FEDERAL PANEL OF JUDGES CONCLUDE, "no existing authority that allows lower court judges to investigate or discipline Supreme Court justices"
“[a] specially appointed federal panel of judges has dismissed all 83 ethics complaints brought against Justice Brett Kavanaugh regarding his conduct at his confirmation hearings,” “conclud[ing] that while the complaints ‘are serious,’ there is no existing authority that allows lower court judges to investigate or discipline Supreme Court justices.”
http://www.scotusblog.com/2018/12/wednesday-round-up-453/#more-278036