Gate-Defined Bilayer Graphene Antidot

• Gate-defined bilayer graphene antidot is a tunable potential hill in Bernal-stacked BLG that leverages electrostatic gating to probe Coulomb-dominated quasiparticle interactions.
• Varying gate voltages induces a crossover from single-dot to double-dot behavior, enabling precise control over charging energy, level spacing, and inter-edge coupling.
• The platform reveals edge-state pairing and conductance oscillation shifts, offering a robust method for studying quantum Hall interferometry and quasiparticle charge detection.

Searching arXiv for the cited paper and closely related background on bilayer graphene quantum Hall antidots. arXiv search query: (Luca et al., 23 Apr 2025) bilayer graphene antidot quantum Hall A gate-defined bilayer graphene antidot is a potential hill in the quantum Hall regime realized in Bernal-stacked bilayer graphene (BLG) by electrostatic gating, and used as a controllable localized object within a split-gate constriction. In the reported implementation, the antidot is operated in the Coulomb-dominated regime, where its charging energy, level spacing, and inter-edge coupling can be tuned by gate voltages. The central result is that varying the antidot potential enables a crossover from single-dot to double-dot behavior, and that in the latter regime strong coupling between the two edge states leads to edge-state pairing, resulting in a measured doubling of the tunneling charge (Luca et al., 23 Apr 2025).

1. Definition and physical setting

Electronic interferometers in the quantum Hall regime are described as one of the best tools to study the statistical properties of localized quasiparticles in the topologically protected bulk. Their behavior is probed through chiral edge modes, so bulk-to-edge and inter-edge interactions are identified as two important effects that affect the observations. The same source emphasizes that almost all kinds of interferometers heavily rely on a pair of high-quality quantum point contacts and that the presence of impurities significantly modifies the behavior of such constrictions, which can alter the outcome of measurements (Luca et al., 23 Apr 2025).

Within that setting, antidots are singled out as especially useful because they overcome the geometric limitations of conventional geometries and act as controlled impurities within a quantum point contact. They also allow for quasiparticle charge detection through simple conductance measurements, replacing the need for complex techniques such as shot noise. In the reported device, the antidot is not defined by etched graphene but by gate patterning, so the active BLG remains encapsulated while the electrostatic potential landscape is sculpted by graphite gates (Luca et al., 23 Apr 2025).

This configuration is specifically used to study how inter-edge interactions can become the dominant energy scale. A plausible implication is that the antidot is not merely a localized scatterer but a tunable many-body subsystem whose internal edge structure can qualitatively reshape the transport response.

2. Device architecture and gate definition

The active region is Bernal-stacked bilayer graphene (BLG) encapsulated between two hexagonal-BN flakes, with bottom hBN $\simeq 33\ \mathrm{nm}$ and top hBN $\simeq 56\ \mathrm{nm}$. Above and below the BLG lie graphite gates: a bottom graphite gate (BG) that globally tunes carrier density and opens a high-resistance $\nu = 0$ gap under the antidot, and a patterned top graphite gate (TG) that defines both the antidot and the side-gate trenches (Luca et al., 23 Apr 2025).

The antidot potential hill is created by etching a circular hole (lithographic diameter $200 \pm 5\ \mathrm{nm}$) in the TG. Two narrow trenches, labeled side gates (SG), connect the TG to its contacts and thereby form a split-gate constriction around the antidot. COMSOL electrostatic simulations (Thomas–Fermi screening) yield an effective antidot diameter $D_{\mathrm{AD}} \simeq 290$–$300\ \mathrm{nm}$ at the graphene plane (Luca et al., 23 Apr 2025).

The fabrication route is specified in detail. The stack is assembled via dry transfer (PC/PDMS). TG contacts (18 nm Pd) are defined by e-beam lithography, after which the graphite gate is etched using $\mathrm{O_2/SF_6/O_2}$ plasmas to form the antidot and SGs. Finally, Cr/Au (5/100 nm) is evaporated to define source, drain and gate bridges, with successive $\mathrm{O_2}$-etch steps ensuring isolation of all gate elements (Luca et al., 23 Apr 2025).

The following table summarizes the structural elements explicitly reported.

Element	Specification	Function
BLG/hBN stack	Bottom hBN $\simeq 33\ \mathrm{nm}$; top hBN $\simeq 56\ \mathrm{nm}$	Encapsulated active region
Bottom graphite gate	BG	Tunes carrier density; opens high-resistance $\simeq 56\ \mathrm{nm}$0 gap under the antidot
Patterned top graphite gate	TG with circular hole	Defines antidot and side-gate trenches
Antidot opening	Lithographic diameter $\simeq 56\ \mathrm{nm}$1	Creates antidot potential hill
Effective antidot size	$\simeq 56\ \mathrm{nm}$2–$\simeq 56\ \mathrm{nm}$3	Electrostatic diameter at graphene plane
Side gates	Two narrow trenches, SG	Form split-gate constriction around the antidot

