Exceptional topology in non-Hermitian twisted bilayer graphene

Twisted bilayer graphene (TBG) has extraordinary electronic properties at the magic angle along with an isolated flat band at the magic angle. However, the non-Hermitian phenomena in twisted bilayer graphene remain unexplored. In this work, we study a non-Hermitian TBG formed by one-layer graphene twisted relative to another layer with gain and loss. Using a non-Hermitian generalization of the Bistritzer-MacDonald model, we find Dirac cones centered at only the ${K}_{M}$ (${K}_{M}^{\ensuremath{'}}$) corner of the moir\'e Brillouin zone at the ${K}^{\ensuremath{'}}$ ($K$) valley deform into rings of exceptional points in the presence of non-Hermiticity, which is different from single-layer graphene with gain and loss, where exceptional rings appear in both $K$ and ${K}^{\ensuremath{'}}$ corners of the Brillouin zone. We show that the exceptional rings are protected by non-Hermitian chiral symmetry. More interestingly, at an ``exceptional magic angle'' larger than the Hermitian magic angle, the exceptional rings coincide and form non-Hermitian flat bands with zero energy and a finite lifetime. These non-Hermitian flat bands in the moir\'e system, which are isolated from dispersive bands, are distinguished from those in non-Hermitian frustrated lattices. In addition, we find that the non-Hermitian flat band has topological charge conserved in the moir\'e Brillouin zone, which is allowed for analogs of non-Hermitian fractional quantum Hall states.