Bilayer Graphene Quantum Dots (BLGQD)

• Bilayer graphene quantum dots are quantum-confined systems exploiting a tunable band gap from an out-of-plane electric field in Bernal-stacked bilayer graphene.
• Diverse device architectures—ranging from fully gate-defined structures to STM-created circular dots—enable precise control over carrier confinement and tunnel barriers.
• Spectroscopy and magneto-transport studies reveal distinct shell structures, spin-valley interactions, and topological boundary states crucial for quantum device applications.

Bilayer graphene quantum dots (BLGQDs) are quantum-confined electronic systems realized in Bernal-stacked bilayer graphene by etched nanostructures, electrostatic gates, circular $p$–$n$ junctions, or finite graphene nanoflakes. Their defining materials property is that an out-of-plane electric field opens a tunable band gap in bilayer graphene, so confinement, tunnel barriers, and carrier polarity can be controlled in ways not available in monolayer graphene. On that basis, the literature spans laterally gated double dots with resolved excited states, fully gate-defined few-electron and few-hole single and double dots, STM-defined circular dots, topological electric-field-defined dots, and finite-cluster BLGQDs studied through tight-binding optics (Volk et al., 2011, Eich et al., 2018, Jaskolski, 13 Mar 2026, Abdelsalam et al., 2016).

1. Device classes and the scope of the term

In the experimental transport literature, BLGQDs most commonly denote electrostatically or lithographically confined carrier islands in bilayer graphene. Early work includes a laterally gated bilayer graphene double quantum dot fabricated from mechanically exfoliated bilayer graphene on highly p-doped Si with $295$ nm SiO$_2$, patterned by electron-beam lithography and Ar/O$_2$ reactive-ion etching, and contacted by Cr/Au electrodes (Volk et al., 2011). A distinct top-gated realization on exfoliated bilayer graphene on GaAs used nanoscale topgates to create low-temperature resistive regions under the gates and thereby define a dot in the ungated central region, with Coulomb blockade oscillations and Coulomb diamonds consistent with the gate layout (Müller et al., 2013).

A second, now central, class consists of fully gate-defined, unetched devices in hBN-encapsulated bilayer graphene with graphite back gates, split gates, and finger gates. In these structures the split gates and back gate open a band gap under selected regions, a narrow channel remains conducting between them, and finger gates define dots and barriers inside that channel (Eich et al., 2018, Eich et al., 2018, Banszerus et al., 2020, Banszerus et al., 2019). This architecture underlies single-electron and few-electron dots, ambipolar electron-hole crossover devices, tunable double dots, and integrated charge sensors (Eich et al., 2018, Banszerus et al., 2020, Kurzmann et al., 2019).

The term BLGQD is also used for exposed circular dots formed by STM-written $p$–$n$ junctions in BLG/hBN heterostructures. There the dot is created by trapped charge in hBN beneath the tip-pulse location, producing a dome-like local potential and a circular $p$–$n$ boundary in bilayer graphene (Jr. et al., 2018). A related STM/STS literature images the real-space orbital structure of electrostatically confined BLGQD states and shows that these states can break rotational symmetry even when the confining potential is approximately circular (Ge et al., 2020).

A broader theoretical literature uses BLGQD for finite AB-stacked bilayer graphene nanoflakes. In that usage, the quantum dot is a finite cluster with specified shape and edge termination, and the focus is on discrete spectra, edge states, and optical absorption under perpendicular electric field rather than transport through gate-defined tunnel barriers (Abdelsalam et al., 2016). A further extension is the topological electric-field-defined dot, in which the interlayer potential changes sign in a finite region and the discrete states are quantized domain-wall modes localized at the dot boundary rather than ordinary bulk-like confined orbitals (Jaskolski, 13 Mar 2026).

2. Confinement mechanisms and tunnel-barrier engineering

The unifying confinement principle in BLGQDs is the displacement-field-induced band gap of bilayer graphene. In gate-defined devices, opposite voltages on back and top gates break inversion symmetry between the layers and render selected regions insulating when the local Fermi level lies in the gap (Eich et al., 2018, Eich et al., 2018, Banszerus et al., 2020). This is the main reason bilayer graphene differs operationally from monolayer graphene quantum dots: electrostatic confinement becomes possible without relying on etched edges, and tunnel barriers can be defined by smooth gated regions rather than edge disorder (Eich et al., 2018, Banszerus et al., 2020).