3. Experimental configuration and transport observables

Measurements are performed in a dilution refrigerator (base $\simeq 56\ \mathrm{nm}$4) with a perpendicular magnetic field $\simeq 56\ \mathrm{nm}$5 up to $\simeq 56\ \mathrm{nm}$6; unless otherwise stated, data are taken at $\simeq 56\ \mathrm{nm}$7. The bulk filling factor $\simeq 56\ \mathrm{nm}$8 is tuned by TG and BG, and oscillations are studied on the integer plateaus $\simeq 56\ \mathrm{nm}$9–$\nu = 0$0. The constriction filling factor $\nu = 0$1 is controlled by SG voltages, enabling selective coupling of the innermost edge(s) to the antidot (Luca et al., 23 Apr 2025).

The conductance measurement is specified as follows: an AC excitation $\nu = 0$2 (33.3 Hz) is applied to the source, the transmitted current $\nu = 0$3 is measured with a transimpedance amplifier, and the voltage drop $\nu = 0$4 between two downstream voltage probes yields the diagonal conductance

$\nu = 0$5

For spectroscopy, a DC bias $\nu = 0$6 is added via a room-temperature adder to map Coulomb diamonds in the $\nu = 0$7 vs. $\nu = 0$8 plane (Luca et al., 23 Apr 2025).

A key experimental datum is the Coulomb diamond map at $\nu = 0$9, $200 \pm 5\ \mathrm{nm}$0, where the trapezoidal regions in $200 \pm 5\ \mathrm{nm}$1 vs. $200 \pm 5\ \mathrm{nm}$2 define $200 \pm 5\ \mathrm{nm}$3–$200 \pm 5\ \mathrm{nm}$4. This establishes that the antidot is being probed in an energy window where charging effects are directly visible in transport (Luca et al., 23 Apr 2025).

4. Coulomb-dominated theoretical description

The reported analysis focuses on the limit where charging energy dominates over level spacing, and where two antidot-bound edges may capacitively or tunnel-couple. In that limit, the effective Hamiltonian is written as

$200 \pm 5\ \mathrm{nm}$5

Here, $200 \pm 5\ \mathrm{nm}$6–$200 \pm 5\ \mathrm{nm}$7 is the charging energy of the antidot island, extracted from Coulomb diamonds; $200 \pm 5\ \mathrm{nm}$8 are the single-particle level energies of the $200 \pm 5\ \mathrm{nm}$9-th edge state; and $D_{\mathrm{AD}} \simeq 290$0 is the inter-edge tunneling amplitude (or hybridization energy) between the two inner edges when they are strongly coupled (Luca et al., 23 Apr 2025).

The level spacing is estimated as

$D_{\mathrm{AD}} \simeq 290$1

with $D_{\mathrm{AD}} \simeq 290$2 and $D_{\mathrm{AD}} \simeq 290$3. This places $D_{\mathrm{AD}} \simeq 290$4 in the same overall energy range as the experimentally extracted charging scale, making the crossover to strongly coupled behavior experimentally accessible by gate tuning (Luca et al., 23 Apr 2025).

When tunneling is suppressed but capacitive coupling is present, the electrostatic energy is also written as

$D_{\mathrm{AD}} \simeq 290$5

where $D_{\mathrm{AD}} \simeq 290$6 is the charge imbalance on edge $D_{\mathrm{AD}} \simeq 290$7, $D_{\mathrm{AD}} \simeq 290$8 its “stiffness,” and $D_{\mathrm{AD}} \simeq 290$9 the inter-edge capacitance. This representation isolates the role of electrostatic coupling independently of coherent hybridization. A plausible implication is that the experimentally observed crossover need not be attributed to tunneling alone; capacitive coupling can serve as an equivalent control parameter when it becomes comparable to the intrinsic edge stiffnesses.

5. Tunable regimes: from single-dot to double-dot behavior

In the weak coupling (single-dot) regime, realized for constriction voltages $300\ \mathrm{nm}$0 with $300\ \mathrm{nm}$1 and $300\ \mathrm{nm}$2, resonant tunneling occurs between the extended inner edge and a single antidot island. The conductance oscillations in $300\ \mathrm{nm}$3 vs. $300\ \mathrm{nm}$4 or $300\ \mathrm{nm}$5 have period

$300\ \mathrm{nm}$6

yielding tunneling charge $300\ \mathrm{nm}$7 and flux period $300\ \mathrm{nm}$8. In this regime, Coulomb diamonds reflect $300\ \mathrm{nm}$9 (Luca et al., 23 Apr 2025).

