Kekulé spiral order in magic-angle graphene: a density matrix renormalization group study

Abstract

When the two layers of a twisted moiré system are subject to different degrees of strain, the effect is amplified by the inverse twist angle, e.g., by a factor of 50 in magic angle twisted bilayer graphene (TBG). Samples of TBG typically have heterostrains of 0.1-0.7%, increasing the bandwidth of the "flat'' bands by as much as tenfold, placing TBG in an intermediate coupling regime. Here we study the phase diagram of TBG in the presence of heterostrain with unbiased, large-scale density matrix renormalization group calculations (bond dimension $\chi =24576$), including all spin and valley degrees of freedom. Working at filling $\nu =-3$, we find a strain of $0.05\%$ drives a transition from a quantized anomalous Hall insulator into an incommensurate-Kekulé spiral (IKS) phase. This peculiar order, proposed and studied at mean-field level by Kwan et al (PRX 11, 041063), breaks both valley conservation and translation symmetry $\hat{T}$, but preserves a modified translation symmetry ${\hat{T}}^{\prime }$ with moiré-incommensurate phase modulation. Even higher strains drive the system to a fully symmetric metal.

4.5 pages and three figures, plus appendices

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• Localization and delocalization errors in density functional theory and implications for band-gap prediction
• All-graphene integrated circuits via strain engineering
• Lattice relaxation and energy band modulation in twisted bilayer graphenes
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• Symmetry-based approach to electron-phonon interactions in graphene
• Gauge field induced by ripples in graphene
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• Weak Coupling Theory of Magic-Angle Twisted Bilayer Graphene
• Nonlocal Moments in the Chern Bands of Twisted Bilayer Graphene
• Twist-tuned quantum criticality in moiré bilayer graphene
• Textured Exciton Insulators
• Fractional Chern Insulator and Quantum Anomalous Hall Crystal in Twisted MoTe${}_2$
• Superconductivity in a Topological Lattice Model with Strong Repulsion
• Chern-Textured Exciton Insulators with Valley Spiral Order in Moiré Materials
• Nonflat bands and chiral symmetry in magic-angle twisted bilayer graphene
• Correlation effects in magic-angle twisted bilayer graphene: An auxiliary-field quantum Monte Carlo study
• Mean-field Modelling of Moiré Materials: A User's Guide with Selected Applications to Twisted Bilayer Graphene
• Kekulé order from diffuse nesting near higher-order Van Hove points
• Flat-band projected versus fully atomistic twisted bilayer graphene