Order of the correlated insulators at two electrons per cell
In plain words
With two electrons added or removed per moire cell the material becomes insulating because of electron repulsion, and the pattern in which the electrons order, and how it changes with small built-in strain, is debated.
Precise statement
Identify the ground state of magic-angle twisted bilayer graphene at $\nu = \pm 2$ ($\nu$ = electrons per moire cell measured from charge neutrality) as a function of uniaxial heterostrain $\epsilon$ ($0 \text{ to } 0.3\%$) and hBN alignment. Candidates include the incommensurate Kekule spiral (IKS), Kramers intervalley-coherent, valley-polarized and spin-polarized states. The answer is a phase diagram in $(\nu, \epsilon)$ with the order parameter identified in each phase.
What would settle it
Atomic-resolution STM imaging of Kekule patterns and magnetotransport on devices with independently measured heterostrain, including strain below 0.05%.
Status in the literature
Unverified note
2023 STM (Nuckolls et al., Nature) imaged Kekule order consistent with the IKS state at $\nu = \pm 2$ in samples with typical strain of order 0.1%; the strain-free ground state remains unsettled as of 2026.