Researchers at Cornell University have used magnetic imaging to directly observe for the first time how electrons flow in a special type of insulator, allowing them to discover that the transport current flows through the interior of the material and not around the edges, as scientists have long assumed.

The discovery sheds light on electron dynamics in quantum anomalous Hall insulators and helps resolve a decades-long debate about how current flows in more general quantum Hall insulators. These insights will inform the development of topological materials for next-generation quantum devices.

The research team's paper was recently published in the journal Nature Materials. The first author of the paper is Matt Ferguson, a Ph.D. for 22 years and currently a postdoctoral researcher at the Max Planck Institute for Solid State Chemical Physics in Germany.

Quantum Hall Effect

The project, led by Katja Nowack, assistant professor of physics in the College of Arts and Sciences and senior author of the paper, originated from what is known as the quantum Hall effect. The quantum Hall effect, first discovered in 1980, causes an unusual phenomenon when a magnetic field acts on a specific material: the inside of a bulk sample becomes an insulator, while electric current moves in one direction along the outer edge. Resistance is quantized, or restricted, to a value defined by a fundamental universal constant, and drops to zero.

Quantum anomalous Hall insulators, first discovered in 2013, achieve the same effect by using magnetized materials. Quantization still occurs, longitudinal resistance disappears, and electrons accelerate along the edge without dissipating energy, somewhat like a superconductor.

Break popular notions

"The picture of current flowing along an edge is a good explanation of how quantization occurs. But it turns out that's not the only picture that can explain quantization," Novak said. "This edge picture has dominated since the spectacular rise of topological insulators at the beginning of this century. The complexity of local voltages and local currents has been largely forgotten. In fact, these situations may be much more complex than the edge picture suggests."

Only a few materials are currently known to be quantum anomalous Hall insulators. In their new work, Nowak's team focused on chromium-doped bismuth antimony telluride - the same compound that was first observed to have the quantum anomalous Hall effect a decade ago.

The sample was grown by collaborators led by Penn State physics professor Nitin Samart. To scan the material, Nowak and Ferguson used their lab's Superconducting Quantum Interference Device (SQUID), an extremely sensitive magnetic field sensor that can operate at cryogenic temperatures and detect the dauntingly tiny magnetic fields. SQUID effectively images the current flow (which is responsible for the magnetic field) and then combines these images to reconstruct the current density.

"The currents we were studying were very, very small, so they were difficult to measure," Novak said. "We needed to have good quantification of the sample at temperatures below one kelvin. I'm proud that we did that."

Discovery and future impact

When the researchers noticed that electrons flowed in the bulk of the material, rather than at the edges, they started looking at previous findings. They found that in the years after the quantum Hall effect was first discovered in 1980, there was a lot of debate about where the electron flow occurred, a debate that most young materials scientists were unaware of.

"I hope that the new generation working on topological materials will take notice of this work and reopen the debate. It's clear that we don't even understand some very fundamental aspects of what happens in topological materials," she said. "If we don't understand how electricity flows, what do we really know about these materials?

Answering these questions may also be relevant to making more complex devices, such as hybrid techniques that couple superconductors with quantum anomalous Hall insulators to create more exotic states of matter.

"I'd be interested to know if the phenomena we observed apply to different material systems. Maybe in some materials, the current flows differently," Novak said. "To me, this highlights the fascination of topological materials - their behavior in electrical measurements is determined by very general principles, independent of microscopic details. However, understanding what is happening at the microscopic scale is crucial, both for our fundamental understanding and for applications. This interplay of general principles and nuances is what makes the study of topological materials so fascinating and fascinating."