Using High Frequency Electric Circuits to Study Topological Insulators

June 16, 2020 by Luke James

Researchers at the University of Illinois at Urbana-Champaign have found evidence of fractional charges in exotic materials known as topological crystalline insulators.

This is despite the fact that electrons are elementary particles that cannot be split, meaning that fractions of electrical charges are not normally encountered. However, the fractional charges that the Illinois team encountered ranged from e/4 to 2e/3. 

The team, led by professors Gaurav Bahl and Taylor Hughes, has been studying topological insulators since 2017, and their recent discovery of fractional charge stems from theoretical works and research into crystalline insulators. 


Topological Insulators

Topological insulators are crystals with an insulating interior and a conducting surface. Unlike in conducting materials where electrons can jump from one atom to another, the electrons in insulators cannot move. However, topological insulators enable the movement of electrons on their conducting surface while retaining an insulating interior. 

In addition to a conducting surface and insulating interior, topological insulators also have many other interesting properties and we are just now starting to understand them better and realize their potential.

For example, topological insulators have robust conductive channels at their boundaries, which remain in pristine condition even when the material has defects. This could be used to make electronic and optical devices more efficient, by protecting the transmission of electricity or electromagnetic waves, even with manufacturing errors or damage.


A 4-fold symmetric topological circuit.

The 4-fold symmetric topological circuit used in the study. Image credited to Christopher Peterson


A Strange Discovery

Physics professor Taylor Hughes explains, "It may seem strange that fractional charges can even exist, given that electrons are indivisible. But when we are looking at the total charge of the material, we are considering the contributions of many electrons. Depending on how the electronic charges are arranged in space, they may cooperate to leave behind a localized and sharply quantized fraction of charge."


Developing Circuits From Microwave Resonators 

Previous theoretical studies have concluded that the measurement of fractional charges is essential to identify a new class of materials called ‘higher-order topological insulators.’ To search for the signature of these fractional charges experimentally, the Illinois research team created circuits made from microwave resonators, which are devices that absorb electromagnetic radiation at a specific frequency comparable to that of a microwave oven. These resonators act like the atoms within a real material and enable the construction and testing of a wide range of material possibilities. 

This approach was used because at present, it is not possible to build a material atom by atom, and it is often difficult to find naturally occurring materials with the ideal properties for experiments. “Using this approach [building circuits], we can measure how these circuits absorb radiation and use that to calculate how electrons would behave in an analogous solid-state crystal,” said lead author Christopher Peterson. After establishing this new method to measure fractional charges, the research team was also able to develop and demonstrate a new metric to identify high-order topology. 

"The new method of identification that we have demonstrated could allow scientists to unambiguously identify topological insulators of any order, using their fractional charge signature,” said Professor Bahl. According to him, this brings us “closer” to more efficient and robust devices based on topological materials.