Parity anomaly detected in topological insulator

Schematic representation of the device used for the experiment. The re-entrant q
Schematic representation of the device used for the experiment. The re-entrant quantum Hall effect, in which the electrical resistance goes back and forth when the magnetic field is increased, is a signature of the parity anomaly. (Image: Li-Xian Wang / University of Würzburg)
Experimental and theoretical physicists at the Würzburg Institute for Topological Insulators have identified an unusual quantum Hall effect in a mercury telluride device as the signature of the parity anomaly.

Topological insulators are materials that can conduct electricity, but only on their surface or edges. No current flows inside them. They are the subject of intensive research worldwide because they have unique electronic properties that are interesting for improving the efficiency of quantum computers, for example, and for other technologies such as encryption and the secure transmission of data.

In the journal Advanced Science, a research team from the Institute for Topological Insulators and the Institute for Theoretical Physics and Astronomy at Julius-Maximilians-Universität Würzburg (JMU) has now presented an unusual quantum Hall effect. It was observed in a microscopically small device made of the topological insulator material mercury telluride (HgTe).

Clear experimental observation

In the device, the electrons on the upper and lower surfaces behave like relativistic Dirac particles. As predicted by particle physics, but not confirmed experimentally, Dirac particles should be subject to the so-called parity anomaly. In solid-state experiments, this anomaly leads to an effect known as spectral asymmetry, which can be measured as an unusual change in electrical resistance.

The occurrence of the parity anomaly in solids has been predicted since the 1980s. One famous theory is the model proposed by Haldane (Nobel Prize in Physics 2016). We have now identified another consequence of the parity anomaly, which was the first to be verified experimentally," says Ewelina Hankiewicz.

Effect is not specific to mercury telluride

The JMU research team has realized this two-dimensional Dirac physics on a single surface of the three-dimensional topological insulator. "We observe an unconventional re-entrant quantum Hall effect that can be directly linked to the occurrence of spectral asymmetry in a single topological surface state. The effect is not specific to mercury telluride, but general to any topological insulator. This universality is what makes our results so exciting," says Wouter Beugeling.

Two challenges had to be overcome for these new findings. Firstly, the signature of the spectral asymmetry had to be identified among the other features of the measured electrical resistance. Secondly, the experiment had to be controlled in such a way that the effects of the two surfaces did not cancel each other out.

High degree of control enables further experiments

"This observation shows that with the high degree of control we have in this device, we can explore many more interesting aspects of the physics of topological insulators than before," says Laurens Molenkamp.

A key factor in achieving the experimental precision required for this observation was the high quality of the HgTe material produced in the molecular beam epitaxy facility at Würzburg Physics. Molecular beam epitaxy (MBE) is a technique for producing wafer-thin layers of material with customized electronic, optical and magnetic properties. With MBE, layer structures can be precisely built up atom layer by atom layer.


Spectral asymmetry induces a re-entrant quantum Hall effect in a topological insulator. Li-Xian Wang, Wouter Beugeling, Fabian Schmitt, Lukas Lunczer, Julian-Benedikt Mayer, Hartmut Buhmann, Ewelina M. Hankiewicz, and Laurens W. Molenkamp. Advanced Science, early view March 13, 2024, DOI: 10.1002/advs.202307447, Open Access: https://onlinelibrary.wiley.­com/doi/10­.1002/advs­.202307447

Cluster of Excellence ct.qmat

The author and the authors of the publication are members of the Cluster of Excellence ct.qmat - Complexity and Topology in Quantum Matter, which has been jointly funded by Julius-Maximilians-Universität (JMU) Würzburg and Technische Universität (TU) Dresden since 2019. The cluster is funded as part of the Excellence Strategy of the German federal and state governments.