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

TL;DR

This study uses large-scale density matrix renormalization group calculations to explore how heterostrain affects the phase diagram of magic-angle twisted bilayer graphene, revealing a transition from a quantum anomalous Hall insulator to an incommensurate Kekulé spiral phase.

Contribution

It provides the first unbiased, large-scale numerical analysis of heterostrain effects on TBG, identifying a novel incommensurate Kekulé spiral phase at finite strain.

Findings

Strain of 0.05% induces a transition to an incommensurate Kekulé spiral phase.

Higher strains lead to a transition into a fully symmetric metallic phase.

The IKS phase breaks valley conservation and translation symmetry but preserves a modified translation symmetry.

Abstract

When the two layers of a twisted moir\'e 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-Kekul\'e 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 $\hat{T}'$ with moir\'e-incommensurate phase modulation. Even higher strains drive the system to a fully symmetric metal.