Nematicity in twisted bilayer graphene: impact of the moiré superlattice

Recent experiments have reported evidence that the threefold rotational symmetry of magic-angle twisted bilayer graphene is broken in several regions of the phase diagram, both in the normal state and in the superconducting state. Here, we theoretically investigate the coupling between electronic nematic and moiré superlattice degrees of freedom. Because the nematic transition is described in terms of a three-state Potts order parameter, we show that a true phase transition can still take place even in the presence of externally applied uniaxial strain. Moreover, the nature of the Potts-nematic transition is fundamentally altered by fluctuating strain modes associated with the domain walls separating AB/BA stacking regions of the triangular moiré superlattice. In particular, these fluctuations mediate an effective nemato-orbital coupling that not only renders the nematic transition mean-field and first-order, but also ties the orientation of the nematic director to certain soft directions in momentum space. Finally, we contrast our results to the more familiar case of Ising-nematic order in a tetragonal rigid lattice.