ABCB-Stacked Tetralayer Graphene

• ABCB-stacked tetralayer graphene is a polytype with a distinct A→B→C→B sequence that creates a noncentrosymmetric lattice and spontaneous out-of-plane ferroelectricity.
• It exhibits a hybrid electronic band structure with nearly Dirac-like and Mexican-hat features, resulting in an intrinsic bandgap between 5.7 and 20 meV.
• The material serves as a platform for exploring correlated phases, quantum anomalous Hall effects, and switchable ferroelectric domains using advanced spectroscopy and microscopy techniques.

ABCB-stacked tetralayer graphene is a distinct polytype of four-layer graphene in which the layers are arranged in an A→B→C→B sequence, leading to a noncentrosymmetric lattice with novel electronic, ferroelectric, and topological properties. Its lack of inversion symmetry is responsible for the emergence of spontaneous out-of-plane electric polarization—an elemental example of electronic ferroelectricity in a two-dimensional van der Waals metal. This stacking yields a platform for exploring flat-band correlated physics, intrinsic polarization switching, nonlinear optics, and quantum anomalous Hall states, all rooted in the symmetry and stacking-induced charge redistribution of the system (Zhou et al., 9 Apr 2025, Zhou et al., 2023, McEllistrim et al., 2023, Singh et al., 10 Apr 2025, Ren et al., 28 Nov 2025, Sarsfield et al., 14 Mar 2024).

1. Crystallography and Symmetry

The ABCB stacking sequence consists of four monolayer graphene sheets labeled from bottom (Layer 1) to top (Layer 4), with the sublattice registry following:

• Layer 1: A site at $z_1=0$
• Layer 2: B site at $z_2=d$
• Layer 3: C site at $z_3=2d$
• Layer 4: B site at $z_4=3d$

where $d \approx 0.335\,\mathrm{nm}$ is the interlayer spacing (Zhou et al., 9 Apr 2025, Singh et al., 10 Apr 2025). The crystallographic point group is $C_{3v}$, featuring threefold rotational symmetry about the out-of-plane axis and three vertical mirror planes, but explicitly lacking an inversion center (Zhou et al., 2023, Sarsfield et al., 14 Mar 2024). This symmetry—distinguishing ABCB from both Bernal (ABAB) and rhombohedral (ABCA) polytypes—permits a spontaneous electric dipole in the out-of-plane direction.

2. Electronic Structure and Intrinsic Bandgap

The electronic bands of ABCB-stacked tetralayer graphene derive from a Slonczewski–Weiss–McClure (SWMcC) tight-binding model incorporating intralayer and interlayer hopping parameters $$\gamma_0, \gamma_1, \gamma_2, \gamma_3, \gamma_4, \gamma_5$$ (Zhou et al., 2023, McEllistrim et al., 2023). In the vicinity of the high-symmetry K point, the Hamiltonian (in the sublattice basis $(A_1,B_1;A_2,B_2;A_3,B_3;A_4,B_4)$) presents a hybrid structure:

• Two nearly overlapping Dirac-like (bilayer) bands at low energy.
• A “Mexican-hat” (rhombohedral-like) feature, producing van Hove singularities near the band edges and extremely flat valence/conduction bands.
• A true intrinsic bandgap at charge neutrality, predicted in various parametrizations as ranging from $5.7{\sim}20\,\mathrm{meV}$ (Zhou et al., 2023, Singh et al., 10 Apr 2025, Ren et al., 28 Nov 2025, Wirth et al., 2022). For example, DFT and fitted tight-binding models yield $\Delta_0\approx 5.7\,\mathrm{meV}$ and $\Delta_{\mathrm{ABCB}}\approx 18\,\mathrm{meV}$.

The local flatness and large density of states near the band edge fuel enhanced electronic correlations, ferrimagnetism, and unconventional superconductivity (Fischer et al., 2023).

