Spontaneous symmetry breaking in electron systems proves elusive

A Fourier transform of an image obtained using scanning tunneling microscopy of electrons on the surface of a crystal of zirconium silicon sulfide, showing the symmetry of the electron system. Reproduced from Ref. 1 and licensed under CC BY 4.0. @ 2025 C. J. Butler et al.

Tiny strains in a crystal can cause electrons to behave in a surprising way that closely resembles a highly sought-after mechanism, RIKEN physicists have found1. Previous studies may need to be re-evaluated in light of this finding.

Symmetry is a hugely important concept in physics because it can greatly simplify the analysis of complex systems. Spontaneous symmetry breaking (SSB) is an area of particular interest to Christopher Butler of the RIKEN Center for Emergent Matter Science.

“SSB is a phenomenon of fundamental importance, underpinning the physics of phase transitions, from the freezing of a liquid to the celebrated Higgs mechanism thought to have conferred mass to all particles in the early Universe,” says Butler.

An example of SSB is a ball perched on top of a perfectly symmetrical hill that starts rolling down the hill. The rolling breaks the initial symmetry of the system despite the law of gravity having no preferred direction.

To gain a better understanding of this key phenomenon, Butler’s team is searching for SSB that emerges in the collective behavior of large numbers of electrons in materials. “Any example of SSB we find in nature will yield profound insights,” Butler says.

At first, his team became highly excited when they thought they had discovered an example of SSB in electrons on the surfaces of crystals of zirconium silicon sulfide using a scanning tunneling microscope.

“We were hugely surprised and excited when we saw the electrons exhibiting wave-like behavior along a preferred axis,” he recalls. “It was like throwing a stone into a pond and observing ripples travelling only left and right, and not in other directions—it seemed like smoking-gun evidence for SSB in a fluid of electrons.”

But then Butler started having doubts. The amount of symmetry breaking varied between samples, which shouldn’t happen if it was due to SSB.

On performing very demanding measurements—monitoring the same 100 or so atoms for ten weeks—the team discovered that the symmetry breaking was due to tiny strains in the crystals introduced during fabrication.

“We found a phenomenon that outwardly resembled SSB but is actually a counterfeit,” says Butler. “The messy realities of real materials (tiny but ubiquitous distortions) contrived to present us with a very convincing fake.”

This effect could be harnessed in devices using strain engineering. But the study also has bigger implications, Butler believes.

“Many findings, including some very high-profile ones, may need to be re-evaluated,” he says. “If some report claims to observe symmetry-breaking electronic behavior, the onus is now to show it’s not simply due to residual strain.”

Undeterred, Butler plans to continue searching for genuine examples of SSB in the fluid of electrons in a crystal. Reference Valley Polarization of Landau Levels in the ZrSiS Surface Band Driven by Residual Strain

Christopher J. Butler, Masayuki Murase, Shunki Sawada, Ming-Chun Jiang, Daisuke Hashizume, Guang-Yu Guo, Ryotaro Arita, Tetsuo Hanaguri, and Takao Sasagawa https://journals.aps.org/prx/abstract/10.1103/PhysRevX.15.011033 RIKEN