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Crystals possessing “handedness” exhibit unusual properties. New evidence suggests that they can host electrons moving like slowed down light and their collective behavior mimics magnetic monopoles.
Image Caption: This image shows a repeated 2-D pattern of a surface Fermi arc in rhodium-silicon crystal samples. Images by the Hasan Lab, Princeton University
An international team of researchers has discovered that certain classes of crystals with an asymmetry like biological “handedness,” known as chiral crystals, may harbor electrons that behave in unexpected ways.
“Before our work, quantum-level properties of electrons in chiral crystals were rarely studied,” said M. Zahid Hasan, the Eugene Higgins Professor of Physics at Princeton University, who led the research. “This decisive work opens up a new continent for explorations in topological materials.”
Chirality, also known as handedness, is a physical property common to all objects that cannot be superimposed on their mirror image. It manifests in everyday objects such as gloves, shoes, screws and multi-level parking garages. Chiral crystals are of great interest to physicists due to their magnetic, optical, conducting and especially their topological properties. In 2016, Duncan Haldane, Princeton’s Sherman Fairchild University Professor of Physics, won the Nobel Prize in Physics for his theories predicting the properties of topological materials.
“The topological properties of matter have emerged as one of the most sought-after treasures in modern physics,” said Hasan, “both from a fundamental point of view and for finding potential applications in next-generation quantum and nanotechnologies.”
Left: This image shows how the electrons are distributed on the surfaces of topological chiral crystals. The extended threads along the diagonal are the “Fermi arc” quantum states revealing the topological behavior of the electrons. The surface Fermi arc is a property that defines topological conductivity — related to the electrical conductivity of the material’s surface — which in these topological chiral crystals was about 100 times larger than that observed in previously identified topological metals. Right: These 3-D images of electron distribution within topological chiral crystals show the helicoid arc quantum state patterns.
In an October 2018 article, Hasan’s team proposed a theory that bridged the gap between the physical chirality of crystals and how electrons behave in those crystals, both quantum mechanically and according to the mathematical laws of topology. The researchers were surprised to discover that all non-magnetic chiral crystals share a universal topological quantum property: all of their electronic structures feature band-touching points governed by the Weyl equation, a quantum equation of motion. Physicist Hermann Weyl predicted such behavior of particles while at Princeton in 1929.
Now, by using the group theory of crystals, Hasan’s team has determined that chiral crystals are capable of hosting novel forms of Weyl fermions — electrons that collectively behave as if they are massless — which they have dubbed “chiral fermions.” The team applied these ideas to chiral crystals and found unexpected results regarding their electronic, optical and topological behaviors, prompting the name “topological chiral crystals.” The researchers were further surprised to find that these topological chiral crystals can exhibit unique phenomena such as large Fermi arcs and electron spins that collectively behave like magnetic monopoles.
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