3. Spontaneous Out-of-Plane Polarization

The noncentrosymmetric ABCB polytype hosts a built-in, layer-resolved charge imbalance, driving a spontaneous polarization $P_z$ in the out-of-plane direction. Theoretically, this is formalized as:

$P_z = \frac{e}{A} \sum_{i=1}^4 z_i \Delta n_i$

where $\Delta n_i$ is the excess electron density on layer $i$, and $A$ is the flake area (Zhou et al., 9 Apr 2025, Singh et al., 10 Apr 2025, Zhou et al., 2023). DFT and SWMcC calculations yield a 2D sheet polarization $|P| \simeq 1.2\,\mu\mathrm{C}/\mathrm{cm}^2$, with the ABCB polytype oriented “upward” along $+\hat{z}$, and the mirror twin ABAC “downward” (Zhou et al., 9 Apr 2025). Experimentally, Kelvin probe force microscopy gives domain work function differences of $\sim 150{-}200\,\mathrm{mV}$, confirming the polar nature (Zhou et al., 9 Apr 2025, Sarsfield et al., 14 Mar 2024). The polarization persists across wide temperature and field ranges, and is robust to external gating and environmental fluctuations (Singh et al., 10 Apr 2025).

4. Experimental Probes and Identification

The detection and distinction of ABCB stacking leverage multiple complementary spectroscopic and microscopies:

• Scanning Near-Field Optical Microscopy (SNOM): Enables optical mapping of polar domains and domain wall (DW) motion via third-harmonic-detected near-field amplitude ($S_3$), sensitive to local permittivity and carrier density, and therefore, stacking and polarization (Zhou et al., 9 Apr 2025, Wirth et al., 2022).
• Raman Spectroscopy: The 2D-peak lineshape for ABCB/ABAC stacking is intermediate between ABAB and ABCA and cannot itself distinguish the two polar twins; only techniques sensitive to polarization (e.g., SNOM, KPFM) can (Zhou et al., 9 Apr 2025, McEllistrim et al., 2023).
• Kelvin Probe Force Microscopy (KPFM): Directly measures work function differences proportional to $P_z$, and, when performed at low temperature and in quantizing magnetic fields, uniquely reveals the “bulges” in potential expected from intrinsic polarization, distinguishing substrate-induced from intrinsic effects (Sarsfield et al., 14 Mar 2024).
• Second Harmonic Generation (SHG): ABCB domains exhibit pronounced SHG response due to their noncentrosymmetric $C_{3v}$ symmetry, with an absolute nonlinear sheet susceptibility $$\chi^{(2)}_{\mathrm{ABCB}} \approx 0.25\times 10^4\,\mathrm{pm}^2/\mathrm{V}$$, providing rapid domain mapping and crystalline orientation characterization. ABAB and ABCA domains (centrosymmetric, $D_{3d}$) are SHG-inactive (Zhou et al., 2023).

Table: Stacking-Dependent Experimental Signatures

Stacking	SHG Signal	Optical Conductivity (mid-IR)	KPFM Potential Contrast
ABAB	Absent	Smooth, featureless	None
ABCA	Absent	Dual peaks ($0.3, 0.4\,\mathrm{eV}$)	None
ABCB	Strong	Single peak ($\sim 0.38\,\mathrm{eV}$)	$150-200\,\mathrm{mV}$ vs. ABAC

5. Ferroelectric Switching and Domain Dynamics

The intrinsic ferroelectric polarization of ABCB-stacked tetralayer graphene is electrically and mechanically addressable:

• Electrical Control: Gate voltage induces DW sliding, switching between ABCB and ABAC (P↑↔P↓) domains. Gate-induced transitions result in hysteresis in longitudinal resistance ($\rho_{xx}$) as a function of gate carrier density or displacement field, with a remanent polarization shift $P_{2D} \approx 0.04\;\mu\mathrm{C}/\mathrm{cm}^2$. The observed critical density offsets for switching are $$\Delta n_t \approx 0.63 \times 10^{12}\,\mathrm{cm}^{-2}$$, $$\Delta n_b \approx 0.70\times 10^{12}\,\mathrm{cm}^{-2}$$ (Singh et al., 10 Apr 2025). This behavior persists with minimal temperature dependence from $5\,\mathrm{K}$ to $300\,\mathrm{K}$.
• Mechanical Manipulation: Deliberate AFM tip scanning (with lateral force $10{-}50\,\mathrm{nN}$) can drag domain walls, switching P over micron scales with observed effective sliding barriers $\Delta E \sim 3.2\,\mathrm{meV}/$unit cell, consistent with calculated Kramers-law switching probabilities (Zhou et al., 9 Apr 2025).
• Domain Wall Kinetics: DWs move under gate field $E_g\sim10^7\,\mathrm{V}/\mathrm{m}$, with velocities $$v \approx 3\times 10^{-3}\,\mu\mathrm{m}/\mathrm{s}$$ at room temperature (Zhou et al., 9 Apr 2025).

