Definition of $D^P$?
The class $\mathsf{D^p}$ was originally introduced in the context of studying the facets of the traveling salesman polytope. It contains all languages that can be considered as the intersection of a language in $\sf NP$ and one in $\sf co\text{-}NP$. Formally, $\mathsf{D^p} = \{ L_1 \cap \overline{L_2} \mid L_1,L_2 \in \mathsf{NP} \}$. It first appeared in [1].



[1] Papadimitriou, Christos H., and Mihalis Yannakakis. "The complexity of facets (and some facets of complexity)." Journal of Computer and System Sciences 28.2 (1984): 244-259.