ABA-Stacked Trilayer Graphene

Updated 1 February 2026

ABA-stacked trilayer graphene is a layered van der Waals material defined by Bernal stacking with a mirror plane and distinct non-centrosymmetric properties.
It hosts coexisting massless Dirac and massive quadratic bands, with gate-tunable semimetallicity and anisotropic low-energy features from trigonal warping.
The material exhibits unique quantum Hall effects, strong second-harmonic generation, and Raman G-peak splitting, making it promising for valleytronic and photonic applications.

ABA-stacked trilayer graphene (ABA-TLG), also termed Bernal-stacked trilayer graphene, is a layered van der Waals material composed of three graphene sheets arranged in a non-centrosymmetric Bernal stacking sequence. This structural arrangement imparts distinctive electronic, vibrational, and topological characteristics that differentiate it from both monolayer, bilayer graphene, and from rhombohedral-stacked trilayer graphene (ABC-TLG). ABA-TLG is a semimetal with coexisting massless and massive Dirac quasiparticles, highly tunable by external electric and magnetic fields, and supports unique nonlinear optical and quantum Hall phenomena.

1. Stacking Geometry, Crystal Symmetry, and Structural Identification

In ABA-TLG, the first (bottom) and third (top) graphene layers are aligned, while the second (middle) layer is laterally shifted by one carbon–carbon bond length. This produces the Bernal (ABA) stacking motif, which yields a horizontal mirror plane (σh) through the middle layer and three vertical mirror planes (σ_v), but crucially lacks inversion symmetry. The overall point group is D₃h (Shan et al., 2018), distinct from the centrosymmetric D₃d group of ABC-TLG. The stacking sequence directly governs selection rules for optical and vibrational processes, enabling unambiguous identification via second-harmonic generation (SHG) and stacking-sensitive Raman signatures (Shan et al., 2018, Lin et al., 2012). Triple G-peak splitting in Raman spectra, ascribed to the non-equivalent EPC strengths of E{a}', E_{b}', and E_{a}'' phonon modes, is a hallmark of ABA stacking under heavy doping (Lin et al., 2012).

2. Electronic Band Structure and Gate Tunability

ABA-TLG hosts hybridized electronic states, decomposed into monolayer-like linear (Dirac) bands (odd under mirror) and bilayer-like quadratic (parabolic) bands (even under mirror) (Bao et al., 2017, Bao et al., 2011, Shimazaki et al., 2016). The effective low-energy Hamiltonian in a mirror-symmetric basis yields a direct sum of 2x2 (MLG-like) and 4x4 (BLG-like) blocks, weakly coupled at zero field. Tight-binding fits yield γ₀ ≈ 3.1–3.2 eV, γ₁ ≈ 0.38–0.40 eV, γ₃ ≈ 0.25–0.32 eV, with additional electron–hole and trigonal-warping asymmetries introduced by γ₄, γ₂, and γ₅ (Datta, 2024, Zhang et al., 2018, Bao et al., 2017, Ubrig et al., 2012).

At the neutrality point, ABA-TLG exhibits a small but finite band overlap (semimetallicity) between the MLG-like and BLG-like subbands. This overlap is gate-tunable but no absolute band gap forms for any displacement field, as mirror symmetry protects the massless Dirac cone even under large applied perpendicular electric fields (Zou et al., 2013, Bao et al., 2011, Bao et al., 2017). Self-consistent Hartree calculations and spectroscopies confirm this robust metallic character, with gate-induced potential differences U_scr saturating without gap formation (Zou et al., 2013, Ubrig et al., 2012).

Trigonal warping (from γ₃) produces pronounced threefold anisotropy at low energies, whose interplay with displacement field D leads to Lifshitz transitions and, above critical thresholds, the emergence of off-center Dirac “gullies” in the Fermi surface topology (Winterer et al., 2021).

3. Quantum Hall Effect, Landau-Level Structure, and Broken-Symmetry States

In magnetic field, ABA-TLG supports a Landau level spectrum that is a direct sum of monolayer- and bilayer-like series: MLG-type LLs with energies $E_n = \pm v_F\sqrt{2e\hbar B|n|}$ and BLG-type LLs $E_n = \pm (e\hbar B/m^*)\sqrt{n(n-1)}$ (Yuan et al., 2011, Shimazaki et al., 2016). The zero-energy LL manifold is thus twelvefold degenerate (including spin and valley), but broken mirror symmetry and non-leading hoppings split these into valley- and orbital-resolved sublevels (Shimazaki et al., 2016, Shizuya, 2014, Zhang et al., 2018).

Application of a perpendicular electric displacement field hybridizes the mirror-even and mirror-odd manifolds, producing anti-crossings and valley Hall effects. Trigonal warping couples every third BLG-like orbital, giving rise to additional anti-crossings. Edge states with nontrivial valley Chern numbers (C^V ≈ ±2.5) appear above a critical D exceeding 0.2 V/nm, consistent with topological valley Hall edge modes observed in non-local transport (Srivastav et al., 2024, Shimazaki et al., 2016, Winterer et al., 2021).

Many-body effects such as interaction-enhanced valley and orbital splitting (“orbital Lamb shift”), and correlated quantum Hall ferromagnetic or nematic phases, are experimentally resolved via LL crossings, energy-dependent effective mass renormalization, and spontaneous gully polarization at high electric field and low temperature (Zhang et al., 2018, Shizuya, 2014, Winterer et al., 2021). The quantum Hall plateau sequence at low field is ν = …–6, –2, 2, 6, 10, 14…, with further symmetry breaking at high field giving rise to all integer ν and enhanced electron–hole asymmetry (Datta, 2024, Henriksen et al., 2011).