6. Correlated Phases and Topological States

The combination of broken inversion symmetry, flat low-energy bands, and enhanced DOS enables a rich array of correlated states:

• Quantum Anomalous Hall (QAH) Insulator: In the presence of strong on-site Hubbard interaction ($U=8\,\mathrm{eV}$) and Ising-type spin-orbit coupling ($\lambda\sim2.5\,\mathrm{meV}$), the intrinsic polarization and correlations together drive a $C=3$ QAH state at zero electric field, with the Hall conductivity $\sigma_{xy} = 3(e^2/h)$ and a QAH gap $\Delta\sim1{-}2\,\mathrm{meV}$. At intermediate $U=6\,\mathrm{eV}$, only a small upward displacement field ($E\sim 4{-}8.5\,\mathrm{mV}/\mathrm{nm}$) is required to induce the QAH phase (Ren et al., 28 Nov 2025).
• Spin/Valley-Polarized Metals: At partial fillings and moderate fields, correlated quarter- and three-quarter-filled metallic states arise, with spin/valley-resolved Fermi pockets shaped by trigonal band warping (Ren et al., 28 Nov 2025).
• Superconductivity and Magnetism: Near van Hove singularities, random-phase-approximation calculations predict competition between ferrimagnetic states and unconventional superconductivity:
  • Short-range interactions (local $U$) favor layer-selective ferrimagnetism and spin-triplet, valley-singlet $f$-wave pairing.
  • Long-range (screened) Coulomb interactions promote $p$-wave superconductivity.
  • The leading superconducting instability, with $T_c$ of $10{-}100\,\mathrm{mK}$, is determined by the balance between local and remote interaction strengths (Fischer et al., 2023).
• Layer-Polarized Insulator: The intrinsic polarization opens a layer-polarized insulating gap (LPI), analogous to a gate-induced gap in centrosymmetric stacks but driven here by symmetry-breaking stacking (Ren et al., 28 Nov 2025).

7. Substrate, Temperature, and Field Effects

The measured polarization is a sum of intrinsic and substrate-induced contributions. For ABCB, at room temperature on SiO$_2$, the observed KPFM potential contrast ($\sim 0.13\,e/\mu\mathrm{m}$) is dominated by substrate-induced energy shifts ($\Delta_s$), with only $\sim 0.01\,e/\mu\mathrm{m}$ from intrinsic polarization (Sarsfield et al., 14 Mar 2024). At $T\lesssim1\,\mathrm{K}$ under quantizing magnetic fields, valley-resolved Landau level structure leads to non-monotonic bulges in the intrinsic polarization, providing a unique fingerprint for ABCB/ABAC twins. This enables experimentally distinguishing the intrinsic polar nature of mixed-stack domains from environmental effects (Sarsfield et al., 14 Mar 2024).

8. Outlook and Device Implications

ABCB-stacked tetralayer graphene is established as the simplest natural example of stacking-driven electronic ferroelectricity in a van der Waals metal. The polarization is stable to room temperature, switchable by both electric field and mechanical intervention, and directly visualized by SNOM and KPFM (Zhou et al., 9 Apr 2025, Singh et al., 10 Apr 2025). Integration into all-2D heterostructure devices (e.g., tunnel junctions, nonvolatile memory, neuromorphic architectures) is enabled by its robust polarization and multiferroic potential (Zhou et al., 9 Apr 2025). The coexistence of tunable ferroelectric, correlated, and topological states—in the absence of moiré or artificial superlattice engineering—positions ABCB-4L graphene as an optimal platform for probing symmetry-driven phenomena, dynamic switching kinetics, and the interplay of electronic order parameters in atomically thin materials.