Two tunnel-barrier mechanisms recur throughout the literature. The first is depletion-style barrier formation, in which gates tune regions close to charge neutrality while the dot remains of the same polarity as the leads. This mechanism was used to define a fully tunable central electron dot between barrier gates L and R in a split-gate channel, with gate M acting as plunger (Eich et al., 2018). The second is the natural $p$–$n$0-junction barrier, enabled by BLG ambipolarity. Here the dot and surrounding channel have opposite carrier polarity, so the interfaces necessarily pass through the local gap and act as tunnel barriers. That mechanism underlies few-hole and few-electron dots formed under finger gates, mixed-polarity $n$1 triple dots, and the monotonic tunnel-rate tuning studied in the few-electron regime (Eich et al., 2018, Eich et al., 2018, Jing et al., 2023).

Several device papers make this barrier physics explicit. In a high-quality hBN-encapsulated device, the few-electron tunnel rate was found to be monotonically tuned by varying neighboring finger-gate voltages or the back gate, and this was interpreted as direct control of the effective thickness of natural $n$2–$n$3-junction barriers through changes in local band gap and carrier density (Jing et al., 2023). In a three-layer metallic top-gate architecture, left and right barrier gates could be held quasi-independently while a separate plunger gate drove a single BLG dot continuously from few-hole, through the displacement-field-induced gap, into few-electron occupation (Banszerus et al., 2020). This suggests that orthogonal control of occupation and barrier transparency, long standard in semiconductor dots, is attainable in BLG when the gate stack is sufficiently stratified.

Not all BLGQD barrier formation is of this standard electrostatic type. In the GaAs-substrate top-gate device, the low-temperature insulating regions beneath grounded narrow gates were attributed to nearest-neighbor hopping through localized states inside a larger transport gap, with the confinement mechanism linked to strain and strain-induced piezoelectric fields rather than a deliberately applied dual-gate BLG gap (Müller et al., 2013). That work is therefore best viewed as a gate-patterned BLGQD with an unconventional barrier mechanism.

3. Spectroscopy, shell structure, and level spacing

Transport spectroscopy established early that BLGQDs support resolvable excited states over substantial energy ranges. In the laterally gated BLG double quantum dot, two etched dots of roughly $n$4 nm diameter connected by three $n$5 nm wide constrictions showed addition energies on the order of $n$6 meV and a clear honeycomb charge-stability diagram (Volk et al., 2011). Finite-bias triangles revealed resonant lines parallel to the triangle baseline at detuning energies $n$7, $n$8, $n$9, $295$0, and $295$1 meV, and analysis of more than $295$2 excited states yielded a constant level spacing $295$3, or $295$4 for the subset plotted in Fig. 4g (Volk et al., 2011). Using the constant low-energy density of states of bilayer graphene,

$295$5

the paper wrote the single-particle spacing for a disk-like BLG dot as

$295$6

and obtained $295$7 for $295$8 nm, in very good agreement with the measured spacing (Volk et al., 2011). The same study also stressed an interpretive caution: not every line in a graphene DQD bias triangle is a true dot excitation, because some lines arise from localized states in the constrictions or from variations in dot-lead coupling (Volk et al., 2011).

Gate-defined single dots likewise show a pronounced shell structure. In an hBN-encapsulated BLGQD, single electron and hole occupancy was realized and charge carriers $295$9 were filled successively, with charging energies exceeding $_2$0 and an orbital energy spacing on the order of $_2$1 for the lowest states (Eich et al., 2018). The low-energy spectrum bunched in groups of four, consistent with spin and valley degeneracy at zero magnetic field, and a comparison to theory used $_2$2, $_2$3, and $_2$4 to reproduce the qualitative behavior (Eich et al., 2018).

