In a landmark achievement for condensed matter physics, an international team of researchers has captured the first direct, unambiguous evidence of universal tunneling for anyons, exotic quasiparticles that exist only in two-dimensional systems. The experiment, conducted on a specially designed semiconductor heterostructure, confirms a foundational, decades-old theoretical prediction about the behavior of these strange particles, resolving long-standing questions about the nature of quantum transport at the edges of fractional quantum Hall liquids. This work provides the final piece of experimental proof needed to fully characterize the topological order of this bizarre state of matter.
The discovery centers on demonstrating that the process of anyons tunneling across a barrier follows a universal scaling law, meaning its behavior is consistently described by a single exponent regardless of variables like temperature or the barrier’s transparency. For years, experimental results failed to align with theoretical predictions, but by engineering an extremely clean and sharp confining potential, the team successfully measured a tunneling exponent of 0.333, in precise agreement with theory. This breakthrough, combined with recent measurements of the anyon’s fractional charge and unique braiding statistics, completes a triad of evidence that solidifies our understanding of one of the most enigmatic phases of matter ever discovered.
A Third Kingdom of Particles
In the quantum world, all known fundamental particles fall into one of two categories: fermions or bosons. Fermions, such as electrons, are staunchly individualistic, refusing to occupy the same quantum state—a principle that gives rise to the structure of the periodic table. Bosons, like the photons that constitute light, are more social and can happily bunch together in the same state. For decades, this binary classification was thought to encompass all of nature’s building blocks. However, in the 1980s, theorists including Nobel laureate Frank Wilczek conceived of a third possibility, which he whimsically named the “anyon.”
Anyons are not fundamental particles found in the vacuum of our three-dimensional universe. Instead, they emerge as collective excitations of electrons trapped in a two-dimensional plane under extreme conditions of cold and powerful magnetic fields. What makes them unique is their “in-between” nature. Their most famous characteristic is their response to “braiding”—the act of looping one anyon around another. While performing this action on identical fermions or bosons leaves no lasting trace, braiding anyons alters their collective quantum wave function in a detectable way. This property gives them a form of “memory” of their interactions, a feature that has made them a focal point for researchers exploring new frontiers in quantum information.
An ‘Electron Maze’ for Anyons
To observe the subtle behavior of anyon tunneling, the research team, which included scientists from Purdue University, fabricated a sophisticated device from a high-purity gallium arsenide and aluminum gallium arsenide heterostructure. This material creates a pristine two-dimensional plane where electrons can move freely. The device was then cooled to a temperature of just 10 millikelvins—a hundredth of a degree above absolute zero—and subjected to an intense 9-Tesla magnetic field. These extreme conditions force the electrons into a collective, strongly correlated state of matter known as a fractional quantum Hall liquid.
In this state, the electrons behave as if they have broken into fractions of their former selves, giving rise to quasiparticles with a fractional electric charge. For this experiment, the system was tuned to the primary Laughlin state, where the emergent anyons are predicted to have exactly one-third the charge of an electron. The researchers etched a constriction, known as a quantum point contact, into the material. This constriction acts as a tunable barrier, separating the counter-propagating “edge modes” of the quantum liquid and allowing the team to precisely measure the rate at which anyons tunneled from one side to the other. This setup effectively functions as a nanoscale interferometer, enabling the direct observation of quantum mechanical transport phenomena.
Universal Scaling and Direct Confirmation
Quantum tunneling is a phenomenon where a particle can pass through a barrier that it classically should not have enough energy to overcome. For anyons in a fractional quantum Hall system, theorist Xiao-Gang Wen predicted decades ago that this tunneling process should be “universal.” This means that the tunneling conductance should follow a predictable power-law scaling relationship governed by a single, universal exponent, regardless of specific experimental conditions like temperature, the voltage bias applied across the barrier, or the barrier’s transmission probability. However, for years, experimental attempts to verify this prediction produced inconsistent results that did not match the theory, creating a significant gap in the field.
The new research finally bridges this gap. By creating a device with an exceptionally sharp and well-defined edge potential, the team was able to observe this universal behavior with unprecedented clarity. They found that for a wide range of conditions, the data collapsed onto a single universal curve. From 29 independent datasets, they measured the critical tunneling exponent to be 0.333 ± 0.005. This result is in remarkable agreement with the theoretically predicted value of 1/3 for Laughlin quasiparticles, providing the first direct and conclusive evidence of this universal tunneling behavior.
A Triad of Experimental Evidence
This measurement of the universal tunneling exponent is the capstone of a multi-year experimental quest to fully define the topological nature of the ν=1/3 fractional quantum Hall state. Topological phases of matter are not defined by conventional properties like crystal structure but by robust, global properties that are immune to local disturbances. To completely characterize such a state, physicists must experimentally verify three key signatures.
The first is the existence of quasiparticles with fractional charge, which for this state is e/3 (one-third the charge of an electron). The second is the anyonic braiding statistics, which describes how the quantum phase of the system changes when particles are exchanged; for these anyons, the statistical angle is 2π/3. Both of these properties had been confirmed in recent years by the same research groups. The third and final piece of the puzzle was the universal tunneling exponent, which is directly related to the quasiparticle’s scaling dimension. The successful measurement of this exponent now provides a complete and self-consistent experimental description of this topological order, locking in the theoretical framework with hard data.
From Fundamental Physics to Quantum Computing
The immediate impact of this discovery is the resolution of a persistent discrepancy between theory and experiment that has puzzled physicists for many years. It provides a powerful validation of the chiral Luttinger liquid theory, which is the foundational model used to describe the edges of fractional quantum Hall systems. This deeper understanding of the fundamental physics of quasiparticles is a major advance in its own right.
Looking further ahead, the unique properties of anyons, particularly their braiding-induced “memory,” make them a leading candidate for building fault-tolerant topological quantum computers. In such a computer, quantum information would be encoded in the topological state of the system, making it inherently robust against noise and local errors from the environment. While the development of a practical topological quantum computer remains a distant goal, foundational discoveries like this one are crucial steps along that path. For now, the work stands as a landmark achievement in humanity’s quest to understand the strange and beautiful quantum world, confirming that in the flatlands of two-dimensional physics, a third kingdom of particles truly reigns.
