Nearly Flat Chern Bands in Moiré Superlattices (1805.08232v2)

Abstract: Topology and electron interactions are two central themes in modern condensed matter physics. Here we propose graphene based systems where both the band topology and interaction effects can be simply controlled with electric fields. We study a number of systems of twisted double layers with small twist angle where a moir\'e super-lattice is formed. Each layer is chosen to be either AB stacked bilayer graphene (BG), ABC stacked trilayer graphene (TG), or hexagonal boron nitride (h-BN). In these systems a vertical applied electric field enables control of the bandwidth, and interestingly also the Chern number. We find that the Chern numbers of the bands associated with each of the two microscopic valleys can be $\pm 0,\pm 1,\pm 2, \pm 3$ depending on the specific system and vertical electrical field. We show that these graphene moir\'e super-lattices are promising platforms to realize a number of fascinating many-body phenomena, including (Fractional) Quantum Anomalous Hall Effects. We also discuss conceptual similarities and implications for modeling twisted bilayer graphene systems.

• The paper demonstrates that electric fields can tune nearly flat Chern bands with versatile Chern numbers (0, ±1, ±2, ±3) in graphene-based moiré superlattices.
• Numerical simulations at magic twist angles reveal significantly reduced bandwidths that promote strong electron correlations and potential emergence of correlated states.
• The study provides a robust platform for exploring topological phase transitions and novel quantum states such as the Fractional Quantum Anomalous Hall effect.

Nearly Flat Chern Bands in Moiré Superlattices

This paper introduces a novel approach utilizing graphene-based systems wherein both band topology and interaction effects can be deftly controlled using electric fields. The paper investigates a variety of systems involving twisted double layers at small twist angles that generate moiré superlattices. Utilizing layers such as AB stacked bilayer graphene, ABC stacked trilayer graphene, and hexagonal boron nitride, the research emphasizes the intriguing possibility of manipulating both the bandwidth and the Chern number of the bands using vertical electric fields. Depending on the particular system and the applied electric field, the Chern numbers associated with the microscopic valleys can assume values like $\pm 0, \pm 1, \pm 2, \pm 3$. This introduces the flexibility to explore numerous many-body phenomena, such as the Fractional Quantum Anomalous Hall Effects.

Key Findings and Numerical Results

One of the critical outcomes of this paper involves the ability to produce nearly flat Chern bands with tunable Chern numbers ($|C|=0, 1, 2, 3$) through electric fields. This manipulation is key for realizing novel topological phases, such as Fractional Chern Insulators. Furthermore, these studies depict how moiré superlattices facilitate a myriad of topological and interaction-dependent phase transitions, potentially clearing pathways to discover new phases of quantum matter.

Numerical simulations demonstrate that at a specific twist angle, known commonly as a magic angle, bilayer systems can manifest narrow bandwidths enhancing the role of electron correlations. For the BG/BG scenario, the calculations show an outstanding reduction in bandwidth at the magic angle, compared to non-magic angles, indicating possible emergence of correlated electronic states akin to those previously observed in twisted bilayer graphene.

Theoretical Implications and Analyses

The presented theoretical models suggest a dynamic correlation between electric fields and Chern numbers that influence the topological properties of graphene-based materials. The paper provides a complete account of the Hamiltonian for these systems, including the formulation of moiré potential effects and interaction terms designed to capture essential physics in low energy scales.

Conceptually, the paper posits similarities between the discussed moiré systems and twisted bilayer graphene systems. The shared topological peculiarities, such as the inability to construct maximally localized Wannier functions while maintaining valley U(1) symmetry, underline deeper topological complexities pervasive in moiré technology.

Practical Implications and Future Directions

Practically, the research suggests that the described graphene-based moiré superlattices with controllable flat Chern bands could serve as excellent platforms for hosting novel quantum states, such as Quantum Anomalous Hall and Fractional Quantum Anomalous Hall states. The ability to electrically tune the interactions and topological indices provides a versatile toolbox for further exploring electronic properties and designing materials with specific electronic characteristics.

Future studies should explore realizing these theoretical predictions experimentally and exploring potential technological applications. From a theoretical standpoint, developing robust models to accurately simulate these tunable moiré systems across different parameter regimes remains a critical objective. There is substantial ground to develop new many-body theories and lattice models to capture the intriguing phenomenology of strongly correlated electrons in partially filled topological bands, especially at zero magnetic fields.

This groundwork promises exciting prospects for engineering new quantum materials by harnessing the intricate interplay between topology and electron interactions, made possible with graphene moiré superlattices and their electrical tunability.