[Paper Review] Correlated Insulator Behaviour at Half-Filling in Magic Angle Graphene Superlattices

Yuan Cao, Valla Fatemi+10 more|RePEc: Research Papers in Economics|Feb 2, 2018

Graphene research and applications3 citations

TL;DR

This study demonstrates correlated insulator behavior at half-filling in magic-angle twisted bilayer graphene (TwBLG), where strong electron correlations lead to Mott insulating states at specific carrier densities. Using transport measurements and a continuum model, the authors identify a parabolic band touching with winding number -2 at the first magic angle (1.064°), explaining the emergence of flat bands and large effective mass (1.1me), which enables strong correlations and insulating phases at half-filling.

ABSTRACT

Van der Waals (vdW) heterostructures are an emergent class of metamaterials comprised of vertically stacked two-dimensional (2D) building blocks, which provide us with a vast tool set to engineer their properties on top of the already rich tunability of 2D materials. One of the knobs, the twist angle between different layers, plays a crucial role in the ultimate electronic properties of a vdW heterostructure and does not have a direct analog in other systems such as MBE-grown semiconductor heterostructures. For small twist angles, the moiré pattern produced by the lattice misorientation creates a long-range modulation. So far, the study of the effect of twist angles in vdW heterostructures has been mostly concentrated in graphene/hexagonal boron nitride (h-BN) twisted structures, which exhibit relatively weak interlayer interaction due to the presence of a large bandgap in h-BN. Here we show that when two graphene sheets are twisted by an angle close to the theoretically predicted 'magic angle', the resulting flat band structure near charge neutrality gives rise to a strongly-correlated electronic system. These flat bands exhibit half-filling insulating phases at zero magnetic field, which we show to be a Mott-like insulator arising from electrons localized in the moiré superlattice. These unique properties of magic-angle twisted bilayer graphene (TwBLG) open up a new playground for exotic many-body quantum phases in a 2D platform made of pure carbon and without magnetic field. The easy accessibility of the flat bands, the electrical tunability, and the bandwidth tunability though twist angle may pave the way towards more exotic correlated systems, such as unconventional superconductors or quantum spin liquids.

Motivation & Objective

• To investigate the emergence of correlated insulating states in magic-angle twisted bilayer graphene (TwBLG) at half-filling.
• To understand the role of band topology and effective mass in enabling strong electron correlations near the first magic angle.
• To establish a connection between topological winding numbers and the formation of flat bands in TwBLG.
• To validate the experimental transport data using a continuum model that captures the low-energy physics near the magic angle.

Proposed method

• Fabricated TwBLG devices using a modified 'tear & stack' technique with exfoliated graphene and hexagonal boron nitride (h-BN) encapsulation.
• Performed low-temperature transport measurements using lock-in techniques with sub-microvolt excitation and current pre-amplification.
• Applied perpendicular magnetic fields to observe Landau level quantization and extract filling factors via periodicity in 1/B.
• Used a continuum Hamiltonian with velocity vF(θ) and mass parameter m to model low-energy band structure near the magic angle.
• Calculated winding numbers and Berry curvature evolution using numerical methods to track topological changes during band merging.
• Computed the single-particle density of states (DOS) using the continuum model for θ = 1.08°, revealing multiple van Hove singularities.

Experimental results

Research questions

• RQ1 What is the nature of the insulating state observed at half-filling in magic-angle TwBLG?
• RQ2 How does the band structure evolve near the first magic angle (1.064°), and what topological features are associated with it?
• RQ3 What is the effective mass of the flat bands at the magic angle, and how does it relate to the vanishing Fermi velocity?
• RQ4 Why do Landau levels in magic-angle TwBLG exhibit a filling sequence of ±(4,8,12,…), differing from monolayer or non-magic-angle bilayer graphene?
• RQ5 How does the winding number of Dirac points change as the twist angle approaches the first magic angle?

Key findings

• A Mott insulating state is observed at half-filling (n ≈ ±1.4×10¹² cm⁻²) in TwBLG with θ ≈ 1.064°, confirmed by transport measurements.
• The superlattice gaps at A⁻ and A⁺ fillings are 32 meV and 40 meV, respectively, indicating strong correlation effects.
• Landau level sequences of ±(4,8,12,…) are observed, indicating a fourfold degeneracy per Landau level, distinct from monolayer or non-magic-angle TwBLG.
• The effective mass of the flat bands at the first magic angle is estimated as 1.1me, consistent with the parabolic band touching limit as vF → 0.
• Near the first magic angle, the winding number of band touching points evolves from (+1,+1) at large angles to (−2,−2) at the magic angle, indicating a net change of Δw = 6.
• Numerical calculations show that the low-energy band structure near θ = 1.064° features a parabolic band touching with winding number -2 at each MBZ corner, analogous to Bernal-stacked bilayer graphene but with identical winding numbers at both corners.