🔬 mesoscale physics

Trapping $e/4$ quasiparticles in bilayer graphene

This study demonstrates the successful trapping and measurement of $e/4$ quasiparticles in even-denominator fractional quantum Hall states of bilayer graphene using a gate-defined antidot, providing strong evidence for non-Abelian ground states and a critical step toward topological quantum computation.

Original authors: Mario Di Luca, Emily Hajigeorgiou, Ning Ma, Alexandra Waldherr, Kenji Watanabe, Takashi Taniguchi, Mitali Banerjee

Published 2026-08-28

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CC BY 4.0

Original authors: Mario Di Luca, Emily Hajigeorgiou, Ning Ma, Alexandra Waldherr, Kenji Watanabe, Takashi Taniguchi, Mitali Banerjee

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the coldest, most controlled corners of the physical world, electrons sometimes stop behaving like individual particles and start acting as a single, fluid substance. When this happens under a powerful magnetic field, the fluid forms a special state of matter known as a fractional quantum Hall state. In these states, the fluid is so rigid that it cannot be compressed, and the electric charge carried by disturbances within it is not the standard unit found in ordinary wires. Instead, the fluid supports excitations that carry only a fraction of an electron's charge. While scientists have long known about states where the charge is a simple fraction like one-third, a more exotic possibility has been predicted for states where the denominator is an even number, such as two. In these specific conditions, the fluid is expected to host excitations carrying a charge of one-quarter. Detecting these quarter-charge particles is a critical step because they are the building blocks for a type of quantum computer that is naturally protected from errors, a technology that could revolutionize how we process information.

A team of researchers at the École Polytechnique Fédérale de Lausanne has now successfully trapped and measured these elusive quarter-charge particles. They did this by creating a tiny, artificial island within a sheet of bilayer graphene, a material made of two layers of carbon atoms. This island, known as an antidot, acts like a small hill in the landscape of the electron fluid. By carefully adjusting the voltage on a gate suspended just above this hill, the researchers could control the number of particles trapped on it. As they tuned this gate, they watched the electrical resistance of the device oscillate. These oscillations revealed the exact amount of charge being added to the island each time a new particle arrived. At specific magnetic conditions corresponding to the even-denominator states, the researchers observed that the charge added in each step was exactly one-quarter of an electron's charge. This finding confirms that the fundamental excitations in these states are indeed the quarter-charge particles predicted by theory.

The experiment relied on a device that was far more precise than previous attempts. The researchers used a suspended metal bridge, shaped like a tiny arch, to apply voltage directly to the antidot region without affecting the surrounding material. This level of control was essential because the even-denominator states are much more fragile and narrow in their range of stability than the more common odd-denominator states. Without this local control, the delicate conditions required to see the quarter-charge particles would have been lost. The team measured the resistance while applying a tiny alternating current and found clear, repeating patterns in the data. At the specific magnetic fields where the even-denominator states exist, the patterns showed that the charge on the antidot changed in steps of one-quarter. They also observed the expected one-third charge at a different, well-known state, which served as a confirmation that their measurement technique was working correctly.

Beyond simply finding the particles, the study explored what happens when the connection between the trapped island and the surrounding electron fluid is strengthened. By adjusting side gates, the researchers could bring the fluid closer to the island, increasing the interaction between them. When they did this, the pattern of oscillations changed. Instead of seeing the small steps of one-quarter charge, the device began to show steps that were twice as large. This doubling of the step size suggests that under stronger interaction, the particles might be pairing up or behaving differently, effectively moving in groups of two. Interestingly, this doubling effect did not happen in the more common states where the charge is one-third, indicating that the behavior is unique to the specific structure of the even-denominator states.

The researchers considered two main explanations for this change in behavior. One possibility is that the particles are physically bunching together, moving as pairs of one-quarter charges to form a unit of one-half. The other possibility is that the system shifts into a different mode of transport where the rules governing the oscillations change entirely. The data showed that this transition depends heavily on the specific type of state and how the edges of the electron fluid are structured, rather than being a simple feature of the device itself. While the exact microscopic reason for the doubling remains a subject for further study, the ability to isolate and measure the individual quarter-charge particles is a major achievement. It proves that these exotic states can be controlled and manipulated, a necessary condition for using them in future quantum technologies. The work demonstrates that bilayer graphene is a powerful platform for studying these complex states, bringing the dream of topological quantum computation one step closer to reality.

Technical Summary: Trapping e/4 Quasiparticles in Bilayer Graphene

Problem and Motivation
Identifying the topology of the ground state in even-denominator fractional quantum Hall (FQH) states is a central challenge in condensed matter physics, as these states are leading candidates for hosting non-Abelian quasiparticles essential for fault-tolerant quantum computation. A necessary condition for non-Abelian statistics is the existence of quasiparticles with charge $e/4$ . While previous experiments in GaAs and bilayer graphene (BLG) have provided evidence for these states, direct measurement of the localized charge of elementary excitations has been complicated by narrow incompressible plateaus and the difficulty of isolating specific quasiparticle charges from interference effects. Specifically, Fabry–Pérot interferometry in BLG has observed that while the localized excitations enclosed by the interferometer carry charge $e/4$ , the observed interference periodicity is consistent with charge- $e/2$ interfering quasiparticles rather than the expected charge- $e/4$ quasiparticles. This discrepancy necessitates a complementary approach to probe the fundamental quasiparticle charge through controlled localization.

