  We study theoretically the competition between directional asymmetric
coupling and disorder in a one-dimensional array of quantum emitters chirally
coupled through a waveguide mode. Our calculation reveals highly nontrivial
phase diagram for the eigenstates spatial profile, nonmonotonously depending on
the disorder and directionality strength. The increase of the coupling
asymmetry drives the transition from Anderson localization in the bulk through
delocalized states to chirality-induced localization at the array edge.
Counterintuitively, this transition is not smeared by strong disorder but
becomes sharper instead. Our findings could be important for the rapidly
developing field of the waveguide quantum electrodynamics, where the chiral
interactions and disorder play crucial roles.
