Ancilla theory of twisted bilayer graphene I: topological Mott localization and pseudogap metal in twisted bilayer graphene

The recent experimental studies of twisted bilayer graphene (TBG) raise a fundamental question: how do we understand Mott localization in a topological band? In this work, we offer a new perspective of Mott physics, which can be generalized to TBG directly in momentum space. In our theory, the Mott gap is understood as from an exciton-like hybridization $\Phi(\mathbf k) c^\dagger(\mathbf k)\psi(\mathbf k)$ between the physical electron $c$ and an ancilla fermion $\psi$. In the conventional Mott insulator of trivial band, the hybridization is $s$-wave with $\Phi(\mathbf k)=\frac{U}{2}$, where $U$ is the on-site Hubbard interaction. On the other hand, the band topology in TBG enforces a topological Mott hybridization with $\Phi(\mathbf k)\sim k_x \pm i k_y$ in a small region around $\mathbf{k}=0$. We dub this new Mott state as topological Mott localization because of the $p\pm ip$ order parameter analogous to the topological superconductor. At $\nu=0$, we find a topological Mott semimetal with a low energy effective theory resembling that of the untwisted bilayer graphene. For $\nu=\pm 1, \pm 2, \pm 3$, we show transitions from correlated insulators to Mott semimetals at smaller $U$. In the most intriguing density region $\nu=-2-x$, we propose a symmetric pseudogap metal at small $x$, which hosts a small Fermi surface and violates the perturbative Luttinger theorem. Interestingly, the quasiparticle is primarily formed by ancilla fermion, which we interpret as a composite fermion formed by a hole bound to a particle-hole pair. Our theory offers a unified language to describe the Mott localization in both trivial and topological bands in momentum space, and we anticipate applications in other moir\'e systems with topological Wannier obstruction, such as the twisted transition-metal dichalcogenide (TMD) homobilayer.