Stovepipe hat

A stovepipe or stove-pipe hat was an unusually tall top hat favoured by the newly-regenerated Second Doctor. He first donned the hat before exploring the planet Vulcan. (DW: The Power of the Daleks) However, he apparently became disenchanted with the hat rather quickly, as he rarely wore it after his adventures with Ben, Polly, and Jamie in Atlantis. (DW: The Underwater Menace) On Trodos, the Doctor used the hat to cover a Dalek's eyestalk, blinding it. (TVC: The Trodos Ambush)

Abraham Lincoln also famously wore a stovepipe hat. Will Johnson once wrote Claire Bartlett a letter describing the president's post-war trip to Richmond, Virginia. He said that the "grand stovepipe" allowed the president to stand "two heads taller than any of those around him", making him easy to identify in a crowd. Peri, who was in that crowd with Erimem, later said that the hat was about the only thing they could see of the president. (TN: Blood and Hope)

Behind the scenes

 * Though the televised series never calls it a "stovepipe hat", at least a couple of works of prose fiction — PDA: The Murder Game and TN: Wonderland — do. Contrariwise, some fashion experts might disagree that it's actually a stovepipe, as it doesn't have a flat top.
 * Although Troughton lost the hat after his third serial, the character was still depicted as wearing it in every one of the Second Doctor annuals and throughout much of his TV Comic run. Thus, stories were being published after Troughton had relinquished the role — like DWAN: The Mystery of the Marie Celeste — which depicted the Second Doctor in an article of clothing he had only worn in his debut and the first few minutes of his second and third serials.
 * The Underwater Menace, episode one, begins with a shot of the hat sitting on a chair in the console room.