Kekulé Spiral Order at All Nonzero Integer Fillings in Twisted Bilayer Graphene

We study magic angle graphene in the presence of both strain and particle-hole symmetry breaking due to nonlocal interlayer tunneling. We perform a self-consistent Hartree-Fock study that incorporates these effects alongside realistic interaction and substrate potentials and explore a comprehensive set of competing orders including those that break translational symmetry at arbitrary wave vectors. We find that at all nonzero integer fillings very small strains, comparable to those measured in scanning tunneling experiments, stabilize a fundamentally new type of time-reversal-symmetric and spatially nonuniform order. This order, which we dub the "incommensurate Kekulé spiral"(IKS) order, spontaneously breaks both the emergent valley-charge conservation and moiré translation symmetries but preserves a modified translation symmetry T^′-which simultaneously shifts the spatial coordinates and rotates the U(1) angle which characterizes the spontaneous intervalley coherence. We discuss the phenomenological and microscopic properties of this order. We argue that our findings are consistent with all experimental observations reported so far, suggesting a unified explanation of the global phase diagram in terms of the IKS order