Kekul\'e spiral order at all nonzero integer fillings in twisted bilayer graphene

TL;DR

This paper predicts a new incommensurate Kekulé spiral order in twisted bilayer graphene at all nonzero integer fillings, stabilized by small strains, which explains various experimental observations.

Contribution

It introduces the incommensurate Kekulé spiral (IKS) order as a novel phase in twisted bilayer graphene, incorporating realistic effects and explaining experimental data.

Findings

IKS order is stabilized at all non-zero integer fillings.

Small strains comparable to experiments induce the IKS order.

IKS order breaks valley-charge conservation and translation symmetry, but preserves a modified translation symmetry.

Abstract

We study magic angle graphene in the presence of both strain and particle-hole symmetry breaking due to non-local inter-layer tunneling. We perform a self-consistent Hartree-Fock study that incorporates these effects alongside realistic interaction and substrate potentials, and explore a comprehensive set of competing orders including those that break translational symmetry at arbitrary wavevectors. We find that at all non-zero integer fillings very small strains, comparable to those measured in scanning tunneling experiments, stabilize a fundamentally new type of time-reversal symmetric and spatially non-uniform order. This order, which we dub the 'incommensurate Kekul\'e spiral' (IKS) order, spontaneously breaks both the emergent valley-charge conservation and moir\'e translation symmetries, but preserves a modified translation symmetry $\hat{T}'$ -- which simultaneously shifts the spatial coordinates and rotates the $U(1)$ angle which characterizes the spontaneous inter-valley coherence. We discuss the phenomenological and microscopic properties of this order. We argue that our findings are consistent with all experimental observations reported so far, suggesting a unified explanation of the global phase diagram in terms of the IKS order.