Bernal-Stacked Graphene Overview

Updated 15 August 2025

Bernal-stacked graphene is a multilayer form of graphene in which adjacent layers adopt the AB stacking order, leading to modified electronic dispersion and tunable bandgaps.
It exhibits unique quantum Hall effects and interaction-driven symmetry breaking, making it valuable for exploring flat-band, half-metallic, and superconducting phases.
Characterization tools such as Raman spectroscopy and STM reveal detailed insights into interlayer coupling, defect physics, and strain-induced modifications of its electronic properties.

Bernal-stacked graphene refers to multilayer graphene in which adjacent layers adopt the AB (Bernal) stacking configuration—the crystallographic arrangement characteristic of graphite—whereby every other layer is shifted so that half of the carbon atoms in one layer (the A sites) sit directly above those in adjacent layers, while the other half (the B sites) are centered above the hexagons. This stacking fundamentally alters the low-energy electronic structure and enables phenomena not present in monolayer graphene, including tunable bandgaps, interaction-driven ordered states, unconventional quantum Hall effects, and a variety of symmetry-breaking electronic phases.

1. Crystallographic Arrangement and Electronic Structure

Bernal (AB) stacking arises when each graphene layer is shifted so that atoms on one sublattice in the upper layer (A) are directly above atoms on the same sublattice in the lower layer, with the other sublattice (B) above the centers of the hexagonal rings. In bilayer systems, this arrangement produces a four-atom unit cell (A1, B1, A2, B2), yielding a four-band model. The key electronic distinction from single-layer graphene is the emergence of low-energy quasiparticles with a parabolic (rather than linear) dispersion near the K and K′ points, separated by an energy scale set by the interlayer coupling γ₁ (typically ~0.4 eV). The electronic Hamiltonian for Bernal-stacked bilayer graphene can be generalized as

$H_0 = \begin{pmatrix} 0 & v_F \pi^\dagger & \gamma_1 & 0 \ v_F \pi & 0 & 0 & 0 \ \gamma_1 & 0 & 0 & v_F \pi^\dagger \ 0 & 0 & v_F \pi & 0 \end{pmatrix},$

where $v_F$ is the Fermi velocity and $\pi = \xi p_x + i p_y$ is the momentum operator near each valley.

In multilayer (N-layer) Bernal graphene, electronic structure features replicate: even-layer stacks yield multiple bilayer-like (quadratic) bands, while odd-layer stacks also host a monolayer-like (linear) band. The dispersions are further perturbed by higher-order hopping terms, trigonal warping, and possible valley/spin order (Nakasuga et al., 2018).

2. Quantum Hall Effect and Landau Quantization

Bernal-stacked bilayer graphene exhibits integer quantum Hall states (QHSs) at filling factors $\nu = 4, 8, 12,\ldots$ , arising from the fourfold spin-valley degeneracy and the parabolic band structure (Fallahazad et al., 2012). Magnetotransport experiments demonstrate that at high magnetic fields (e.g., $B = 25$  T, $T = 0.3$  K), the longitudinal resistivity $\rho_{xx}$ vanishes and the Hall resistivity $\rho_{xy}$ exhibits clear quantization at integer fractions $h/\nu e^2$ . The Landau fan diagrams for Bernal-stacked multilayer graphene (e.g., in AB-stacked hexlayer) reveal zero-mode Landau levels with high degeneracy (eightfold for bilayer-like bands), as well as clear electric-field-induced splitting and ridge structures in resistance maps (Nakasuga et al., 2018).

Trigonal warping (associated with the hopping parameter γ₃) modifies the fine structure of the Landau levels, splitting Dirac points into multiple pockets and inducing mini-Dirac cones and topological transitions in the Fermi surface when a perpendicular electric field is applied (Joucken et al., 2019, Nakasuga et al., 2018). These features are probed via quantum oscillations, scanning tunneling spectroscopy, and quasiparticle interference mapping.

3. Tunable Band Gap, Symmetry Breaking, and Ordered States

A prominent feature of Bernal-stacked bilayer graphene (and even-layer multilayers) is the ability to tune the electronic band gap by applying a perpendicular electric displacement field, breaking the inversion symmetry between the two layers. This field-induced asymmetry opens a gap at the K and K' points whose magnitude is proportional to the potential difference between the layers (Boschi et al., 7 Jun 2024), enabling electrostatic control of semiconducting-to-semimetallic transitions.

Bernal-stacked multilayers exhibit interaction-driven broken-symmetry phases at low temperature. In such phases, a self-consistent, valley- and spin-dependent staggered potential emerges, resulting in a finite-temperature second-order phase transition with a critical temperature $T_c$ that grows with the number of layers; in hexalayer and heptalayer systems, $T_c$ can reach 90–100 K (Nam et al., 2018). Charge-ordered ground states have also been identified, in which a spontaneous sublattice asymmetry yields a band inversion and an intrinsic insulating gap at zero field (Jiang et al., 31 Mar 2024).

4. Spectroscopic, Raman, and Structural Characterization

Bernal stacking is identified by the broadening and asymmetry of the 2D Raman band (FWHM ≈ 45–54 cm⁻¹ for AB stacking), contrasted with the narrow 2D band of twisted or turbostratic bilayers (Fallahazad et al., 2012). Isotopic labelling with $^{12}$ C and $^{13}$ C permits direct layer-specific tracking of vibrational shifts, revealing that in CVD-grown Bernal bilayers, both layers have nearly identical thermal responses and act as a strongly coupled unit (Weis et al., 2014, Costa et al., 2021). The Raman 2D′ mode in AB bilayers decomposes into three components: contributions from each layer and a mixed mode—thus enabling precise evaluation of strain, doping, and interlayer coupling.

