A Heavy Fermion Theory of the Ubiquitous Incommensurate Kekule Spiral in Twisted Bilayer Graphene

The experimental reality of twisted bilayer graphene cannot be described without strain, which deforms its flat bands. This intermediate coupling regime gives rise to the Incommensurate Kekule Spiral (IKS), a mean-field order which preserves a valley-boosted translation symmetry, along with inversion and time-reversal. We study this state in the Topological Heavy Fermion (THF) model obtained by projecting strain and lattice relaxation to the c- and f-electron basis. The THF model reveals a hierarchy of scales that divides the strong-coupling ferromagnetic regime from the strained regime based on parent state ansatze which we propose at each integer filling. We then demonstrate that the unboosted phase is gapless due to symmetry-protected Dirac nodes. However, we show analytically that the remaining variational parameter, IKS boost, drives these Dirac nodes through a multi-band non-abelian braiding process which opens gaps and stabilizes a lower energy state. Finally, we give estimates of the optimal IKS boost vector and discuss the role of particle-hole breaking, in good agreement with experiment. The ability to incorporate these effects within the THF model allows us to perform dynamical mean-field theory calculations, which show good agreement with recent experiments at temperatures above ordering.