🔬 mesoscale physics

Tunable inter-edge interactions in a bilayer graphene quantum Hall antidot

This paper demonstrates that gate-defined bilayer graphene quantum Hall antidots enable a tunable crossover from Coulomb-dominated to Aharonov-Bohm transport regimes, evidenced by a doubling of conductance oscillation periods and a shift in magnetic field periodicity as the coupling between localized antidot states and extended edge states is controlled.

Original authors: Mario Di Luca, Emily Hajigeorgiou, Zekang Zhou, Tengyan Feng, Kenji Watanabe, Takashi Taniguchi, Ferdinand Kuemmeth, Mitali Banerjee

Published 2026-09-29

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CC BY 4.0

Original authors: Mario Di Luca, Emily Hajigeorgiou, Zekang Zhou, Tengyan Feng, Kenji Watanabe, Takashi Taniguchi, Ferdinand Kuemmeth, 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 world of electricity, we are used to the idea that current flows like water in a river, spreading out across a wide channel. But under extreme conditions—specifically when a material is chilled to near absolute zero and subjected to a powerful magnetic field—electrons behave very differently. They stop flowing freely and instead line up in a rigid, one-dimensional highway along the very edge of the material. This phenomenon, known as the quantum Hall effect, creates a state where electricity moves without resistance, but only along these narrow boundaries. Scientists have long been fascinated by what happens when they try to force these electrons to interact with one another or to interfere with themselves, much like ripples on a pond crossing paths. To study this, researchers build tiny traps and loops in the material, creating devices that act as interferometers. The goal is to understand the fundamental nature of electrons and the strange, exotic particles they can form when crowded together, which could one day help build computers that are far more powerful and stable than anything we have today.

A team of researchers at the École Polytechnique Fédérale de Lausanne and collaborating institutions has now created a new kind of trap using a sheet of bilayer graphene, a material made of two layers of carbon atoms. They built a device that functions as an antidot, which is essentially a small, empty island surrounded by the flowing electron highway. By adjusting the voltage on tiny metal gates placed above and below the graphene, they could control the size of this island and how strongly the electrons in the main highway interacted with the electrons trapped around the island. The researchers were looking for a specific transition: a shift from a state where the electrons are dominated by their own electric charge and repel each other, to a state where they behave like waves that interfere with one another in a predictable pattern.

The experiment revealed that by simply turning a knob to change the voltage on the top gate, the team could switch the behavior of the system. When the connection between the main electron highway and the island was weak, the electrons behaved in a way dominated by their electric charge, creating a specific rhythm in the electrical current. However, as they strengthened the connection, the rhythm changed completely. At certain settings, the pattern of the current oscillations doubled in length, and the way the system responded to the magnetic field shifted. This change signaled that the electrons had moved from a charge-dominated state to a state governed by wave interference, where the path the electrons take around the island matters more than their individual electric repulsion.

The researchers observed this shift most clearly at two specific settings of the electron density, known as filling factors of 2 and 4. At the lower setting, the change was sharp and distinct. The time it took for the electrical signal to repeat itself doubled, and the magnetic field required to see one full cycle of the pattern changed from a fraction of a standard unit to the full unit itself. This confirmed that the electrons were now interfering with themselves as they circled the island, a behavior that had been difficult to isolate in previous experiments because other factors often got in the way. At the higher setting, the system appeared to be in a middle ground, showing signs of both behaviors, which suggests that the transition is not always a sudden jump but can be a gradual evolution depending on the conditions.

To understand what was happening inside the device, the team had to rule out several other possibilities. They considered whether the electrons were interacting with the outer edge of the highway or with a pool of charge sitting in the middle of the island, but their data did not support these ideas. Instead, the evidence pointed to a scenario where the innermost path of the electron highway was being split and recombined around the island, effectively turning the device into a loop where the electrons could interfere with themselves. This interpretation was supported by computer simulations that showed how the size of the island shrank as the voltage was increased, matching the changes they saw in the electrical measurements. The team also noted that the strength of the signal depended on the temperature and the energy of the electrons, which helped confirm that they were observing a genuine quantum effect rather than random noise.

This work is significant because it provides a clean, controllable way to study how electrons interact in these extreme quantum states. Previous devices often suffered from unwanted interactions between the edge of the material and the bulk, which could hide the delicate interference patterns scientists were trying to see. By using this gate-defined antidot, the researchers created a system where they could tune the interactions at will, moving from one regime to another without changing the physical structure of the device. The ability to switch between these states so precisely opens the door to future experiments that could probe even more complex behaviors, such as the interference of exotic particles that might exist in the fractional quantum Hall regime. By mastering this control, scientists are taking a step closer to understanding the deep rules that govern the quantum world and potentially harnessing them for new technologies.

