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Electrons in two-dimensional (2D) systems placed under strong magnetic fields often behave in unique ways, prompting the emergence of so-called fractional quantum Hall liquids. These are exotic states of matter in which electrons behave collectively and form new quasiparticles carrying only a fraction of an electron's charge and obeying unusual quantum statistics.

In the 1990s, physicists introduced a theory known as the chiral Luttinger liquid theory, which describes the collective movements of these fractional excitations moving in 1D channels along the boundary of 2D fractional quantum Hall states. Nonetheless, past experimental findings were not always aligned with theoretical predictions.

Researchers at Purdue University recently carried out a study aimed at further testing some of the predictions of chiral Luttinger liquid theory by measuring tunneling between 1D edge modes in a device in which a fractional quantum Hall liquid state emerges. Their paper, in Nature Â鶹ÒùÔºics, offers direct experimental evidence of universal anyon tunneling for the n=1/3 fractional quantum Hall state, confirming theoretical predictions made by X. -G. Wen and collaborators in the early 1990s.

"For several years now, my group has used Fabry-Pérot interferometers to measure fractionalized charge and anyon braiding statistics in the fractional quantum Hall regime," Michael Manfra, senior author of the paper, told Â鶹ÒùÔº.

"Quantum point contacts are the 'beam splitters' in an electronic Fabry-Perot interferometer. We began to think about what else we could measure with these devices. It turns out that the edge modes circulating around the boundary of a fractional quantum Hall effect state are best described as a 'chiral Luttinger liquid'—a one-dimensional strongly interacting electron liquid first theoretically understood by the theorist X.-G Wen."

Chiral Luttinger liquids have various unusual properties that set them apart from well-known Fermi liquids. One of the most notable is that while in normal ohmic resistors current increase linearly in relation to the applied voltage, in a chiral Luttinger liquid the link between current and voltage is nonlinear and is described by a so-called power law.

"One of the predictions of Wen's chiral Luttinger liquid theory concerned tunneling between two counterpropagating edge modes," explained Manfra. "He predicted that for a chiral Luttinger liquid associated with a fractional quantum Hall state with filling factor n=1/3, the tunneling conductance should be described by a scaling exponent g=n=1/3 when two counterpropagating edge modes are brought into proximity."

While chiral Luttinger liquid theory dates back to the early 1990s, the experiments conducted since then were unable to conclusively confirm its predictions. Manfra and his colleagues tried to fill this gap in the literature by measuring tunneling in a newly designed heterostructure.

"Our idea was that our new heterostructure design may overcome a major challenge with demonstration of chiral Luttinger liquid properties, namely soft edge mode confinement that leads to edge reconstruction and non-ideal behavior," said Manfra.

"Our design has proven crucial to the demonstration of anyonic braiding statistics, so we thought it may also help with edge mode tunneling experiments as well. We thought it was time to revisit this problem with new materials in hand. This was just a speculation one year ago, but it turned out to be a good guess."

To conduct their experiments, the researchers used a quantum point contact, a structure that consists of two narrow metallic gates that come within 300 nm from each other. This structure allowed them to bring two counterpropagating modes of the n=1/3 fractional quantum Hall state into close proximity.

"When this is done, anyons can tunnel from one edge to the other edge, generating a tunneling current that we can measure with sensitive amplifiers," explained Manfra. "By studying the voltage and magnetic field dependence of the tunneling conductance, we were able to establish that the scaling exponent is g=1/3, as predicted by Wen's chiral Luttinger liquid theory. These experiments required us to measure very small currents (~ 1 picoAmp) at milliKelvin temperatures and high magnetic field (B~10Tesla)."

The researchers performed their measurements in a dilution refrigerator, a special cooling device that can reach extremely low temperatures and was especially configured for the purpose of their study. A unique feature of the samples they used is that they followed a newly introduced 'screening well' heterostructure design. This design ultimately leads to sharp edge confinement, making chiral Luttinger liquid properties observable experimentally.

"With this experiment we have demonstrated that the topological order responsible for quantization of the bulk fractional quantum Hall state may be completely determined using a Fabry-Pérot device," said Manfra. "We have now measured the scaling exponent, anyon charge, and anyonic braiding statistics in a single device platform. This completely specifies the topological order at n=1/3."

This recent study has opened new possibilities for the study of fractional quantum Hall liquids and for testing theoretical predictions that have not yet been conclusively validated. In the future, Manfra and his colleagues hope to use the same experimental methods to study other interesting states, such as the putative non-abelian state at n=5/2.

"I hope that our device architecture will be applied to other interesting material systems to explore states not found in the GaAs-based heterostructures studied in our experiment," added Manfra. "It would be cool if the 2D material community or the quantum spin liquid community leverages the concepts outlined in our paper.. In fact, we are already seeing this happen in graphene. Some beautiful interference and tunneling experiments are now down in graphene in the groups of Andrea Young at UCSB and Philip Kim at Harvard."