Direct evidence for universal Anyon tunneling in a Luttinger chiral liquid revealed in an edge-mode experiment

Electrons in two-dimensional (2D) systems placed under strong magnetic fields often behave in unique ways, causing the emergence of what are 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 the charge of an electron and obeying unusual quantum statistics.

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

Researchers at Purdue University recently conducted a study to further test some of the predictions of Luttinger’s chiral liquid theory by measuring tunneling between 1D edge modes in a device in which a fractional quantum Hall liquid state emerges. Their article, published in Natural physicsoffers direct experimental proof of universal Anyon tunneling for the fractional quantum Hall state n = 1/3, confirming the theoretical predictions made by X.-G. Wen and colleagues in the early 1990s.

“For several years now, my group has used Fabry-Pérot interferometers to measure fractional charge and anyon braiding statistics in the fractional Hall quantum regime,” Michael Manfra, lead author of the paper, told Phys.org.

“Quantum point contacts are the ‘beam splitters’ in an electronic Fabry-Perot interferometer. We started thinking about what else we could measure with these devices. It turns out that the edge modes flowing around the boundary of a fractional quantum Hall effect state are best described as a ‘chiral Luttinger liquid’ – a strongly interacting one-dimensional electronic liquid theoretically understood for the first time by theorist X.-G Wen. “

Luttinger chiral liquids have various unusual properties that distinguish them from the well-known Fermi liquids. One of the most notable is that, while in normal ohmic resistors the current increases linearly with respect to the applied voltage, in a chiral Luttinger liquid the relationship between current and voltage is nonlinear and is described by the so-called power law.

“One of the predictions of Wen’s Luttinger chiral liquid theory was about tunneling between two counter-propagating edge modes,” Manfra explained. “He predicted that for a Luttinger chiral liquid associated with a fractional quantum Hall state with a filling factor n = 1/3, the tunneling conductance should be described by a scaling exponent g = n = 1/3 when two counter-propagating edge modes are brought together.”

While Luttinger’s chiral theory of liquids dates back to the early 1990s, experiments since have failed to conclusively confirm his predictions. Manfra and colleagues attempted to fill this gap in the literature by measuring tunneling in a newly designed heterostructure.

“Our idea was that our new heterostructure design could overcome a major challenge by demonstrating the chiral properties of Luttinger liquid, namely soft-edge confinement that leads to edge reconstruction and non-ideal behavior,” Manfra said.

“Our design proved crucial in demonstrating the statistics of anyonic braiding, so we thought it could also help in edge-mode tunneling experiments. We figured it was time to revisit this problem with new materials in hand. This was just a speculation a year ago, but it turned out to be a good guess.”

To conduct their experiments, the researchers used a quantum point contact, a structure composed of two narrow metal gates 300 nm apart. This structure allowed them to bring together two counter-propagation modes of the fractional quantum Hall state n = 1/3.

“When this is done, anyone can pass from one edge to the other, generating a tunneling current that we can measure with sensitive amplifiers,” Manfra explained. “By studying the dependence of the tunnel conductance on voltage and magnetic field, 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 a high magnetic field (B~10 Tesla).”

The researchers carried out their measurements in a dilution refrigerator, a special cooling device that can reach extremely low temperatures and was specially configured for the purposes of their study. A unique feature of the samples they used is that they followed a novel “screening well” heterostructure design. This design ultimately leads to sharp-edged confinement, making the chiral properties of the Luttinger liquid observable experimentally.

“With this experiment, we demonstrated that the topological order responsible for quantifying the global fractional quantum Hall state can be completely determined using a Fabry-Pérot device,” said Manfra. “We have now measured the scaling exponent, anyonic charge, and anyonic braiding statistics on 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 materials community or the quantum spin liquid community exploited the concepts described in our paper. In fact, we already see this happening in graphene. Beautiful interference and tunneling experiments are now underway in graphene in the groups of Andrea Young at UCSB and Philip Kim at Harvard.”

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