In the single-electron double-dot regime, addition energies remained in the few-meV range but were small enough that individual occupations could be counted precisely. An electrostatically defined BLG DQD operated from $_2$5 up to about five electrons per dot showed first-to-second-electron addition energies $_2$6 and $_2$7 meV for individually formed dots and $_2$8 and $_2$9 meV in the two-dot regime, with estimated dot diameters $_2$0–$_2$1 nm and $_2$2–$_2$3 nm, respectively (Banszerus et al., 2019). A different ambipolar single-dot device extracted first-hole and first-electron addition energies $_2$4 and $_2$5 meV, total capacitances $_2$6 and $_2$7 aF, and effective diameters of roughly $_2$8 nm for the hole dot and $_2$9 nm for the electron dot, illustrating that the same electrostatic island can change size and charging scale across the electron-hole crossover (Banszerus et al., 2020).

The spectroscopy literature also clarifies what BLGQD regularity does and does not imply. The nearly carrier-number-independent spacing observed in the etched BLG double dot was taken as evidence for bilayer band structure rather than a monolayer-like $p$0 law, but the authors explicitly noted that a disorder-induced effective constant density of states could, in principle, mimic that behavior over a restricted range (Volk et al., 2011). Their argument against that interpretation relied on the much larger energy range covered by the spectroscopy.

4. Spin, valley, magnetic response, and many-body structure

Magnetic-field spectroscopy shows that BLGQDs are simultaneously spin and valley systems. In gate-defined single dots, the low-lying fourfold shell splits under perpendicular field into two pairs with opposite slope, and this was identified as valley splitting that is linear in $p$1 at low field and about $p$2 times stronger than free-electron Zeeman splitting (Eich et al., 2018). By contrast, parallel-field data yielded a spin $p$3-factor

$p$4

which is consistent with ordinary Zeeman physics in carbon-based systems (Eich et al., 2018).

The clearest two-particle assignment was obtained in a few-hole BLGQD by combining finite-bias transport with parallel, perpendicular, and tilted magnetic fields. In that device the first-hole addition energy was $p$5, the lever arm was $p$6, the valley $p$7-factor was $p$8–$p$9, and the spin $n$0-factor was $n$1 (Kurzmann et al., 2019). The lowest four single-particle states formed a spin-valley shell, and the six possible two-hole states organized into a spin-triplet/valley-singlet manifold and a spin-singlet/valley-triplet manifold. The central result was that the two-hole ground state is a spin triplet and valley singlet, while the lowest excited two-hole states are spin singlets with valley-triplet character, with an exchange energy

$n$2

(Kurzmann et al., 2019). This was interpreted as Hund’s rule for a valley-degenerate shell and explicitly contrasted with carbon nanotube and GaAs quantum dots (Kurzmann et al., 2019).

Parallel-field spectroscopy in the early etched BLG double dot also showed splittings of individual excited-state lines. Under $n$3 up to $n$4 T, the triangle positions stayed nearly fixed, indicating that the orbital part of the wavefunctions was essentially unaffected, while several excited-state lines showed slopes $n$5 or approximately $n$6, and one peak-pair separation split at about $n$7, close to the Zeeman scale $n$8 for $n$9 (Volk et al., 2011). The interpretation was deliberately cautious: likely Zeeman spin splitting, but with unresolved total carrier number, total spin, and valley-lifting details (Volk et al., 2011).

Dynamics entered the field through high-frequency transport spectroscopy of a single-electron BLGQD. In an hBN-encapsulated device driven at $p$0 MHz, transient currents through three excited states ES$p$1, ES$p$2, and ES$p$3 were observed once the tunnel rates had been lowered sufficiently by $p$4 T, with $p$5 MHz from DC transport (Banszerus et al., 2020). All three excited-state energies tracked the Zeeman shift expected for $p$6, so they were identified as excited states that require a spin flip to relax to the ground state (Banszerus et al., 2020). Fitting the transient signal with

$p$7

gave blocking times $p$8 ns, $p$9 ns, and $n$0 ns (Banszerus et al., 2020). The important nuance is that $n$1 ns is only a lower bound on the lifetime of the excited spin state, because direct tunneling into lower states can block transport before intrinsic spin relaxation occurs (Banszerus et al., 2020).

