Heat capacity measurements reveal Majorana fermions.

08 Apr 2024 Isabelle Dumé

In the lab The evidence for Majorana fermions appeared in the thermodynamic behaviour of a so-called Kitaev magnet. (Courtesy: T Shibauchi)

Researchers in Japan and Korea claim to have found “conclusive evidence” for the existence of theoretically-proposed particles called Majorana fermions. The evidence for these long-sought-after particles appeared in the thermodynamic behaviour of a so-called Kitaev magnet, and the researchers say their observations cannot be explained by alternative theories.

Majorana fermions are named after the Italian physicist Ettore Majorana, who predicted their existence in 1937. These particles are unusual in that they are their own antiparticles, and in the early 2000s, the theoretical physicist Alexei Kitaev predicted that they could exist in the form of quasiparticles made up of two paired electrons.

These quasiparticles are known as non-Abelian anyons, and one of their main attractions is that they are robust to external perturbations. Specifically, Kitaev showed that, if used as quantum bits (or qubits), certain states would be “topologically protected”, meaning that they can’t be randomly flipped by external noise. This is important because such perturbations are one of the main stumbling blocks to making a practical, error-resistant quantum computer.

Kitaev later proposed that these Majorana states might be engineered as electronic defect states that occur at the ends of quantum nanowires made from a semiconductor located near a superconductor. Much subsequent work has therefore focused on looking for Majorana behaviour in semiconductor-superconductor heterostructures.

A different approach

In the latest study, researchers led by Takasada Shibauchi of the Department of Advanced Materials Science at the University of Tokyo, Japan, together with colleagues at the Korea Advanced Institute of Science and Technology (KAIST), took a different approach. Their work focuses on a material called α-RuCl3, which is a potential “host” for Majorana fermions because it may belong to a class of materials known as Kitaev spin liquids (KSLs).

These materials are themselves a subtype of quantum spin liquids – solid magnetic materials that cannot arrange their magnetic moments (or spins) into a regular and stable pattern. This “frustrated” behaviour is very different from that of ordinary ferromagnets or antiferromagnets, which have spins that point in the same or alternating directions, respectively. In QSLs, the spins constantly change direction in a fluid-like way, even at ultracold temperatures.

To qualify as a KSL, a material must have a perfect (exactly solvable) two-dimensional honeycomb-shaped lattice, and the spins within this lattice must be coupled via unusual (Ising-type) exchange interactions. Such interactions are responsible for the magnetic properties of everyday materials such as iron, and they occur between pairs of identical particles such as electrons – with the effect of preventing the spins of neighbouring particles from pointing in the same direction. KSLs are thus said to suffer from “exchange-coupling” frustration.

In α-RuCl3, which has a layered honeycomb structure, each Ru3+ ion (with an effective spin of -1/2) has three bonds. Shibauchi and colleagues explain that a cancelation of interactions between the two shortest Ru-Cl-Ru 90° paths leads to Ising interactions with the spin axis perpendicular to the plane that includes these two paths.

“The hallmark of Majorana excitations”

In their experiments, the researchers measured the heat capacity of a single crystal of α-RuCl3 using a state-of-the-art high-resolution setup. This setup was contained in a dilution refrigerator equipped with a piezo-based two-axis rotator and a superconducting magnet that applies a rotating magnetic field to the sample’s honeycombed plane. These measurements revealed a topological edge mode in the material with a very peculiar dependence on the magnetic field angle. Specifically, the researchers found that at very low temperatures, the material’s heat capacity (a thermodynamic quantity) shows gapless excitations that change to gapped ones when the angle of the magnetic field is tilted by just a few degrees. This dependence on field angle is, they say, is characteristic of Majorana quasiparticle excitations.

“This is the hallmark of Majorana excitations expected in the spin liquid state, which was theoretically formulated by Kitaev in 2006,” Shibauchi tells Physics World. “We believe that this cannot be explained alternative pictures and thus provides conclusive evidence for these excitations.”

Shibauchi acknowledges that previous results of such measurements have been controversial because researchers found it hard to tell whether a phenomenon known as the half-integer quantum Hall effect – a signature of the Majorana edge mode – appeared or not. While some samples showed the effect, others did not, leading many to believe that a different phenomenon might be responsible. However, Shibauchi says the team’s novel approach, focusing on the angle-dependent gap closing feature specific to Majorana excitations, “addresses these challenges”.

Still a long road ahead

According to the researchers, the new results show that Majorana fermions can be excited in a spin liquid state of a magnetic insulator. “If one can find a way to manipulate these new quasiparticles (which will not be an easy task, that said), fault-tolerant topological quantum computations may be realized in the future,” Shibauchi says.

In their work, which is detailed in Science Advances, the researchers needed to apply a relatively high magnetic field to achieve the Kitaev spin liquid state that hosts the Majorana behaviour. They are now looking for alternative materials in which the Majorana state might appear at lower, or even zero, fields. Emilio Cobanera, a physicist at the SUNY Polytechnic Institute in New York who was not involved in the study, agrees that such materials are possible.READ MORE

Majorana modes continue to elude

“Thanks to the detective work of Shibauchi and colleagues, we can add to the list the layers of the stable phase of RuCl3 with confidence, and perhaps we are finally developing the experimental techniques and ingenuity to reveal anyons in many other materials,” he says. “In their work, the team had to differentiate between two exotic scenarios: the physics of the Kitaev honeycomb model on one hand, an exactly solvable model of anyons, and another piece of new physics, magnons associated to topologically non-trivial band structures.”

Cobanera points out that, as Shibauchi and colleagues themselves note, these two scenarios would yield very different predictions for the behaviour of the thermal Hall conductance under changes in direction of an applied, in-plane magnetic field. They therefore followed this observation with state-of-the-art mesoscopic thermal measurements that, Cobanera says, are clearly inconsistent with a magnonic explanation and support semi-quantitatively the scenario with anyons.

Isabelle Dumé is a contributing editor to Physics World

from physicsworld.com   9/4/2024