Fractional Chern insulators in magic-angle twisted bilayer graphene

Abstract: Fractional Chern insulators (FCIs) are lattice analogues of fractional quantum Hall states that may provide a new avenue toward manipulating non-abelian excitations. Early theoretical studies have predicted their existence in systems with energetically flat Chern bands and highlighted the critical role of a particular quantum band geometry. Thus far, however, FCI states have only been observed in Bernal-stacked bilayer graphene aligned with hexagonal boron nitride (BLG/hBN), in which a very large magnetic field is responsible for the existence of the Chern bands, precluding the realization of FCIs at zero field and limiting its potential for applications. By contrast, magic angle twisted bilayer graphene (MATBG) supports flat Chern bands at zero magnetic field, and therefore offers a promising route toward stabilizing zero-field FCIs. Here we report the observation of eight FCI states at low magnetic field in MATBG enabled by high-resolution local compressibility measurements. The first of these states emerge at 5 T, and their appearance is accompanied by the simultaneous disappearance of nearby topologically-trivial charge density wave states. Unlike the BLG/hBN platform, we demonstrate that the principal role of the weak magnetic field here is merely to redistribute the Berry curvature of the native Chern bands and thereby realize a quantum band geometry favorable for the emergence of FCIs. Our findings strongly suggest that FCIs may be realized at zero magnetic field and pave the way for the exploration and manipulation of anyonic excitations in moir\'e systems with native flat Chern bands.

• The paper presents the discovery of eight distinct FCI states in MATBG, achieved at a low magnetic field of 5 T.
• It employs precision measurements with scanning single electron transistors to reveal flat Chern bands with controlled Berry curvature distributions.
• The findings suggest potential for engineering topological quantum devices that operate with minimal magnetic field dependence.

Fractional Chern Insulators in Magic-Angle Twisted Bilayer Graphene

In the study of topological matter, the concept of a Fractional Chern Insulator (FCI) has gained prominence as a lattice analogue to fractional quantum Hall states, offering potential for hosting non-abelian excitations and advancing the field of topological quantum computation. The realization of FCIs has been restricted primarily to systems like Bernal-stacked bilayer graphene with hexagonal boron nitride alignment. However, these systems demand high magnetic fields, limiting their practical applicability. This paper documents the significant advancement in observing FCI states at low magnetic fields in magic-angle twisted bilayer graphene (MATBG), thereby enhancing prospects for zero-field FCI realizations.

The observation of eight distinct FCI states in MATBG demonstrates the capability of this system to support intrinsic flat Chern bands. These bands, distinguished by a highly controlled Berry curvature distribution, create a fertile ground for reclaiming quantum geometric conditions conducive to FCIs without the dependency on large external magnetic fields. Notably, the FCI states, first observed at 5 T, emerge alongside the suppression of topologically-trivial charge density wave states, indicating a preference for FCI stabilization under the influence of a modest magnetic redistribution of Berry curvature.

To comprehend the transition of MATBG from charge density wave-dominated phases to those favoring FCI states, the study examines the quantum-geometric properties of the underlying band structures. The role of the applied magnetic field is crucial in homogenizing the Berry curvature distribution. Through carefully orchestrated local electronic compressibility measurements using scanning single electron transistors, this research discerns five potential classes of incompressible states, characterized by distinct pseudo-spin and orbital quantum numbers satisfying a specific Diophantine equation.

Within the promising MATBG framework, observations extend to various ranges of filling factors. In the region where the system effectively isolates a single Chern band (around filling factors 3<ν<4), FCI states demonstrate stability even in near-zero field conditions. Here, electron-electron interactions drive the emergence of these states without necessitating translational symmetry breaking, thus denoting them as symmetry-preserving FCIs.

Unexpectedly, the research also identifies a family of FCI states characterized by fractional values of both quantum numbers (t, s), suggesting the presence of incompressible states indicative of FCIs in weak magnetic fields. These states exhibit remarkable resistance to requiring symmetry-breaking for stabilization, instead showing configurations suggestive of novel spatial orders with possible enlarged unit cells following non-conventional charge distribution formats.

The implications of this work reach beyond the observed MATBG system, intimating at the potential for engineering other low-dimensional materials with native Chern bands towards achieving FCIs without magnetic field assistance. The research thereby opens avenues for innovative electronic and spintronic devices within the topological quantum framework. Future explorations could focus on refining the quantum-geometric conditions through experimental modulation of interlayer parameters like twisting angles or leveraging novel material stacks to achieve even more robust topological orders free from external magnetic constraints.

Overall, this paper enhances our comprehension of FCIs within the domain of MATBG and lays a substantial foundation for further investigations into non-abelian phases within moiré superlattices, contributing valuable insights into the complex interplay of geometry and topology in engineered quantum materials.