Technical Summary: Tunable Inter-Edge Interactions in a Bilayer Graphene Quantum Hall Antidot

Problem and Motivation
Quantum Hall (QH) interferometers are essential tools for probing the statistical exchange properties of emergent quasiparticles. While the dot-like Fabry–P´erot interferometer (FPI) is the most common realization, it suffers from bulk-to-edge coupling and bulk impurities. When interfering edge states couple strongly to compressible bulk states, this coupling can dominate the response, masking the expected Aharonov–Bohm (AB) oscillations. Alternative geometries, such as Mach-Zehnder interferometers, avoid bulk-to-edge coupling but lack the specific advantages of antidot (AD) geometries. QH antidots, where interference occurs around a potential hill, offer a route free of bulk-to-edge coupling. While previous experiments have utilized ADs to localize quasiparticles in the fractional regime or as tools to measure charge and temperature in the Coulomb-dominated (CD) regime, the ability to tune an AD between the CD and AB regimes has not been fully explored. This work addresses the need for a controllable platform to study the transition between these distinct interaction regimes.

Methodology
The authors investigate a gate-defined bilayer graphene (BLG) antidot, fully electrostatically controlled via a dual-gate architecture. The device consists of BLG encapsulated between hexagonal boron nitride (hBN) layers, with top and bottom graphite gates. The antidot is defined by an etched hole in the top graphite gate.

Control Mechanism: The bottom gate (BG) tunes the antidot potential, while the top gate (TG) sets the bulk filling factor ( $\nu_b$ ) to an integer quantum Hall state and drives the oscillations. Side gates are fixed to maintain the system in specific coupling regimes.
Coupling Tuning: By varying the TG voltage, the authors tune the constriction filling factor ( $\nu_c$ ), thereby controlling the coupling between the extended quantum Hall edge states and the states localized around the antidot. This allows the system to be moved from a weakly coupled regime to a strongly coupled regime.
Measurements: The study focuses on diagonal conductance ( $G_d$ ) and longitudinal resistance ( $R_{xx}$ ) as functions of magnetic field ( $B$ ) and TG voltage ( $V_{tg}$ ) at filling factors $\nu = 1, 2, 3,$ and $4$ (at $B=5$ T). The oscillations are analyzed via 2D-Fast Fourier Transform (FFT) to determine magnetic field and gate voltage periods.

Key Results
The study identifies four distinct transport regions based on the relationship between the bulk filling factor ( $\nu_b$ ) and the antidot filling factor ( $\nu_c$ ):

Decoupled (High $\nu_c$ ): The innermost edge is fully transmitted; the antidot is decoupled from extended edges.
Weakly Coupled: As $\nu_c$ decreases, a current path opens through the antidot. This regime exhibits Coulomb-dominated (CD) oscillations, characterized by dips in conductance, a magnetic field period of $\phi_0/\nu$ , and a gate voltage period set by the electron tunneling charge.
Strongly Coupled: As $\nu_c$ decreases further, the innermost edge is increasingly reflected, and the antidot couples strongly to the extended edges.
Decoupled (Low $\nu_c$ ): The innermost edge is fully reflected while the outer edge is fully transmitted ( $\nu_c = \nu - 1$ ).

Observations in the Strongly Coupled Regime:

Selectivity: Strongly coupled oscillations are observed only at even filling factors ( $\nu = 2, 4$ ), whereas odd filling factors ( $\nu = 1, 3$ ) exhibit only weakly coupled oscillations.
Oscillation Character: Unlike the CD regime (dips), the strongly coupled regime exhibits conductance peaks, indicating that a path through the antidot increases conductance.
Periodicity Shifts:
- At $\nu = 2$ , the magnetic field period shifts from $\phi_0/2$ (CD) to $\phi_0$ (AB), and the gate voltage period doubles ( $\Delta V_s / \Delta V_w \approx 1.81$ ).
- At $\nu = 4$ , the system exhibits an intermediate behavior with a gate period ratio of $\approx 2.37$ and a flux periodicity of $\approx 1.21 \phi_0$ , suggesting a transition state between CD and AB regimes.
Phase Behavior: Phase slips are observed in the strongly coupled oscillations, particularly at $\nu = 4$ , consistent with boundaries between different inter-edge coupling regimes.
Mechanism Identification: The authors rule out scenarios involving edge-to-edge tunneling (energetically expensive) or charge puddles. They conclude that the strongly coupled oscillations correspond to AB oscillations of the inner edge, where the system effectively behaves as an interferometer with the inner edge partitioned twice before and after the antidot. The positive slope of equiphase lines in the ( $V_{tg}, B$ ) plane supports the AB interpretation, as increasing $V_{tg}$ reduces the effective antidot area.

Significance and Claims
The paper establishes that gate-defined bilayer graphene antidots serve as a controllable platform for quantum Hall interferometry. By varying the antidot potential, the authors demonstrate a tunable crossover from a Coulomb-dominated regime to an Aharonov–Bohm regime. This tunability allows the system to avoid the bulk-to-edge coupling that limits conventional FPIs. The observed crossover highlights the critical importance of coupling between the antidot and extended edge states. The authors posit that this platform is suitable for future studies of quasiparticle interactions and anyonic interference in the fractional quantum Hall regime, provided the system can be tuned into the appropriate coupling regime.

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