In the strong coupling (double-dot) regime, reached as $\mathrm{O_2/SF_6/O_2}$0 is made more negative so that the constriction is more pinched, level spacing $\mathrm{O_2/SF_6/O_2}$1 shrinks and $\mathrm{O_2/SF_6/O_2}$2 (or $\mathrm{O_2/SF_6/O_2}$3) grows. When $\mathrm{O_2/SF_6/O_2}$4 or equivalently $\mathrm{O_2/SF_6/O_2}$5, the two innermost edges—for even $\mathrm{O_2/SF_6/O_2}$6, comprised of $\mathrm{O_2/SF_6/O_2}$7 and $\mathrm{O_2/SF_6/O_2}$8 LLs with same spin/valley—hybridize into a double-dot system (Luca et al., 23 Apr 2025).

Two transport signatures are emphasized in that strong-coupling regime. First, $\mathrm{O_2/SF_6/O_2}$9 oscillations double their gate period, so that $\mathrm{O_2}$0, extracted from

$\mathrm{O_2}$1

Second, the flux period shifts to $\mathrm{O_2}$2, consistent with two-edge coupling; for $\mathrm{O_2}$3 one measures $\mathrm{O_2}$4–$\mathrm{O_2}$5 (Luca et al., 23 Apr 2025).

The transition from single- to double-dot behavior is summarized by the crossover condition

$\mathrm{O_2}$6

The source further reports a coexistence region with both $\mathrm{O_2}$7 and $\mathrm{O_2}$8 oscillations near the crossover, observed as continuous evolution of oscillation modes as $\mathrm{O_2}$9 is varied, which is presented as confirmation of $\simeq 33\ \mathrm{nm}$0 tuning (Luca et al., 23 Apr 2025).

6. Dominance of inter-edge interactions and implications for interferometry

The strongly coupled regime is characterized by an energy-scale hierarchy in which the effective pairing energy (either $\simeq 33\ \mathrm{nm}$1 or $\simeq 33\ \mathrm{nm}$2) can exceed $\simeq 33\ \mathrm{nm}$3 and even approach $\simeq 33\ \mathrm{nm}$4, making inter-edge interactions the leading energy scale. This is the principal physical conclusion of the study: in some operating windows, the antidot does not primarily function as a weakly perturbing interferometric element, but as an interacting two-edge system whose internal coupling controls the measured oscillations (Luca et al., 23 Apr 2025).

The reported impact on interference is explicit. Because the paired states carry charge $\simeq 33\ \mathrm{nm}$5, AB-type oscillations at period $\simeq 33\ \mathrm{nm}$6 are replaced by larger-period ($\simeq 33\ \mathrm{nm}$7-like) oscillations. In addition, strong coupling suppresses single-electron interference and leads to phase slips characteristic of Coulomb-dominated double-dot systems, thereby diminishing visibility of conventional anyonic braiding signals in the QH interferometer (Luca et al., 23 Apr 2025).

This point addresses a common interpretive issue in quantum Hall interferometry: oscillation periods are not determined solely by ideal single-edge Aharonov–Bohm physics. In the present system, phase slips (diagonal jumps) in the raw $\simeq 33\ \mathrm{nm}$8 data attest to capacitive double-dot physics, and the 2D-FFT analysis shows that the dominant peak shifts from the weak-coupling location, consistent with $\simeq 33\ \mathrm{nm}$9, $\simeq 56\ \mathrm{nm}$0, to a strong-coupling location with $\simeq 56\ \mathrm{nm}$1 and $\simeq 56\ \mathrm{nm}$2 (Luca et al., 23 Apr 2025). This suggests that inter-edge coupling can mask or even supersede the interference signatures the devices are mainly designed to probe.

7. Experimental significance of gate-defined bilayer graphene antidots

The study concludes that gate-defined bilayer graphene antidots constitute a highly tunable platform for studying Coulomb-dominated quasiparticle interactions, from single-electron resonances to paired edge-state behavior, with direct control over charging, level spacing, and inter-edge coupling (Luca et al., 23 Apr 2025). That significance follows directly from the combination of architectural and spectroscopic features: the antidot is gate-defined rather than structurally etched into the BLG, the constriction filling factor can be independently tuned through SG voltages, and the crossover between regimes is tracked by changes in Coulomb diamonds, oscillation periods, and phase-slip structure.

Within quantum Hall interferometry, the reported platform is valuable for two distinct reasons. First, it supplies a controlled impurity within a quantum point contact, addressing the sensitivity of conventional constrictions to uncontrolled disorder. Second, it provides quasiparticle charge detection through simple conductance measurements, rather than requiring complex techniques such as shot noise (Luca et al., 23 Apr 2025).

A broader implication, stated cautiously, is that the gate-defined BLG antidot functions as both a probe and a source of interaction physics. It is designed to interrogate quantum Hall edge transport, yet the experiments show that the device’s own inter-edge interactions can become decisive. In that sense, the platform clarifies a central methodological point for antidot-based interferometry: the observable oscillation spectrum reflects not only enclosed flux and filling factor, but also the relative magnitudes of $\simeq 56\ \mathrm{nm}$3, $\simeq 56\ \mathrm{nm}$4, $\simeq 56\ \mathrm{nm}$5, and $\simeq 56\ \mathrm{nm}$6.