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At certain angles of rotation called `magic angles' twisted bilayer graphenefeatures almost flat bands. The resulting strong correlations drive the systemto novel phases which have been observed in experiments recently. A completeunderstanding of the `magic' angle physics---both at the single-particle aswell as the many-particle level---is still missing, and the search is ongoing.Here, we identify a new set of `magic' angles, where locally flat bands with avariety of possible many-body instabilities arise, but where thesingle-particle problem admits an exact solution. This occurs in the presenceof an external perpendicular electric field at multicritical Lifshitz points.At these angles, which can be quantified exactly, the central band features amonkey saddle, resulting in strong electronic correlations.

Prediction of novel `magic' angles and correlations for twisted bilayer graphene in a perpendicular electric field