Some crystal materials boast ‘hourglass’ figure

A team of researchers at Princeton University has predicted the existence of a new state of matter in certain crystal materials that only allows current to flow through a set of surface channels that resemble an hourglass. These channels are created through the action of a newly theorized particle, dubbed the ‘hourglass fermion’, which arises due to a special property of these crystal materials. The tuning of this property can sequentially create and destroy the hourglass fermions, suggesting a range of potential applications such as efficient transistor switching.

In an article published in Nature, the researchers theorize the existence of these hourglass fermions in crystals made of potassium and mercury combined with either antimony, arsenic or bismuth. Known as topological insulators, these crystals are insulators in their interiors and on their top and bottom surfaces, but perfect conductors on two of their sides. Now, the Princeton University researchers propose that this conductivity is due to fermions creating hourglass-shaped channels that permit electrons to flow.

The research was performed by Princeton University postdoctoral researcher Zhijun Wang and former graduate student Aris Alexandradinata, now a postdoctoral researcher at Yale University, working with Robert Cava, professor of chemistry, and B. Andrei Bernevig, associate professor of physics.

Topological insulators were first observed experimentally in the mid-2000s and have since become one of the most active and interesting branches of quantum physics research. Their bulk, or interior, acts as an insulator, which means it prohibits the travel of electrons, but the surface of the material is conducting, allowing electrons to travel through a set of channels created by particles known as Dirac fermions.

Fermions are a family of subatomic particles that include electrons, protons and neutrons, but they also appear in nature in many lesser-known forms such as the massless Dirac, Majorana and Weyl fermions. After years of searching for these particles in high-energy accelerators and other large-scale experiments, researchers found they could detect them in table-top laboratory experiments on crystals. Over the past few years, researchers have used these ‘condensed matter’ systems to first predict and then confirm the existence of Majorana and Weyl fermions in a wide array of materials.

The next frontier in condensed matter physics is the discovery of particles that can exist in the so-called ‘material universe’ inside crystals, but not in the universe at large. Such particles arise due to the properties of the materials and, unlike other subatomic particles, cannot exist outside the crystal. Classifying and discovering all the possible particles that can exist in the material universe is just beginning. The work reported by the Princeton team lays the foundations for one of the most interesting of these systems, according to the researchers.

In the current study, the researchers theorize that the laws of physics prohibit electrons from flowing in the crystal's bulk and top and bottom surfaces, but permit them to flow in a completely different way on the side surfaces through the hourglass-shaped channels. This type of channel, known more precisely as a dispersion, was completely unknown before.

The researchers then asked whether this dispersion is a generic feature found in certain materials or just a fluke arising from a specific crystal model. It turned out to be no fluke.

As part of a long-standing collaboration with Cava, a material science expert, Bernevig, Wang and Alexandradinata were able to uncover more materials exhibiting this remarkable behavior. "Our hourglass fermion is curiously movable but unremovable," said Bernevig. "It is impossible to remove the hourglass channel from the surface of the crystal."

This robust property arises from the intertwining of spatial symmetries, which are characteristics of the crystal structure, with the modern band theory of crystals, Bernevig explained. Spatial symmetries in crystals are distinguished by whether a crystal can be rotated or otherwise moved without altering its basic character.

In a forthcoming paper in Physical Review X, the team detail a theory that explains how the crystal structure leads to the existence of the hourglass fermion. "Our work demonstrates how this basic geometric property gives rise to a new topology in band insulators," Alexandradinata said. The hourglass is a robust consequence of spatial symmetries that translate the origin by a fraction of the lattice period, he explained: "Surface bands connect one hourglass to the next in an unbreakable zigzag pattern."

The team found esoteric connections between their system and high-level mathematics. Origin-translating symmetries, also called non-symmorphic symmetries, are described by a field of mathematics called cohomology, which classifies all the possible crystal symmetries in nature. For example, cohomology reveals that the number of different crystal types that exist in three spatial dimensions is 230.

"The hourglass theory is the first of its kind that describes time-reversal-symmetric crystals, and moreover, the crystals in our study are the first topological material class which relies on origin-translating symmetries," added Wang.

From the cohomological perspective, there are 230 ways to combine origin-preserving symmetries with real-space translations, known as ‘space groups’. The theoretical framework to understand the crystals in the current study requires a cohomological description with momentum-space translations.

Out of the 230 space groups in which materials can exist in nature, 157 are non-symmorphic, meaning they can potentially host interesting electronic behavior such as the hourglass fermion. "The exploration of the behavior of these interesting fermions, their mathematical description, and the materials where they can be observed, is poised to create an onslaught of activity in quantum, solid state and material physics," Cava said. "We are just at the beginning."

This story is adapted from material from Princeton University, with editorial changes made by Materials Today. The views expressed in this article do not necessarily represent those of Elsevier. Link to original source.