either trivial or non-trivial, like a ball, a donut, or even more complex shapes.

The newly described effect

“The existence of edge currents in topologically non-trivial materials has been known and understood for decades,” says Mark Mitchison, Assistant Professor in Trinity’s School of Physics, lead author of the study and PI of the ToCQS group at Trinity“But we didn’t expect to see robust edge currents appear in topologically trivial systems as well.”

Prof. Mitchison and his colleagues from Madrid, Profs. Ángel Rivas and Miguel-Ángel Martin Delgado, showed that this can happen if the system is subject to a temperature gradient, e.g. if one end of the system is hotter than the other.

The circulating edge currents are largely unaffected by defects and, counterintuitively, they transport energy against the temperature gradient in some places. But what about the second law of thermodynamics? Doesn’t this forbid energy from flowing from cold to hot?

“The overall, net transfer of heat is always from the hot to the cold reservoir. The second law of thermodynamics is never violated,” clarifies Prof. Mitchison.

“But locally, on one edge, the current flows in the other direction so a being that lives on that surface would observe very strange physics! The current would be flowing the wrong way from their perspective, almost like watching a movie in reverse.”

Controlling heat flow through small structures is currently a hot topic of research due to its many applications: for example, in the design of more energy-efficient processors or circuit elements for recycling waste heat.

Prof. Mitchison and colleagues now aim to see if similar effects can be engineered in more complex geometries, relevant for real devices.

The paper can be read here.