Observation of fractional Chern insulators in a van der Waals heterostructure (1706.06116v2)

Abstract: Topologically ordered phases are characterized by long-range quantum entanglement and fractional statistics rather than by symmetry breaking. First observed in a fractionally filled continuum Landau level, topological order has since been proposed to arise more generally at fractional filling of topologically non-trivial "Chern" bands. Here, we report the observation of gapped states at fractional filling of Harper-Hofstadter bands arising from the interplay of a magnetic field and a superlattice potential in a bilayer graphene/hexagonal boron nitride heterostructure. We observe new phases at fractional filling of bands with Chern indices $\mathcal{C} = -1, \pm 2,$ and $\pm 3$. Some of these, in $\mathcal{C}=-1$ and $\mathcal{C}=2$ bands, are characterized by fractional Hall conductance---they are `fractional Chern insulators' and constitute a new example of topological order beyond Landau levels.

• The paper demonstrates the formation of fractional Chern insulators in engineered van der Waals heterostructures under high magnetic fields.
• It employs magnetocapacitance measurements to identify gapped states at fractional filling factors and distinct Chern numbers.
• The findings extend topological order beyond conventional Landau levels and open new avenues for fault-tolerant quantum computing.

Observation of Fractional Chern Insulators in a van der Waals Heterostructure

This paper presents exploratory research into the observation of fractional Chern insulators (FCIs) within a specifically engineered van der Waals heterostructure consisting of bilayer graphene encapsulated by hexagonal boron nitride (hBN). The paper investigates the formation and behavior of gapped states at fractional filling factors of Harper-Hofstadter bands, which arise due to the interplay between an external magnetic field and the engineered superlattice potential within the heterostructure. Such states are indicative of topologically ordered phases described more generally by the phenomenon of FCIs.

Key Aspects and Findings

1. Topological Order and Chern Bands:
   • The research identifies gapped states at fractional filling factors in Harper-Hofstadter bands corresponding to various Chern numbers ($\mathcal{C}$): $-1, \pm 2, \pm 3$. Notably, bands with Chern number $\mathcal{C}=-1$ and $\mathcal{C}=2$ showed evidence of fractional Hall conductance.
   • The findings emphasize the extension of topological order beyond conventional Landau levels (LLs), which have historically been constrained to integer or fractional quantum Hall effects.
2. Experimental Design and Observation:
   • Utilizing a heterostructure comprising bilayer graphene aligned with hBN crystals allows for the manifestation of superlattice-induced Chern bands under high magnetic fields.
   • The novel experimental approach captures signature features of topological order including fractionalized charges, validated through magnetocapacitance measurements that discern between compressible and incompressible phases across varied electron densities and magnetic flux densities.
3. Fractional Chern Insulators (FCIs):
   • A detailed analysis reveals the existence of FCIs in experimental data, demonstrating distinct gapped states with fractional conductance arising from fractional band fillings.
   • The paper observed fractional quantization analogous to fractional quantum Hall (FQH) states but within a non-Landau band context – notably characterized by fractional $t$ (Hall conductance) and fractional $s$ (charge bound to the unit cell) values.
   • The robustness of these phases against disorder and their stability with respect to band dispersion underpins the presence of interaction-driven topological order.
4. Implications and Future Directions:
   • The findings imply potential applications in quantum computing through topological phases that offer robust fault tolerance due to their intrinsic properties.
   • From a theoretical perspective, FCIs broaden the understanding of topological phases of matter beyond the frameworks of symmetry and translation invariance, prompting further exploration into lattice engineering in pursuit of new quantum phases.
   • The research prompts speculation on the engineering of synthetic lattice structures as a method for realizing desired Chern bands, offering avenues for further investigation in programmable quantum materials.

Speculation on AI Developments

While the primary focus of the paper is rooted in condensed matter physics, one can speculate on potential AI advancements in simulating and predicting topological phenomena. The computational approaches like infinite density matrix renormalization group (iDMRG) used in the paper pave the way for AI-driven simulation models capable of identifying and optimizing conditions for desired quantum states, thus accelerating the discovery and characterization of novel topological phases such as FCIs.

In essence, this research contributes significantly to the field of quantum materials by unlocking new paradigms of topological order while simultaneously laying the groundwork for future explorations in both experimental and theoretical frameworks.