Methodology
The authors utilize a gate-defined quantum Hall antidot (AD) in Bernal-stacked bilayer graphene to perform charge spectroscopy. A key innovation in their device design is the inclusion of a suspended air-bridge gate (ADG) that predominantly couples to the antidot region, distinct from the top and bottom graphite gates used to set the bulk filling factor. This local control is critical for resolving oscillations in even-denominator states, which possess significantly narrower stability ranges than odd-denominator states.

The experiments are conducted at a magnetic field of $B = 14$ T in a dilution refrigerator with a base temperature of approximately 10 mK, resulting in an estimated electron temperature of 30–50 mK. The device is operated in a current-biased configuration with a cold-grounded contact to ensure thermalization. The researchers measure the variation in transmitted resistance ( $\delta R_t$ ) as a function of the antidot gate voltage ( $V_{adg}$ ) and magnetic field ( $B$ ). By analyzing the periodicity of these oscillations relative to a reference state ( $\nu = -1$ ), they extract the localized charge $q$ using the relation $q/e = \Delta V / \Delta V_1$ , where $\Delta V$ is the gate voltage period at the filling factor of interest and $\Delta V_1$ is the period for single-electron addition.

Key Results

Observation of $e/4$ Charge: At the even-denominator filling factors $\nu = -5/2$ , $-1/2$ , and $3/2$ , the authors observe Coulomb-dominated (CD) oscillations with gate-voltage periods corresponding to a localized charge of $q = e/4$ . This is consistent with the minimal excitation expected for leading candidate ground states (such as Pfaffian or anti-Pfaffian orders).
Observation of $e/3$ Charge: At the hole-conjugate state $\nu = 2/3$ , the oscillations correspond to a charge of $q = e/3$ . The authors attribute the observation of $e/3$ (rather than the $2e/3$ reported in previous studies) to their lower electron temperature (of the order of 30–50 mK compared to 150 mK in previous work) and improved control over the coupling between the antidot-bound states and extended edge states.
Crossover to Double Periodicity: By tuning the side gates to increase the coupling between the antidot-bound states and the extended edge states, the authors observe a crossover from the minimal-excitation period to a regime where the gate-voltage period is approximately doubled.
- This doubling occurs for the even-denominator states ( $\nu = -5/2, -1/2, 3/2$ ) and the hole-conjugate state ( $\nu = 2/3$ ).
- Crucially, no such doubling is observed at the conventional odd-denominator states ( $\nu = -1/3, -4/3$ ) under similar conditions, suggesting the effect is linked to the specific edge structure of the even-denominator and hole-conjugate states rather than a generic device artifact.
Anomalies at $\nu = -1/2$ : The state $\nu = -1/2$ exhibits anomalous behavior, including a magnetic-field periodicity significantly larger than other states and a different temperature dependence for the doubled-period oscillations (persisting up to 120 mK compared to 60 mK for other states).

Discussion of the Crossover
The paper discusses two primary interpretations for the observed period doubling:

Quasiparticle Bunching: The system may transition to a regime where two minimal quasiparticles (e.g., two $e/4$ particles) tunnel together, effectively changing the charge addition unit to $2e^*$ . This would imply a renormalization of edge dynamics due to interactions.
Aharonov–Bohm (AB) Crossover: The system may transition from a Coulomb-dominated regime to an AB-dominated or mixed regime. In the AB limit, the gate-voltage periodicity is determined by the filling factor of the partially occupied Landau level rather than the quasiparticle charge. The observed gate periods in the doubled regime ( $\Delta V/\Delta V_1 \approx 1/2$ for even-denominator states and $\approx 2/3$ for $\nu=2/3$ ) phenomenologically match the filling of the partially occupied Landau level ( $\nu_{LL}$ ), consistent with recent AB interferometry results in BLG.

The authors note that the selective appearance of doubling only in specific states suggests the crossover involves the microscopic edge structure and the competition between different quasiparticle processes, rather than a simple global transition.

Significance and Claims
The paper claims that its results demonstrate the ability to localize and resolve elementary $e/4$ quasiparticles in bilayer graphene, a necessary ingredient for topological quantum computation. By confirming the presence of $e/4$ excitations at $\nu = -5/2, -1/2,$ and $3/2$ , the work supports the compatibility of even-denominator FQH states in BLG with non-Abelian ground states. Furthermore, the observation of the crossover to a doubled period provides a new probe into how quasiparticle dynamics evolve as the coupling to edge states is strengthened. The authors conclude that while the microscopic origin of the crossover (bunching vs. AB transition) remains an open question due to the complexity of edge reconstruction and interactions, the ability to access these elementary charges in a gate-defined antidot establishes a platform for future experiments aimed at probing exchange statistics and controlled braiding.

Technical Summary: Trapping e/4 Quasiparticles in Bilayer Graphene

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