Theoretical many-body work places these observations in a broader BLG context. For a parabolic BLGQD with two interacting electrons, exact diagonalization of

$n$2

predicted magnetic-field-driven valley transitions rather than only the usual semiconductor singlet-triplet sequence, including a fourfold-degenerate state in which spin singlet and triplet sectors are degenerate because intervalley exchange vanishes (Zarenia et al., 2013). This theoretical result implies that valley is an active many-body quantum number in BLGQDs, not merely a passive degeneracy.

5. Real-space structure, topology, and finite-cluster BLGQDs

Real-space imaging showed that BLGQD wavefunctions are not generically circular even when the confinement is. STM/STS visualization of electrostatically defined BLGQDs in Bernal-stacked BLG on hBN revealed confined states with robust broken rotational symmetry: constant-energy $n$3 maps inside approximately circular $n$4–$n$5 junctions repeatedly displayed $n$6-like nodal structures rather than circular orbitals (Ge et al., 2020). Tight-binding simulations reproduced the observed asymmetry only when both a finite gap and the skew interlayer hopping $n$7 were included, and the comparison between hole-confined and electron-confined dots showed a $n$8 rotation of the LDOS pattern, interpreted as a Berry-curvature-related manifestation of BLG’s nontrivial band topology (Ge et al., 2020). The topological interpretation remained indirect, however, because the sign of the interlayer potential difference $n$9 was not reversed in situ and time-reversal symmetry preserves valley degeneracy (Ge et al., 2020).

An earlier STM study of exposed circular BLGQDs created by tip-induced local embedded gates in hBN established a complementary picture of charging-dominated circular confinement. There the local trapped charge beneath the pulse site created a circular $p$0–$p$1 junction, and $p$2 spectroscopy showed sharp resonances dispersing with back-gate voltage together with concentric rings in spatial maps (Jr. et al., 2018). The system was interpreted as a double-barrier Coulomb-blockaded quantum dot formed by the vacuum gap to the STM tip and the gapped BLG $p$3–$p$4 interface to the surrounding graphene, with

$p$5

The paper estimated $p$6, $p$7, and a low-bias addition-energy scale $p$8, concluding that the realized dots were strongly charging-dominated (Jr. et al., 2018).

A distinct topological BLGQD concept is obtained by reversing the sign of the perpendicular electric field inside a finite region. In that setting, both the inside and outside are gapped, but the sign change in interlayer potential creates a domain wall carrying 1D chiral topological modes; finite-size quantization of those modes yields discrete bound states localized at the dot boundary (Jaskolski, 13 Mar 2026). Atomistic tight-binding calculations for rectangular dots showed that armchair-oriented and zigzag-oriented sides produce qualitatively different spectra: armchair-derived levels remain doubly degenerate, whereas zigzag-derived levels display branch duplication and nearly flat branches associated with the projected valley momentum $p$9 (Jaskolski, 13 Mar 2026). These are therefore boundary-localized topological BLGQD states rather than ordinary interior-confined orbitals.

Finite-cluster BLGQDs form another branch of the subject. In AB-stacked bilayer graphene nanoflakes, a perpendicular electric field modifies the low-energy spectrum through the competition between finite-size gaps and smeared zero-energy-state manifolds. Tight-binding calculations found that small zigzag triangular BLGQDs show a blue shift of the absorption edge with field, small zigzag hexagonal BLGQDs show a red shift, and armchair BLGQDs show a red shift for both triangular and hexagonal shapes (Abdelsalam et al., 2016). Because this literature concerns finite nanoflakes rather than transport-defined dots, it emphasizes shape, edge termination, and optical response instead of tunnel-coupled spectroscopy.

