---
title: ABCB-Stacked Tetralayer Graphene
url: https://www.emergentmind.com/topics/abcb-stacked-tetralayer-graphene
type: topic
---

# ABCB-Stacked Tetralayer Graphene

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 [2504.06874, 2311.16797, 2302.07374, 2504.07935, 2511.22980, 2403.09354].

## 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 [2504.06874, 2504.07935]. 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 [2311.16797, 2403.09354]. 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 \(\gamma_0, \gamma_1, \gamma_2, \gamma_3, \gamma_4, \gamma_5\) [2311.16797, 2302.07374]. 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 \(5.7{\sim}20\,\mathrm{meV}\) [2311.16797, 2504.07935, 2511.22980, 2203.07971]. 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 [2305.14438].

## 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 [2504.06874, 2504.07935, 2311.16797]. 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” [2504.06874]. Experimentally, Kelvin probe force microscopy gives domain work function differences of \( \sim 150{-}200\,\mathrm{mV} \), confirming the polar nature [2504.06874, 2403.09354]. The polarization persists across wide temperature and field ranges, and is robust to external gating and environmental fluctuations [2504.07935].

## 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 [2504.06874, 2203.07971].
- **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 [2504.06874, 2302.07374].
- **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 [2403.09354].
- **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 [2311.16797].

### 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 \(\Delta n_t \approx 0.63 \times 10^{12}\,\mathrm{cm}^{-2}\), \(\Delta n_b \approx 0.70\times 10^{12}\,\mathrm{cm}^{-2}\) [2504.07935]. 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 [2504.06874].
- **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 [2504.06874].

## 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 [2511.22980].
- **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 [2511.22980].
- **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 [2305.14438].
- **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 [2511.22980].

## 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 [2403.09354]. 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 [2403.09354].

## 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 [2504.06874, 2504.07935]. Integration into all-2D heterostructure devices (e.g., tunnel junctions, nonvolatile memory, neuromorphic architectures) is enabled by its robust polarization and multiferroic potential [2504.06874]. 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.

Source: https://www.emergentmind.com/topics/abcb-stacked-tetralayer-graphene