4. Nonlinear and Infrared Optical Properties

ABA-TLG is non-centrosymmetric (D₃h), enabling electric-dipole allowed second-harmonic generation (SHG)—forbidden in inversion-symmetric ABC-TLG (Shan et al., 2018). The SHG signal is strong (χ_{aaa}^{{(2)}(1300 nm)} ≈ 0.9×10⁻¹⁰ m/V), with sixfold polarization anisotropy directly reflecting point-group symmetry. SHG intensity is threefold larger than hBN monolayer and within an order of MoS₂, without reliance on excitonic resonance. SHG microscopy thus gives high-contrast domain mapping and orientation assignment of ABA domains (Shan et al., 2018).

Infrared spectroscopy detects a weak IR-active phonon near 1584 cm⁻¹ (E′′) with spectral weight only mildly tunable by electrostatic gating, as the relevant interband transitions in ABA-TLG are far above the phonon energy. The charged-phonon anomaly is much weaker than in ABC-TLG, due to less favorable resonance conditions and stronger cancellation by symmetry (Lui et al., 2013).

Optical conductivity is dominated by low-energy Drude response and pronounced interband absorption peaks, arising from “band nesting” of two parabolic subbands separated by Δ ≈ √2γ₁ ≈ 0.56 eV, yielding a strong and gate-tunable mid-IR resonance (Rashidian et al., 2014, Ubrig et al., 2012). The characteristic frequency and peak intensity are robust to temperature.

5. Phonon Properties, Raman Spectroscopy, and Vibrational Anomalies

The Γ-point E₂g mode of monolayer graphene splits in ABA-TLG into three optical phonons (Eₐ′, E_{b}′, Eₐ″). EPC strengths (λ{Eₐ′}>λ{E_{b}′}>λ_{Eₐ″}) lead to clearly resolved triple G-peak splitting under heavy doping. Spatial G-peak variations encode local interlayer coupling fluctuations, which track nonuniform charge distribution across layers (Lin et al., 2012).

In magnetic field, the E_{2g} phonon exhibits pronounced magnetophonon resonance (MPR) oscillations in ABA stacking, corresponding to well-spaced J=1 inter-LL transitions. For ABC stacking, higher chiralities (J=3) compactify the LLs and suppress the oscillatory MPR in experimentally accessible fields, making MPR a fingerprint of ABA stacking (Cong et al., 2015).

6. Edge Modes, Nonlocal Transport, and Topological Phenomena

A dual-gate architecture allows independent control of carrier density (n) and displacement field (D), which at D > 0.2 V/nm nucleates dispersive, valley-Hall edge modes traversing the bulk gap (Srivastav et al., 2024). Nonlocal resistance (R_NL) measurements show R_NL ≫ R_NL^classical when above the threshold field and at low temperatures (T < 25 K), consistent with edge conduction described by a dissipative resistor-network model. The presence and tunability of edge channels are theoretically supported by tight-binding calculations, showing their emergence only for D > Dₙ (Srivastav et al., 2024). These modes are valley Hall in origin but are not topologically protected against intervalley scattering. By tuning D, devices can be switched between bulk-dominated and edge-dominated transport regimes.

Dirac gullies—off-center Dirac points in reciprocal space—emerge under sufficiently strong displacement field and trigonal warping. With Coulomb interactions, these can undergo spontaneous nematic polarization transitions, as confirmed by abrupt LL splitting and changes in QH degeneracy (Winterer et al., 2021).

7. Transport, Thermoelectricity, and Device Implications

At zero magnetic field, ABA-TLG exhibits robust semimetallic conduction with V-shaped G(V_g) and high minimum conductance even at charge neutrality (Bao et al., 2011, Datta, 2024). Electric bias and field tuning do not produce a gap, but can modulate the band overlap and promote two-band transport regimes, as observed by characteristic resistance peaks and negative differential resistance at large D (Zou et al., 2013).

Under magnetic field, thermoelectric and thermal conductivities display signatures of both monolayer- and bilayer-like Landau quantization. The transverse thermoelectric conductivity α{xy} exhibits linear-T scaling at low temperature and saturates at α{xy} → 2.77 k_Be/h at each LL center for high temperatures (Ma et al., 2012). The longitudinal resistivity and thermopower near the Dirac point remain finite at all T, with enhanced Nernst and thermopower response due to the semi-metallic band structure.

The unique structure-property relationship of ABA-TLG—combining absence of an electric-field tunable gap, non-centrosymmetry, high-mobility semimetallicity, gate-tunable nontrivial edge states, and strong nonlinear optical response—positions it as a compelling platform for 2D nonlinear photonics, valleytronic devices, and for studies of topological and correlated electron phenomena.

References: (Shan et al., 2018, Srivastav et al., 2024, Zou et al., 2013, Bao et al., 2017, Shimazaki et al., 2016, Bao et al., 2011, Ubrig et al., 2012, Shizuya, 2014, Cong et al., 2015, Lin et al., 2012, Lui et al., 2013, Yuan et al., 2011, Winterer et al., 2021, Datta, 2024, Rashidian et al., 2014, Zhang et al., 2018, Henriksen et al., 2011, Ma et al., 2012).