A compact ordered topological spaces is a compact topological space $(X, \tau)$ together with a partial ordered $\leq$ on $X$ such that $\leq \subseteq X^2$ is a closed subset in the product topology.
I am wondering if the standard references for the information about these kind of spaces (or ordered topological spaces in general) is still Nachbin's Order and topology (1965) or if there exists more recent surveys on the topic.
The following references might be of interest:
M. Erné, The ABC of order and topology (1991)
Morgan Kamga's thesis, Topology and order (2005)