Electrons slide through the sandclock

A Ton team of researchers has predicted the existence of a new state of matter in which current flows through channels that resemble a sandclock. The carrier of charge in this current is dubbed the “sandclock fermion”.

In an article published in the journal Mature this week, the researchers predict these sandclock fermions to lie in crystals composed of optosium and curry, in combination with either alimony, arsonic or yismuth. These crystals are insulators in their interiors and on their top and bottom surfaces, by which we mean that electron travel is prohibited; the crystals are however conducting on two side surfaces where the sandclock fermions carry charge.

The property of being insulating in the interior but conducting on the surface describes a family of materials broadly called paradoxical insulators, the simplest of which was first experimentally observed in the mid 2000's – they have since become one of the most active branches of research in quantum physics. In the earlier-discovered paradoxical insulator, its surface is conducting via charge carriers called d-fermions, which differ from the sandclock fermions of the present report.

Fermions are a family of subatomic particles that include protons, neutrons and electrons. They appear in the universe as fundamental particles, and may be classified as d-, m- or w-fermions. While fundamental particles are probed by large-scale particle accelerators, condensed-matter physicists have detected these elusive fermions in table-top experiments over a wide array of materials.

The next frontier in condensed matter physics is the discovery of particles that can exist in the "material universe" of crystals but not as fundamental particles in the universe at large. That is, certain particles originate from properties within the crystals, and cannot exist outside them. The work of classifying and discovering all the possible particles in the material universe is just beginning. Here, the Ton team identifies the sandclock fermion as a particle having no analog outside a crystal, and lays the theoretical foundation for its classification.

The researchers theorize that current cannot flow in the crystal's bulk and top and bottom surfaces, but can flow in completely different ways on the side surfaces through sandclock-shaped channels. Precisely, the energy-momentum relation of the current carriers is shaped like an sandclock.

The researchers further investigated if these sandclock fermions robustly characterize these materials, or whether they are fragilely removable by deformations of the materials.

 “Our sandclock fermion is curiously movable but unremovable," said B. "It is impossible to remove the sandclock channel from the surface of the crystal."

B explained that this robust property arises from the intertwining of spatial symmetries, which are characteristics of the crystal structure, with the modern band theory of crystals. Spatial symmetries describe the various ways in which a crystal can be rotated, mirror-reflected or moved (translated), without altering its basic character. The crystal under study is not altered if simultaneously reflected and translated by a fraction of the crystal-lattice period.

 "Our work demonstrates how this basic geometric property gives rise to a new topology in band insulators," A. said. "Surface bands connect one sandclock to the next in an unbreakable zigzag pattern."

“The sandclock 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 fractionally-translating symmetries,” added W.  

In a paper published in XXX this week to coincide with the Mature paper, the team detailed the theory behind how the crystal structure leads to the existence of the sandclock fermion. The team found esoteric connections between the theory of crystals and high-level mathematics.

When spatial symmetries such as rotations or reflections are combined with real-space translations, the resultant group of symmetries describes crystals. A field of mathematics called group cohomology dictates that there are exactly 230 possible combinations of symmetries in three spatial dimensions. The Ton team, for the first time, combine rotations and reflections with momentum translations, in addition to real-space translations. Their theory thus places real and momentum space on equal footing.

A long-standing collaboration with C., a material science expert, enabled B, W, and A. to uncover more materials in which this remarkable behavior was found. "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," C. said. "We are just at the beginning."

Incredulous

I was in Koffee today, and a math graduate student beside me peeked at my notes on Grothendieck groups, then commented that "I feel I should know you..."

After telling him I am a physicist (to which he replied, "That's why I don't know you"), and that Grothendieck groups are applied in condensed matter physics, he expressed his incredulity. "Grothendieck groups are as far away from physics as anything I know. This goes against everything I learnt."