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 χ = 24576), including all spin and valley degrees of freedom. Working at filling ν = −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 in Ref. [1], breaks both valley conservation and translation symmetry T , but preserves a modified translation symmetry T with moiré-incommensurate phase modulation. Even higher strains drive the system to a fully symmetric metal.

Magic-angle helical trilayer graphene

“…We briefly discuss the incommensurate Kekulé spiral state, which was recently found to be important in strained TBG (76)(77)(78)(79). We expect that these incommensurate orders are less likely in h-HTG since their energetics appear to rely on a large, peaked Hartree dispersion.…”