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Uncovering the Mystery of the Quasicrystal

Some solids, like table salt, are crystalline. This means they’re made of a regularly repeating pattern of atoms. Others, like glass, are amorphous, meaning their atoms are arranged at random. In the middle are curious materials called “quasicrystals.”

A new paper sheds some light on the behavior of these materials. Professor Sarang Gopalakrishnan (College of Staten Island, The Graduate Center) was an author on the study, which appears in Nature Communications.

The atoms that form quasicrystals do have order and patterns, Gopalakrishnan says, but the patterns don’t repeat exactly. However, they are highly structured materials and can have certain types of symmetry. Scientists predicted their existence several decades ago, and have since produced them in laboratories. The only examples seen in nature have been in a rock from a Russian mountain range, which may have crashed to Earth as a meteorite.

Graph showing how apparently random-looking quasicrystalline patterns emerge from sampling a wave at certain fixed intervals.

Plot showing how apparently random-looking quasicrystalline patterns emerge from sampling a wave at certain fixed intervals.

Quasicrystals can have magnetic properties. This happens when the “spins” of all the negatively-charged electrons in the material align. Electron spin is a quantum property and can be thought of as tiny magnetic moments within each particle. Gopalakrishnan and his co-authors wanted to understand what happens in the transition between a quasicrystal’s non-magnetic and magnetic states.

In the new paper, they present a precise mathematical description of this transition in one-dimensional quasicrystals.

“Our work shows that the problem is somewhat simpler than had previously been expected,” Gopalakrishnan said. “Certain mathematical structures, like the Fibonacci sequence, seem to emerge and serve as organizing principles.”

The work has also led to predictions that can be tested in lab experiments, on how the quasicrystalline system’s behavior changes when it gets close to the magnetic transition.

Beyond SUM

Explore This Work

Universality and quantum criticality in quasiperiodic spin chains
Nature Communications, 2020

Work By

Sarang Gopalakrishnan (Assistant Professor, Physics) | Profile 1 | Profile 2