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Researchers at Purdue demonstrate bulk-edge coupling of anyons



Professor Michael Manfra (left) and Dr. James Nakamura (postdoc and lead author) were able to quantify the impact of bulk-edge coupling on anyonic braiding and measure in new regimes of interferometer operation.  Photo by Vincent Walter


In July of 2020, exciting news was reported: a team of researchers had discovered strong  evidence for fractional statistics of anyons, a quasiparticle thought to exist at the time, but never proven until observed in the lab of Dr. Michael Manfra, Bill and Dee O’Brien Distinguished Professor of Physics and Astronomy, Professor of Electrical and Computer Engineering, and Professor of Materials Engineering at Purdue University.  Now this team of researchers has built on that discovery by designing devices to probe anyon physics over a broad range of parameters, paving the way for future designs and more complex manipulation of anyons. They demonstrated fine control of bulk-edge coupling, how anyons at the edge of the interferometer interact with anyons in the interior of the interferometer, which will be important for designing future experiments probing more complex non-Abelian anyons.

So what exactly is an anyon? Dr. James Nakamura, postdoc and lead author working with Manfra, explains that anyons are a quasiparticles which are categorized as neither bosons or fermions.  He says, “all fundamental particles can be categorized as bosons or fermions. These classes of particles are distinguished by the quantum mechanical phase that occurs when the positions of two particles is exchanged: for bosons the phase is zero, while for fermions it is π. Anyons are a type of quasiparticle that can emerge from systems of many electrons which are neither fermions nor bosons, but have a phase that is a fractional value of π -  2π/3 in the case of the anyons measured in our experiment.”

Now that this team has proven the existence of anyons, they are tasked with learning more about anyonic behavior.  On Monday, they published “Impact of bulk-edge coupling on observation of anyonic braiding statistics in quantum Hall interferometers” in Nature Communications where they outline new breakthroughs they’ve discovered in this exciting new science.

The team is comprised of Manfra, Nakamura, Shuang Liang (graduate student), and Geoffrey Gardner (researcher with the Microsoft Quantum Lab West Lafayette).  Manfra is the director of the Microsoft Quantum Lab West Lafayette.

In this publication, the team provides confirmation of previous results where anyons could be observed, but more importantly, demonstrate rational design and control of interferometers to explore different aspects of the physics of anyons. This is an ongoing field of research for the team and follow-up research is expected for years to come.   With this publication, the team was able to directly observe anyonic statistics in both the incompressible and compressible regimes of the n=1/3 fractional quantum Hall state. They also quantified the impact of bulk-edge coupling on anyon visibility and provide evidence that the anyons at the edge of device form a strange 1-dimensional liquid known as a Luttinger liquid.

“This paper extends our previous work detecting the anyonic phase by making the interferometer (the device used to measure phase) smaller, which makes the anyon quasiparticles more strongly confined inside the interferometer,” says Nakamura. “This has improved how precisely we are able to detect the anyonic phase because the interferometer signal is not degraded by the number of anyons inside the interferometer fluctuating, which allowed us to measure over a wider range of magnetic field.”

Theoretical physicists have predicted how electrostatic coupling between anyons inside the interferometer (known as “in the bulk”) and the charge at the edge of the interferometer will alter the phase detected by interferometer.

“Through conductance measurements we were able to determine the size of this bulk-edge coupling, and we determined that the anyonic phase jumps measured by the interferometer were shifted by the amount predicted by the theorists,” furthers Nakamura. “This provides validation for that theoretical work and paves the way for future designs and more complex manipulation of anyons.”

In the graphic depiction above, anyonic behavior is demonstrated.  In figure a, the quantum Hall interferometer is displayed with yellow depicting metal gates used to define the interference path, blue depicts the 2DES. A center gate in the middle has been kept grounded and does not affect the 2DES density.  The red path indicates the edge state trajectories and backscattering paths are shown by dashed lines.  In figure b, bulk Rxy measurement showing the ν = 1/3 conductance plateau.  The approximate positions in magnetic field where the interferometer transitions from negatively sloped Aharonov-Bohm behavior to flat lines of constant phase with Φ0 modulations are marked with dashed lines. Figure c, depicts interference at v = 1/3 at the mixing chamber temperature of 10 mK.  Near the center are several discrete jumps in phase which are associated with the removal of quasiparticles localized by disorder in the interior of the interferometer.  At high and low field, the lines of constant phase become nearly independent of magnetic field, but modulations with period approximately Φ0 can be seen. These modulations are more prominent in the high-field region, particularly close to the transition point at approximately 7.7 T.


A technical challenge of this research was that, theoretically, if there is a strong electrostatic interaction between anyons inside the interferometer and the charge at the edge of the interferometer (i.e. bulk-edge coupling), it would be impossible for the interferometer to measure the anyonic phase. This technical challenge had to be overcome in order to conduct these experiments.  The team achieved reducing the bulk-edge coupling by growing a semiconductor structure with screening layers above and below the interferometer, which screen out the electrostatic interaction and reduce the bulk-edge coupling. They were then able to determine the value of the small amount of bulk-edge coupling that remained after adding the screening layers, which will be important for designing future experiments.  

“Theoretical physicists predict that there are different types of anyons called ‘non-Abelian’ anyons.  If the statistical properties are demonstrated, these types of anyons could be used to achieve a robust form of quantum computing called ‘topological quantum computing,’” says Nakamura. 

Although this discovery is considered basic science, the study of anyons is central to concept of topological quantum computing.  Their work with anyons may serve as a bridge to discovery of non-Abelian anyons because they have now demonstrated how the defining property of anyons, unusual statistics, can be detected in an interferometer.

Because of the collection of research specialists and facilities, Purdue University is poised to be at the forefront of this type of discovery.  Nakamura explains that “possibly most critical is the molecular beam epitaxy (MBE) machine used to grow the specific gallium arsenide (a very high-quality semiconductor) structure used for the interferometers. This MBE is owned and operated by Prof. Manfra’s academic research group, and this system produces some of the highest quality gallium arsenide material in the world.”  He goes on to say that Purdue has extensive nanofabrication facilities in the Birck Nanotechnology Center which make it possible to build the interferometer from the starting semiconductor material. Additionally, the Manfra group has extensive low-temperature measurement systems which are needed to measure the anyonic phase in the interferometers. Having all three of these critical elements (the MBE, nanofabrication facility, and low-temperature measurement equipment) on one campus made this research possible. 

This work is supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under award number DE-SC0020138. 


Contact: Michael Manfra

Writer: Cheryl Pierce

Photo credit: Vincent Walter Photography

Graphic credit: Michael Manfra and James Nakamura



Last Updated: Jan 18, 2022 2:04 PM

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