Tunable Correlated Chern Insulator and Ferromagnetism in Trilayer Graphene/Boron Nitride Moiré Superlattice (1905.06535v1)

Abstract: Studies on two-dimensional electron systems in a strong magnetic field first revealed the quantum Hall (QH) effect, a topological state of matter featuring a finite Chern number (C) and chiral edge states. Haldane later theorized that Chern insulators with integer QH effects could appear in lattice models with complex hopping parameters even at zero magnetic field. The ABC-trilayer graphene/hexagonal boron nitride (TLG/hBN) moir\'e superlattice provides an attractive platform to explore Chern insulators because it features nearly flat moir\'e minibands with a valley-dependent electrically tunable Chern number. Here we report the experimental observation of a correlated Chern insulator in a TLG/hBN moir\'e superlattice. We show that reversing the direction of the applied vertical electric field switches TLG/hBN's moir\'e minibands between zero and finite Chern numbers, as revealed by dramatic changes in magneto-transport behavior. For topological hole minibands tuned to have a finite Chern number, we focus on 1/4 filling, corresponding to one hole per moir\'e unit cell. The Hall resistance is well quantized at h/2e2, i.e. C = 2, for |B| > 0.4 T. The correlated Chern insulator is ferromagnetic, exhibiting significant magnetic hysteresis and a large anomalous Hall signal at zero magnetic field. Our discovery of a C = 2 Chern insulator at zero magnetic field should open up exciting opportunities for discovering novel correlated topological states, possibly with novel topological excitations, in nearly flat and topologically nontrivial moir\'e minibands.

• The paper demonstrates a tunable Chern insulator with C=2 in the hole minibands of trilayer graphene/hBN moiré superlattices.
• The paper reveals that vertical electric gating effectively switches between correlated insulator states, showing clear topological phase transitions.
• The paper provides experimental and theoretical evidence of spontaneous ferromagnetism and the quantum anomalous Hall effect, highlighting strong electron interactions.

Tunable Correlated Chern Insulator and Ferromagnetism in Trilayer Graphene/Boron Nitride Moiré Superlattices

This paper reports on a novel experimental observation of a correlated Chern insulator in ABC-trilayer graphene aligned with hexagonal boron nitride (TLG/hBN) moiré superlattices. The paper reveals insights into managing electron correlation and topological states through electrostatic gating in this two-dimensional material system, which offers a tunable platform for exploring quantum anomalous Hall (QAH) effects and spontaneous ferromagnetism.

Key Observations

1. Chern Insulator Transition: The researchers have demonstrated that the TLG/hBN system can harbor a Chern insulator with C = 2, observable through a quantized Hall resistance at zero magnetic field. This occurs exclusively for hole minibands with a non-zero Chern number (C ≠ 0), tuned via a displacement field.
2. Tunability via Electric Field: By manipulating the vertical electric field, the paper showcases that the moiré minibands' topology is switchable. This capability facilitates transitioning between correlated insulator states at 1/4 and 1/2 fill of the hole minibands.
3. Ferromagnetic Behavior: The correlated Chern insulator in the studied moiré superlattice system prompts spontaneous breaking of time-reversal symmetry, rendering ferromagnetic characteristics. The observed ferromagnetic hysteresis and prominent anomalous Hall signals further highlight the robust inherent electronic interactions within the system.
4. Quantum Anomalous Hall Effect: The manifestation of the QAH effect at 1/4 filling with C = 2 was identified, not typical in conventional Landau level graphs. This result suggests electron-electron interactions in this prepared state leading to a reduced valley Chern number to 2.
5. Numerical and Theoretical Insight: The empirical observations have been substantiated by theoretical calculations incorporating electron-electron interaction effects through a Hartree-Fock approach. These calculations suggest the potential transition of valley polarization states influenced by interactions, an intriguing theoretical proposition connecting closely with the quantum Hall effect.

Implications and Future Directions

The empirical realization of a tunable Chern insulator in TLG/hBN moiré superlattices opens pathways to studying novel correlated topological states and crafting sophisticated electronic devices based on van der Waals heterostructures. These materials might provide a fertile ground for discovering fractional Chern insulators and exploring strongly correlated phases such as non-Abelian states and gapped excitations.

From a theoretical perspective, the paper showcases how the inclusion of interaction effects can drastically alter the electronic band topology, indicating the potential of creating states that are absent in single-particle frameworks. This insight might propel further inquiries into electron interactions within flat-band topologies, fostering further development in quantum material research.

In sum, this research serves as a significant development in the field of condensed matter physics, particularly in the manipulation of correlated and topological states in graphene-based superlattices, advancing the understanding of how tunable electronic properties can be harnessed in moiré systems. As material fabrication techniques continue to advance, the possibility of exploring even richer complexes of phase transitions and exotic quantum states remains promising.