Ground-state order in magic-angle graphene at filling <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>ν</mml:mi><mml:mo>=</mml:mo><mml:mo>−</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:math>: A full-scale density matrix renormalization group study
Tianle Wang, Daniel E. Parker, Tomohiro Soejima, Johannes Hauschild, Sajant Anand, Nick Bultinck, Michael P. Zaletel
Abstract
We investigate twisted bilayer graphene (TBG) at filling $\ensuremath{\nu}=\ensuremath{-}3$ in the presence of realistic heterostrain. Strain amplifies the band dispersion and drives the system beyond the strong-coupling regime of previous theoretical studies. We use DMRG to conduct an unbiased, large-scale numerical calculations that include all spin and valley degrees of freedom, up to bond dimension $\ensuremath{\chi}=24\phantom{\rule{0.16em}{0ex}}576$. We establish a global phase diagram that unifies a number of theoretical and experimental results. Near zero strain we find an intervalley-coherent quantized anomalous Hall (QAH-IVC) state, a competitive strong-coupling order that evaded past numerical studies. A tiny strain around $0.05%$ drives a transition into an incommensurate Kekul\'e spiral (IKS) phase, supporting the mean-field prediction in [Kwan et al., Phys. Rev. X 11, 041063 (2021)]. Even higher strains above $0.2%$ favor a flavor-symmetric metallic order, which may explain metals found at $\ensuremath{\nu}=\ensuremath{-}3$ in many experiments.