Probably one of the most famous single-justice decisions was that of Justice Hugo Black in supporting the contested election of Lyndon Johnson in 1948. Black did this in the face of the fact that the full court itself could have heard the case in three weeks. Black's ruling put Johnson into the Senate despite seemingly clear evidence that Johnson had lost the election.
That would have been in his capacity as a Circuit Court Judge. It is the Circuit making the decision, not the Supreme Court. The losing side would have had the option of appealing to the full court (minus Black) if they chose to.
In the past it is was common for members of the SCOTUS to rule on cases within their assigned circuits.
That is not at all true, as Robert A Caro details in his book "The Years of Lyndon Johnson: Means of Assent". What Justice Black did, in his role as the justice responsible for the 5th Circuit, was issue a stay of the lower courts injuction pending a review by the entire Supreme Court. On October 5th the Supreme Court refused to hear Coke Stevenson's petition to consider Justice Black's stay. So it wasn't a case of a single justice speaking for the entire court, it was a single justice acting so the matter could be brought before the entire court, should the court choose to hear it.
Care to try again?