  We prove a rank-two potential automorphy theorem for mod $l$ representations
satisfying an ordinary condition. Combined with an ordinary automorphy lifting
theorem, we prove a rank-two, $p \ne l$ case of local-global compatibility for
regular algebraic cuspidal automorphic representations of arbitrary weight over
CM fields that is $\iota$-ordinary for some $\iota:
\overline{\mathbb{Q}}_l\xrightarrow{\sim}\mathbb{C}$.
