# A quest for symmetry: Purdue physicists discover symmetry in the Wigner solid

**2021-09-16**

###### Sean Myers, Physics and Astronomy graduate student, assembles the cryogenic instrument in preparation for an experiment. Photo provided by Gábor Csáthy

An exciting and expanding branch of physics research involves topological properties in electronic systems. The physics community has placed particularly large efforts on investigating topological properties which involve electron-electron interaction. There is an ongoing quest to see if two-dimensional topological matter displays a fundamental link, or symmetry, between the stability regions of the electronic phases. This symmetry is commonly referred to by physicists as “particle-hole symmetry.”

According to Gábor Csáthy, Professor and Interim Head at Purdue University Department of Physics and Astronomy, particle-hole symmetry was already discovered and known in the fractional quantum Hall regime, but his lab has recently published “Particle-hole symmetry and the reentrant integer quantum Hall Wigner solid” in Communications Physics in which they have discovered that this symmetry also applies to the Wigner solid.

“A well-known example of a topological system in which correlated insulators and topological states compete is the two-dimensional electron gas hosted in the GaAs/AlGaAs material system,” says Csáthy. “At the largest magnetic fields, i.e. the lowest filling factors, the most studied correlated insulator, the Wigner solid, develops. The Wigner solid is known to compete with the n=1/5 fractional quantum Hall state, by straddling this topological state.”

The results obtained in Csáthy’s lab indicate that Wigner solids in the GaAs/AlGaAs system straddle other filling factors, such as n = 2+1/5 and n = 2-1/5. Therefore, particle–hole symmetry of the Wigner is more pervasive than previously thought, and that this symmetry leads to competing Wigner solids and fractional quantum Hall states in unexpected parts of the phase diagram.

This finding was published with equal contributions to the measurement process at Purdue University by Csáthy and graduate students Vidhi Shingla and Sean A. Myers. The GaAs/AlGaAs system is especially relevant in that in has a very low number of defects and therefore supports an astonishing variety of electronic phases. The material for these experiments was grown by collaborators Kirk Baldwin and Loren Pfeiffer at Princeton University.

With the expansion of the family of correlated insulators, the competition of topological states and collective insulators is actively investigated in several systems. Some examples are the electronic bubble phases, stripe phases, and solids formed of composite fermions, the basic building blocks of the fractional quantum Hall states. According to Csáthy, the fundamental properties of these collective insulators as well as their completion with topological phases is under investigation in several labs, so the quest for guiding principles on their formation soldiers on across the physics landscape.

“Many of the secrets of topological materials are still unlocked, so at this stage we try learning about basic properties. Any possible applications of these materials for dissipationless energy transport or in quantum information processing will have to take into account the competition of topological phases with collective insulators.”

Source: Gábor Csáthy

Writer: Cheryl Pierce

*Last Updated*: Sep 16, 2021 1:12 PM