You can mention a publication, but you can also simply refer to what you have done, as in "I have researched / worked on / etc. [subject matter]. I am interested in exploring it further.". If you are certain that the relevance of this is obvious to the people reading the letter, then you don't need to be explicit about it; mention some keywords in [subject matter]. If you are not certain the target audience knows of the connection, then you should certainly mention how [subject matter] is connected to whatever they are investigating.
The full bibliographic details are presumably available in your CV or list of publications (or both), so I would not mention anything more than the title of the paper or some prestigious collaborator (in my paper with professor blargh, we discovered...).