6. Coupled dots, charge sensing, and quantum-device directions

BLGQD architectures are now sufficiently controllable to realize reconfigurable multi-dot systems. In a single device with three active finger gates above a split-gate channel, electrostatic tuning produced a central single $n$00-dot, a serial $n$01–$n$02 double dot, and a $n$03 triple dot with outer few-hole dots tunnel-coupled through natural $n$04–$n$05-junction barriers to a many-electron central dot (Eich et al., 2018). In the single-dot regime the charging energy was $n$06, the plunger lever arm was $n$07, and the barrier gates tuned the tunnel coupling by more than two orders of magnitude between deep Coulomb blockade and Fabry-Pérot-like transport (Eich et al., 2018). In the double-dot regime the charging energies were $n$08 and $n$09, and finite-bias triangles confirmed serial transport through the two dots (Eich et al., 2018).

The single-electron BLG double dot pushed this control to the qubit-relevant occupancy range. With a graphite back gate, split gates, and two finger gates, the electron number on each dot could be tuned independently between zero and five, and finite-bias spectroscopy in the $n$10 transition yielded an interdot tunnel coupling

$n$11

corresponding to an interdot tunnel rate of

$n$12

(Banszerus et al., 2019). Finite-bias magnetospectroscopy of the first electrons was found to be compatible with spin- and valley-conserving interdot tunneling, while at higher occupation interaction effects and exchange produced richer spectra (Banszerus et al., 2019).

Readout has advanced in parallel. An integrated charge detector in fully gate-defined BLGQDs used a second nearby BLG dot as sensor and resolved single charging events in a target dot as step-like detector-current changes as large as $n$13, with $n$14 for one charging event and an estimated maximal bandwidth of $n$15 (Kurzmann et al., 2019). The same sensing concept detected the first hole, dots with tunable tunnel barriers, and charge configurations consistent with double-dot honeycombs and triple-dot behavior (Kurzmann et al., 2019). Combined with MHz pulsed-gate transport on single-electron BLGQDs (Banszerus et al., 2020), this establishes that both charge sensing and high-frequency gate control are available in the platform.

Ambipolarity adds another control axis. A gate-defined BLGQD with independent barrier and plunger control was tuned continuously from few-hole, through a $n$16 meV gap, into few-electron occupation while maintaining single-dot behavior, and the extracted maximum valley $n$17-factor was approximately $n$18 for electrons and $n$19 for holes (Banszerus et al., 2020). This directly demonstrated the opposite sign of the orbital magnetic moments for confined electron and hole states associated with Berry curvature (Banszerus et al., 2020).

Beyond quantum-dot transport, BLGQD arrays have also been proposed as synthetic many-body systems. A chain of electrostatically defined BLGQDs with two electrons per dot was modeled atomistically and, after exact diagonalization of the interacting few-electron problem, mapped onto a bilinear-biquadratic spin-1 chain

$n$20

with the fitted $n$21 values lying in the Haldane-phase range $n$22 (Miravet et al., 16 Sep 2025). This suggests that BLGQDs can serve not only as qubit elements but also as a programmable platform for topological quantum matter.

A parallel methodological development is the automated identification of BLGQD bound states from spectroscopy. A Hamiltonian-guided random search framework fitted transport-extracted $n$23 curves using the low-energy BLGQD Hamiltonian and recovered continuous parameters with average relative error $n$24 on simulated data and about $n$25 statistical error on experimental data, while robustly assigning the lowest experimental pair to $n$26 (Bucko et al., 2022). This indicates that BLGQD spectroscopy is becoming sufficiently structured for automated state reconstruction, an important prerequisite for scalable control.

Taken together, these developments place BLGQDs at the intersection of semiconductor-style electrostatic tunability and graphene-specific spin-valley physics. The established capabilities now include ambipolar single-dot confinement, few-electron and few-hole occupation, tunable natural $n$27–$n$28-junction barriers, GHz-scale interdot coupling, integrated charge sensing, pulsed-gate spectroscopy, direct real-space imaging, and topological boundary-state design (Eich et al., 2018, Banszerus et al., 2019, Kurzmann et al., 2019, Jaskolski, 13 Mar 2026). The remaining technical themes in the literature are equally clear: more orthogonal barrier control, stronger suppression of residual disorder and parasitic channels, direct measurements of intrinsic $n$29 and coherence times, and systematic incorporation of valley, topology, and crystallographic orientation into device design.