Magic angles in equal-twist trilayer graphene

We consider a configuration of three stacked graphene monolayers with equal consecutive twist angles Formula Presented. Remarkably, in the chiral limit when interlayer coupling terms between Formula Presented sites of the moiré pattern are neglected we find four perfectly flat bands (per valley and spin) at a sequence of magic angles which are exactly equal to the twisted bilayer graphene (TBG) magic angles divided by Formula Presented. Therefore, the first magic angle for equal-twist trilayer graphene (eTTG) in the chiral limit is Formula Presented. We prove this relation analytically and show that the Bloch states of the eTTG's flat bands are nonlinearly related to those of TBG. Additionally, we show that at the magic angles, the upper and lower bands must touch the four exactly flat bands at the Dirac point of the middle graphene layer. Finally, we explore the eTTG's spectrum away from the chiral limit through numerical analysis.