Kekulé spirals and charge transfer cascades in twisted symmetric trilayer graphene

Abstract

We study the phase diagram of magic-angle twisted symmetric trilayer graphene in the presence of uniaxial heterostrain and interlayer displacement field. For experimentally reasonable strain, our mean-field analysis finds robust Kekulé spiral order whose doping-dependent ordering vector is incommensurate with the moiré superlattice, consistent with recent scanning tunneling microscopy experiments, and paralleling the behavior of closely related twisted bilayer graphene (TBG) systems. Strikingly, we identify a possibility absent in TBG: the existence of commensurate Kekulé spiral order even at zero strain for experimentally realistic values of the interlayer potential in a trilayer. Our studies also reveal a complex pattern of charge transfer between weakly and strongly dispersive bands in strained trilayer samples as the density is tuned by electrostatic gating, that can be understood intuitively in terms of the "cascades"in the compressibility of magic-angle TBG.