Scanning tunneling microscopy (STM) and spectroscopy (STS) further resolve domain boundaries, stacking order, and native defects. Controlled horizontal shearing of the top graphene layer (for example, via STM tip manipulation) interconverts Bernal (ABA) and rhombohedral (ABC) stacking, with energy barriers anisotropic in direction: the pathway toward the "no overlap" configuration presents a low barrier (~1.5 meV/atom), while the route toward AA stacking has a higher barrier (~15 meV/atom) (Xu et al., 2015).

5. Impurity, Midgap, and Defect Physics

Native or extrinsically introduced defects in Bernal-stacked bilayer graphene induce both midgap and resonant states that are highly sensitive to sublattice placement: midgap states appear for dopants on non-dimer (A1 or B2) sites and are highly localized both energetically and spatially, while dopants on dimer sites induce sharp resonances at band extrema (Joucken et al., 2021). Gate-induced modulation can tune the bandgap and thus the energetic position and visibility of these localized states. Such impurity states have direct implications for low-energy transport (e.g., conductivity plateaus), optical absorption, and quantum coherence in devices.

Atomically resolved STM reveals that native defects (e.g., nitrogen dopants) are ubiquitous in exfoliated and device-grade graphite, exhibiting areal densities of up to $6.6 \times 10^{-6}$ per layer and acting as scattering centers that limit carrier mobility—especially at low temperatures ( $T < 1$ K)—as confirmed by Boltzmann transport theory and T-matrix analysis (Joucken et al., 2021). The magnetic properties of single adatoms (e.g., transition-metal impurities) are themselves sublattice-dependent, with enhanced local moments retained on A sites (due to lower local density of states) and stronger Kondo screening on B sites (Sun et al., 2012).

6. Correlated, Superconducting, Topological, and Flat-Band Phases

Bernal stacking accommodates a variety of interaction-driven phases. Half-metallic states can be induced in electric-field-tuned, slightly doped even-layer multilayers (such as tetralayer): application of a gate field and minimal doping drive one spin channel metallic while the other remains insulating. A band inversion in the spin-polarized conduction and valence bands is predicted as the field is increased, enabling control and inversion of the net magnetic moment (Liang et al., 2021).

Superconductivity has been observed in displacement-field-flattened Bernal bilayers, with the superconducting state emerging only when an in-plane magnetic field or Ising spin–orbit coupling is present. Theoretical analysis using functional renormalization group and random-phase approximation demonstrates that the pairing arises from a purely electronic p-wave (Kohn–Luttinger) instability, enhanced by these tuning effects, and rooted in the overscreening of intra- relative to inter-pocket Coulomb interactions in a three-pocket Fermi surface (Wagner et al., 2023).

When a superlattice potential (e.g., moiré or patterned substrate) is imposed, Bernal-stacked multilayers can, depending on stacking and applied field, realize isolated topological flat bands (with nonzero Chern number), especially at weak fields. However, the ability to produce a stack of many flat bands is more naturally realized in chirally stacked multilayers; Bernal stacking with two superlattice potentials can enhance the flatness and topological isolation of bands, enabling exploration of correlated topological phases (Ghorashi et al., 2022).

7. Modelling, Strain Effects, and Device Realization

State-of-the-art device-scale modelling of Bernal-stacked bilayer graphene is made possible by a four-band effective square-lattice discretization of the low-energy continuum Hamiltonian, which captures the physics at both K and K′ valleys while bypassing the fermion doubling problem. Such models are validated against both tight-binding and experiment, enabling large-scale quantum transport simulations—e.g., for nanoribbons, quantum rings, magnetic focusing geometries—over a broad range of magnetic field (Chen et al., 5 Mar 2024).

Strain acts as a pseudo-gauge field in Bernal bilayers, inducing pseudo Landau quantization into highly degenerate pseudo Landau levels—most notably a dispersionless (flat) zeroth and sometimes first level—hosting sublattice-polarized states. Analytical reduction of strained ribbons to a coupled Dirac-Su–Schrieffer–Heeger model demonstrates that these flat bands enhance interaction-driven magnetism, with global antiferromagnetic order realized at half filling (Liu et al., 29 Oct 2024). This finding advances the use of strain engineering as a tuning parameter for magnetism and correlated phases.

Recent work has also identified the formation of a spontaneous “Bernal gap” in BLG embedded in large-angle-twisted MLG/BLG/hBN stacks, with the gap (~10 meV) stemming from proximity-induced energy shifts and requiring a compensating displacement field of ~0.14 V/nm to close—thereby providing a route to deterministic, scalable gap engineering for nanoelectronics (Boschi et al., 7 Jun 2024).

In summary, Bernal-stacked graphene is a paradigmatic two-dimensional electron system in which stacking geometry, external fields, strain, and disorder interplay to yield a diverse set of highly tunable quantum phases, band structure phenomena, and device functionalities. The stacking order influences not only single-particle dispersion and quantum Hall sequences, but also symmetry breaking, interaction-driven gaps, half-metallic and superconducting states, flat-band topologies, and defect-mediated effects—features of direct relevance for nanoelectronics, optoelectronics, and fundamental condensed matter research.