Strain-induced Kekul'e spiral order in magic-angle graphene: a density matrix renormalization group study

Strain in moir'e systems is amplified by the inverse twist angle --- two orders of magnitude in magic angle twisted bilayer graphene (TBG). Samples of TBG typically have heterostrains of $0.1-0.7\%$. This increases bandwidth of the `flat' bands 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 including all eight flat bands. Working at filling $ { u} = 3$, we find a strain of $0.1\%$ drives a transition from a quantized anomalous Hall insulator into an incommensurate-kekul'e spiral (IKS) phase. This peculiar order, proposed and studied at mean-field level in Ref. cite{Kwan2021}, breaks both valley conservation and translation symmetry $hat{T}$, but preserves a modified translation symmetry $hat{T}'$ with moir'e-incommensurate phase modulation. Beyond the transition, we find IKS is only one state in a low-energy manifold, whose common characteristic is depleted charge density at the $Gamma$ point.