Interaction-Driven Chern Insulator at Zero Electric Field in ABCB-Stacked Tetralayer Graphene

TL;DR

The paper addresses whether intrinsic spontaneous polarization in ABCB-stacked tetralayer graphene can substitute for an external electric field to realize a Chern insulator. Using a refined $\mathbf{k}\cdot\mathbf{p}$ model with self-consistent Hartree-Fock, benchmarked against DFT, it shows that strong interactions $U$ together with SOC can produce a zero-field QAH state with $C=3$, while weaker interactions require a small applied field. A rich phase diagram emerges, including correlation-driven metallic states at fractional fillings and a tunable window for the QAH phase controlled by $U$, $\lambda$, and $E$. The work highlights ABCB as a highly tunable, non-moiré platform for crystalline-topological phenomena, with practical implications for low-field topological control in clean devices and guidance for exploring polarization-enabled topology.

Abstract

ABCB-stacked tetralayer graphene, with intrinsic spontaneous polarization, offers a unique platform to explore electron correlation effects, whose interplay with spin-orbit coupling may engender topological phases. Here, employing a $\mathbf{k}\cdot\mathbf{p}$ model with self-consistent Hartree-Fock calculations, we investigate its electronic ground states. Remarkably, we find that the intrinsic polarization, in conjunction with strong interactions ($U=8 \text{ eV}$) and SOC, is sufficient to drive a $C=3$ quantum anomalous Hall state, obviating the need for an external electric field typical in ABCA stacks. Conversely, at moderate interactions ($U=6 \text{ eV}$), a minimal electric field is necessary. Furthermore, calculations predict other correlation-driven metallic phases such as quarter- and three-quarter-filled states. These results establish that the synergy of intrinsic polarization, correlations, and SOC governs the rich topological phenomena, suggesting ABCB-stacked graphene as a highly tunable platform for exploring emergent topological phenomena.

Figures (17)

• Figure 1: Schematic comparison of interaction-driven symmetry-broken states in ABCA and ABCB. (a, c, e) The four spin-valley channels in ABCA under interaction (a), interaction with SOC (c) and with electric field $E$ (e). (b, d) The channels in ABCB under interaction (b) and with SOC (d). (f) Side view of the lattices defining the non-dimer sites (A$_1$, B$_4$, B$_3$), the direction of $E>0$, and the spontaneous polarization $P$. Blue/red bands denote wavefunction localization on A$_1$/B$_4$ (for ABCA) and A$_1$/B$_3$ (for ABCB) sites. Solid/dashed bands represent Chern numbers $C=\pm 2$ for ABCA and $C=\pm 3/2$ for ABCB, respectively. Black arrows indicate energy shifts, and the dashed box highlights a channel tending towards band inversion.
• Figure 2: Bands and Landau levels of ABCB for the non-interacting Hamiltonian $\mathcal{H}_{\text{eff}}$ without electric field and SOC. (a) Site-resolved projection of the band structure with red representing the B$_3$ site (on layer 3) and blue representing the A$_1$ site (on layer 1). Black arrows indicate the spin direction of the bands. (b) Calculated Landau levels as a function of magnetic field. Solid (dashed) lines represent states from one valley (the other valley).
• Figure 3: Landau fan diagram for ABCB. The plot shows the DOS as a function of carrier density $n$ (negative values denote hole doping, positive values denote electron doping) and magnetic field $B$. Red (blue) color indicates high (low) DOS.
• Figure 4: Projected band structure for ABCB calculated with an SOC strength of $\lambda = 2.5 \text{ meV}$. The left and right panels display results for the $K$ and $K^{\prime}$ valleys, respectively. Black arrows indicate the spin polarization of the bands. Red (blue) representing the B$_3$ (A$_1$) site.
• Figure 5: Projected band structure for ABCB calculated with an interaction strength of $U = 8 \text{ eV}$. The left and right panels display results for the $K$ and $K^{\prime}$ valleys, respectively. Black arrows indicate the spin polarization of the bands. Red (blue) representing the B$_3$ (A$_1$) site.